43-Meta-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Meta-analysis\n",
    "\n",
    "Meta-analysis is used to combine evidence from multiple studies, usually clinical trials testing the effectiveness of therapies or tests. The pooled evidence from multiple studies can give much more precise and reliable answers than any single study can. Although many researchers are convinced that meta-analyses are hugely important and helpful, others doubt that meta-analysis can consistently overcome the huge challenges and produce consistently useful results:\n",
    "\n",
    "- inconsistent criteria to define a disease -> define which patients are included\n",
    "- different outcome variables -> define which outcomes are included\n",
    "- unpublished studies/publication bias -> seek unpublished data, review registries of study protocols\n",
    "- some studies are of higher quality than others -> define what makes a study of high enough quality to be included\n",
    "- different languages -> arrange for translation\n",
    "- not enough information to perform a proper analysis -> estimate data from figures, obtain unpublished details from investigators\n",
    "- published data may be internally inconsistent -> resolve inconsistencies without bias, request details from investigators\n",
    "- data from some patients may be included in multiple publications, redundant analyses -> ask investigators to clarify which patients were included in more than one publication\n",
    "\n",
    "A meta-analysis pools weighted effect sizes, it calculates a pooled P value from the pooled effect size.\n",
    "\n",
    "Meta-analyses don't have to be huge, it can be helpful to combine the results from as few as two studies.\n",
    "\n",
    "## Assumptions of meta-analysis\n",
    "\n",
    "There are two general methods that are used, each of which is based on different assumptions:\n",
    "\n",
    "- _fixed effects_: this model assumes that all the subjects in all the studies were really sampled from one large population. Thus, all teh studies are estimating the same effect, and the only difference between studies is due to random selection of subjects.\n",
    "- _random effects_: this model assumes that each study population is unique. The difference among study results is due both to differences between the populations and to random selection of subjects. This model is more realistic and is used more frequently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We use the data extracted from Figure 43.1 on page 455\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = np.array([2.5, 1.4, 1.1, 1.2,  .8,  .8, 1.1, np.NaN, 1.2])\n",
    "lower= np.array([1.8,  .8,  .8,  .8,  .5,  .4,  .6, np.NaN,  .9])\n",
    "upper= np.array([4.4, 2.2, 1.8, 1.9, 1.4, 1.6, 2,   np.NaN, 1.4])\n",
    "W = (upper-lower)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,5))\n",
    "plt.errorbar(\n",
    "    x=np.flip(mean),\n",
    "    y=np.arange(len(mean)),\n",
    "    xerr=np.flip(W),\n",
    "    fmt='o',\n",
    "    ms=8,\n",
    "    ecolor=['red']+['blue']*8,\n",
    "    elinewidth=3,\n",
    ")\n",
    "\n",
    "plt.xlabel(\"Odds ratio (with 95% CI)\")\n",
    "plt.xticks([0.5, 1, 2, 4.0])\n",
    "plt.ylabel(\"Trial ID\")\n",
    "plt.yticks(\n",
    "    list(range(0,9)),\n",
    "    ['Total', '', '49', '45', '50', '47', '46', '15', '14'])\n",
    "plt.axvline(x=1, color='red', linestyle='--')\n",
    "sns.despine();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results from a meta-analysis\n",
    "\n",
    "Part of a meta-analysis is a narrative report that summarizes the studies that have been done and evaluates their strengths and weaknesses. The rest of a meta-analysis is quantitative. The results of each study are summarized by one value, called the **effect size**, along with its CI. The effect size is usually a relative risk or odds ratio, but it could also be some other measure of treatment effect. Combining all the studies, the meta-analysis computes the pooled treatment effect, its CI and a pooled P value.\n",
    "\n",
    "The results for the individual studies and the pooled results are plotted on a **forest plot** or **blobbogram**.\n",
    "\n",
    "In the example above, the forest plot shows the results from 7 studies of the effectiveness of a drug, the horizontal axis is the odds ratio, a value of 1.0 means no effect; a value greater than 1.0 means the drug works better than placebo. The top 7 lines are results of individual studies. For each study, the plot shows the odds ratio and 95% confidence interval. At the very bottom, the graph shows the total (pooled) effect computed from all studies, also shown as an odds ratio with its 95% CI.\n",
    "\n",
    "In 6 of the 7 studies, the 95% CI includes 1.0. With 95% confidence, you cannot conclude from these six studies that the treatment works better than placebo. In only 1 of the studies, does the 95% CI not include 1.0. The data from this study, but not the others, would lead you to conclude with 95% confidence that the treatment worked better than placebo. The bottom part of the graph shows the total (pooled) effect as computed by the meta-analysis. The 95% CI ranges from 0.98 to 1.56, so the P value must be greater than 0.05. The overall odds ratio is 1.24. That is a small effect, but not a tiny one. The 95% CI includes 1.0 (no effect), but just barely.\n",
    "\n",
    "### Meta-analysis of individual participant data (IPD meta-analysis)\n",
    "\n",
    "A newer approach is for the meta-analysts to obtain the original data for each participant of each study, and reanalyze all the data together. This approach is considered the gold standard of meta-analysis and has determined definitive answers to clinical questions, which might not have been obtained from meta-analysis of summay data. This type of analysis ensures that the outcomes are defined in a consistent way, and that the data are analyzed using the same methods. Moreover, it can include more data than did the original paper because one get data at the root from the investigators, it can answer questions not posed by the original investigators, run subgroup analyses and account for confounding variables not considered by the original investigators."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meta-analysis of continuous data (standardized mean difference or SMD)\n",
    "\n",
    "### Implementation with statsmodels.stats.meta_analysis\n",
    "\n",
    "Statsmodels include basic methods for [meta-analysis](https://www.statsmodels.org/stable/examples/notebooks/generated/metaanalysis1.html). The support for meta-analysis has 3 parts:\n",
    "\n",
    "- effect size functions: this currently includes `effectsize_smd` computes effect size and their standard errors for standardized mean difference, `effectsize_2proportions` computes effect sizes for comparing two independent proportions using risk difference, (log) risk ratio, (log) odds-ratio or arcsine square root transformation\n",
    "- The `combine_effects` computes **fixed and random effects estimate** for the overall mean or effect. The returned results instance includes a forest plot function.\n",
    "- helper functions to estimate the random effect variance, tau-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.meta_analysis import (\n",
    "    effectsize_smd,\n",
    "    effectsize_2proportions,\n",
    "    combine_effects,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [\n",
    "    [\"Carroll\", 94, 22, 60, 92, 20, 60],\n",
    "    [\"Grant\", 98, 21, 65, 92, 22, 65],\n",
    "    [\"Peck\", 98, 28, 40, 88, 26, 40],\n",
    "    [\"Donat\", 94, 19, 200, 82, 17, 200],\n",
    "    [\"Stewart\", 98, 21, 50, 88, 22, 45],\n",
    "    [\"Young\", 96, 21, 85, 92, 22, 85],\n",
    "]\n",
    "colnames = [\"study\", \"mean_t\", \"sd_t\", \"n_t\", \"mean_c\", \"sd_c\", \"n_c\"]\n",
    "dframe1 = pd.DataFrame(data, columns=colnames).set_index('study')\n",
    "\n",
    "mean2, sd2, nobs2, mean1, sd1, nobs1 = np.asarray(\n",
    "    dframe1\n",
    ").T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_t</th>\n",
       "      <th>sd_t</th>\n",
       "      <th>n_t</th>\n",
       "      <th>mean_c</th>\n",
       "      <th>sd_c</th>\n",
       "      <th>n_c</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>study</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Carroll</th>\n",
       "      <td>94</td>\n",
       "      <td>22</td>\n",
       "      <td>60</td>\n",
       "      <td>92</td>\n",
       "      <td>20</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Grant</th>\n",
       "      <td>98</td>\n",
       "      <td>21</td>\n",
       "      <td>65</td>\n",
       "      <td>92</td>\n",
       "      <td>22</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Peck</th>\n",
       "      <td>98</td>\n",
       "      <td>28</td>\n",
       "      <td>40</td>\n",
       "      <td>88</td>\n",
       "      <td>26</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Donat</th>\n",
       "      <td>94</td>\n",
       "      <td>19</td>\n",
       "      <td>200</td>\n",
       "      <td>82</td>\n",
       "      <td>17</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Stewart</th>\n",
       "      <td>98</td>\n",
       "      <td>21</td>\n",
       "      <td>50</td>\n",
       "      <td>88</td>\n",
       "      <td>22</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Young</th>\n",
       "      <td>96</td>\n",
       "      <td>21</td>\n",
       "      <td>85</td>\n",
       "      <td>92</td>\n",
       "      <td>22</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean_t  sd_t  n_t  mean_c  sd_c  n_c\n",
       "study                                        \n",
       "Carroll      94    22   60      92    20   60\n",
       "Grant        98    21   65      92    22   65\n",
       "Peck         98    28   40      88    26   40\n",
       "Donat        94    19  200      82    17  200\n",
       "Stewart      98    21   50      88    22   45\n",
       "Young        96    21   85      92    22   85"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dframe1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "# one-step chi2, DerSimonian-Laird estimate for random effects variance tau\n",
    "eff1, var_eff1 = effectsize_smd(mean2, sd2, nobs2, mean1, sd1, nobs1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.09452437, 0.2773564 , 0.36654635, 0.6643851 , 0.46180798,\n",
       "       0.18516464])"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eff1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Uone-step chi2, DerSimonian-Laird estimate for random effects variance tau\n",
    "res1 = combine_effects(eff1, var_eff1, method_re=\"chi2\", use_t=False, row_names=dframe1.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: chi2\n",
      "tau2= 0.03723180584080541\n"
     ]
    }
   ],
   "source": [
    "print(\"method RE:\", res1.method_re)\n",
    "print(\"tau2=\", res1.tau2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        eff    sd_eff    ci_low    ci_upp      w_fe      w_re\n",
      "Carroll            0.094524  0.182680 -0.263521  0.452570  0.123885  0.157529\n",
      "Grant              0.277356  0.176279 -0.068144  0.622857  0.133045  0.162828\n",
      "Peck               0.366546  0.225573 -0.075569  0.808662  0.081250  0.126223\n",
      "Donat              0.664385  0.102748  0.463002  0.865768  0.391606  0.232734\n",
      "Stewart            0.461808  0.208310  0.053527  0.870089  0.095275  0.137949\n",
      "Young              0.185165  0.153729 -0.116139  0.486468  0.174939  0.182736\n",
      "fixed effect       0.414961  0.064298  0.288939  0.540984  1.000000       NaN\n",
      "random effect      0.358486  0.105462  0.151785  0.565187       NaN  1.000000\n",
      "fixed effect wls   0.414961  0.099237  0.220460  0.609462  1.000000       NaN\n",
      "random effect wls  0.358486  0.090328  0.181446  0.535526       NaN  1.000000\n"
     ]
    }
   ],
   "source": [
    "nobs=np.array(nobs1 + nobs2)\n",
    "print(res1.summary_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.26719942, -0.07141628, -0.08244568,  0.46238908,  0.04820269,\n",
       "        -0.1183121 ]),\n",
       " array([0.45624817, 0.62612908, 0.81553838, 0.86638112, 0.87541326,\n",
       "        0.48864139]))"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1.conf_int_samples(use_t=True, nobs=np.array(nobs1 + nobs2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1.plot_forest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another example with the effect being the mean of measurements (fixed-effect)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "eff2 = np.array(\n",
    "    [61.00,  61.40,  62.21,  62.30,  62.34,  62.60,  62.70,  62.84,  65.90 ]\n",
    ")\n",
    "var_eff2 = np.array(\n",
    "    [0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225]\n",
    ")\n",
    "rownames2 = [\n",
    "    \"PTB\",   \"NMi\",  \"NIMC\", \"KRISS\",\"LGC\",  \"NRC\",  \"IRMM\", \"NIST\", \"LNE\" \n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: dl\n",
      "                       eff  sd_eff   ci_low   ci_upp    w_fe    w_re\n",
      "PTB                61.0000  0.4500  60.1180  61.8820  0.0574  0.1231\n",
      "NMi                61.4000  1.1000  59.2440  63.5560  0.0096  0.0403\n",
      "NIMC               62.2100  0.3000  61.6220  62.7980  0.1292  0.1597\n",
      "KRISS              62.3000  0.4500  61.4180  63.1820  0.0574  0.1231\n",
      "LGC                62.3400  0.6200  61.1248  63.5552  0.0303  0.0898\n",
      "NRC                62.6000  0.7500  61.1300  64.0700  0.0207  0.0710\n",
      "IRMM               62.7000  0.2600  62.1904  63.2096  0.1721  0.1698\n",
      "NIST               62.8400  0.1500  62.5460  63.1340  0.5169  0.1945\n",
      "LNE                65.9000  1.3500  63.2540  68.5460  0.0064  0.0286\n",
      "fixed effect       62.5834  0.1078  62.3347  62.8321  1.0000     NaN\n",
      "random effect      62.3901  0.2457  61.8234  62.9568     NaN  1.0000\n",
      "fixed effect wls   62.5834  0.1899  62.1455  63.0213  1.0000     NaN\n",
      "random effect wls  62.3901  0.2948  61.7104  63.0699     NaN  1.0000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\statsmodels\\stats\\meta_analysis.py:106: UserWarning: `use_t=True` requires `nobs` for each sample or `ci_func`. Using normal distribution for confidence interval of individual samples.\n",
      "  warnings.warn(msg)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res2_DL = combine_effects(eff2, var_eff2, method_re=\"dl\", use_t=True, row_names=rownames2)\n",
    "print(\"method RE:\", res2_DL.method_re)\n",
    "print(round(res2_DL.summary_frame(), 4))\n",
    "fig = res2_DL.plot_forest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step-by-step Woolf method (fixed-effect)\n",
    "\n",
    "A very common and simple version of the meta-analysis procedure is commonly referred to as the inverse-variance method. This approach is implemented in its most basic form in RevMan, and is used behind the scenes in many meta-analyses of both dichotomous and continuous data.\n",
    "\n",
    "The inverse-variance method is so named because the weight given to each study is chosen to be the inverse of the variance of the effect estimate (i.e. 1 over the square of its standard error). Thus, larger studies, which have smaller standard errors, are given more weight than smaller studies, which have larger standard errors. This choice of weights minimizes the imprecision (uncertainty) of the pooled effect estimate.\n",
    "\n",
    "We assign **weights** based on the inverse of the variance rather than sample size. The inverse variance is roughly proportional to sample size, but is a more nuanced measure, and serves to minimize the variance of the combined effect so that $ w_i = \\frac{1}{v_i} $ with $v_i$ the within-study variance for studi $i$.\n",
    "\n",
    "A fixed-effect meta-analysis using the inverse-variance method calculates a weighted average as, i.e. the weighted mean is then computed as the sum of the products $w_iE_i$, where $E_i$ is the effect size if the individual study, divided by the sum of the weights:\n",
    "\n",
    "$$ \\bar{E} = \\frac{\\sum_{i=1}^kw_iE_i}{\\sum_{i=1}^kw_i} = \\frac{\\sum E_i(1/\\mathrm{SE_i}^2)}{\\sum (1/\\mathrm{SE_i}^2)} $$\n",
    "\n",
    "A fixed-effect meta-analysis is valid under an assumption that all effect estimates are estimating the same underlying intervention effect, which is referred to variously as a 'fixed-effect' assumption, a 'common-effect' assumption or an 'equal-effects' assumption.\n",
    "\n",
    "The variance of the combined effect is $ v = \\frac{1}{\\sum_{i=1}^kw_i} $, and $ \\mathrm{SE}(\\bar{E}) = \\sqrt{v} $.\n",
    "\n",
    "The 95% confidence interval for the mean combined effect would then be $ \\bar{E} \\pm z_{\\alpha/2}*\\mathrm{SE}(\\bar{E}) $ (see the video [\"Meta-analysis Prediction Intervals\"](https://www.youtube.com/watch?v=DPo88xtPUaA)), it tells nothing about the distribution of the different effect sizes measured but the precision of the mean effect sizes, depending on the number of studies.\n",
    "\n",
    "Finally, $ Z = \\frac{\\bar{E}}{\\mathrm{SE}(\\bar{E})} $, so for a two-tailed test $ p = 2[1-(\\phi(|Z|))] $ with $\\phi$ the standard normal cumulative function. In the context of Cochrane reviews is either an assumption of 'no effect of the intervention' or 'no differences in the effect of intervention between studies' (_no heterogeneity_). Thus, a P value that is very small indicates that the observed effect is very unlikely to have arisen purely by chance, and therefore provides evidence against the null hypothesis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.9382716 ,  0.82644628, 11.11111111,  4.9382716 ,  2.60145682,\n",
       "        1.77777778, 14.79289941, 44.44444444,  0.54869684])"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights2 = 1 / var_eff2\n",
    "weights2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.9382716 ,  0.82644628, 11.11111111,  4.9382716 ,  2.60145682,\n",
       "        1.77777778, 14.79289941, 44.44444444,  0.54869684])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# getting weights from the combined results\n",
    "res2_DL.weights_fe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05743554, 0.00961215, 0.12922996, 0.05743554, 0.03025675,\n",
       "       0.02067679, 0.17205172, 0.51691983, 0.00638173])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# below corresponds to the `w_fe` column\n",
    "res2_DL.weights_fe / sum(res2_DL.weights_fe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 301.2345679 ,   50.74380165,  691.22222222,  307.65432099,\n",
       "        162.1748179 ,  111.28888889,  927.5147929 , 2792.88888889,\n",
       "         36.15912209])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E2 = eff2 * weights2\n",
    "E2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Combined effect size = 62.5834 with SE = 0.1078 and the 95% CI ranging from 62.3347 to 62.8321\n"
     ]
    }
   ],
   "source": [
    "df2 = len(eff2) - 1\n",
    "\n",
    "E_bar2 = sum(E2) / sum(weights2)\n",
    "var_bar2 = 1 / sum(weights2)\n",
    "SE_bar2 = var_bar2**.5\n",
    "t_crit2 = stats.t(df=df2).ppf((1+.95)/2) # we used t-distribution with combine_effect()\n",
    "\n",
    "# Z2 = E_bar2/SE_bar2\n",
    "# pvalue_2 = 2 * (1 - stats.t.cdf(x = abs(Z2), df=df2))\n",
    "\n",
    "print(f\"Combined effect size = {E_bar2:.4f} with SE = {SE_bar2:.4f} and the 95% CI ranging from {E_bar2 - t_crit2*SE_bar2:.4f} to {E_bar2 + t_crit2*SE_bar2:.4f}\")\n",
    "#print(f\"Z statistic = {Z2:.2f} with an associated P value = {pvalue_2:.5f}\") # not sure that works"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Heterogeneity\n",
    "\n",
    "The classical measure of heterogeneity is **Cochran's $Q$**, which is calculated as the weighted sum of squared differences between individual study effects and the pooled effect across studies, with the weights being those used in the pooling method with $ Q = \\sum w_i(E_i-E)^2 $ where $ E = \\frac{\\sum w_iE_i}{\\sum w_i} $.\n",
    "\n",
    "$Q$ is distributed as a chi-square statistic with k (numer of studies) minus 1 degrees of freedom $Q \\sim \\chi^2(k-1)$.\n",
    "\n",
    "$Q$ has low power as a comprehensive test of heterogeneity, especially when the number of studies is small, i.e. most meta-analyses. Conversely, $Q$ has too much power as a test of heterogeneity if the number of studies is large.\n",
    "\n",
    "The $I^2$ statistic describes the percentage of variation across studies that is due to heterogeneity rather than chance\n",
    "\n",
    "$$ I^2 = 100\\%  \\frac{Q - \\mathrm{Df}}{Q} $$\n",
    "\n",
    "$I^2$ is an intuitive and simple expression of the inconsistency of studies' results. Unlike $Q$ it does not inherently depend upon the number of studies considered.\n",
    "\n",
    "A confidence interval for $I^2$ is constructed using either i) the iterative non-central chi-squared distribution method of Hedges and Piggott; or ii) the test-based method of Higgins and Thompson. The non-central chi-square method is currently the method of choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.base.HolderTuple'>\n",
       "statistic = 24.80189774185419\n",
       "pvalue = 0.001679351463714887\n",
       "df = 8\n",
       "distr = 'chi2'\n",
       "tuple = (24.80189774185419, 0.001679351463714887)"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res2_DL.test_homogeneity()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cochrane Q = 24.802 and I² = 67.74%, with P value for homogeneitiy = 0.001679\n"
     ]
    }
   ],
   "source": [
    "Q2 = sum(res2_DL.weights_fe * (res2_DL.effect - res2_DL.mean_effect_fe)**2)\n",
    "I2 = (Q2 - df2)/Q2\n",
    "pvalue_homogen = 1 - stats.chi2.cdf(x = Q2, df=df2)\n",
    "\n",
    "print(f\"Cochrane Q = {Q2:.3f} and I² = {100*I2:.2f}%, with P value for homogeneitiy = {pvalue_homogen:.6f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6774440374173594"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res2_DL.i2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random-effects models\n",
    "\n",
    "A variation on the inverse-variance method is to incorporate an assumption that the different studies are estimating different, yet related, intervention effects. This produces a random-effects meta-analysis, and the simplest version is known as the _DerSimonian and Laird method_.\n",
    "\n",
    "The random-effects meta-analysis approach incorporates an assumption that the different studies are estimating different, yet related, intervention effects. The approach allows us to address heterogeneity that cannot readily be explained by other factors. A random-effects meta-analysis model involves an assumption that the effects being estimated in the different studies follow some distribution. The model represents our lack of knowledge about why real, or apparent, intervention effects differ, by considering the differences as if they were random. The centre of the assumed distribution describes the average of the effects, while its width describes the degree of heterogeneity. The conventional choice of _distribution is a normal distribution_. It is difficult to establish the validity of any particular distributional assumption, and this is a common criticism of random-effects meta-analyses. The importance of the assumed shape for this distribution has not been widely studied.\n",
    "\n",
    "To undertake a random-effects meta-analysis, the standard errors of the study-specific estimates ($\\mathrm{SE}_i$) are adjusted to incorporate a measure of the extent of variation, or heterogeneity, among the intervention effects observed in different studies (this variation is often referred to as Tau-squared, $\\tau^2$, or Tau2). The amount of variation, and hence the adjustment, can be estimated from the intervention effects and standard errors of the studies included in the meta-analysis.\n",
    "\n",
    "In a heterogeneous set of studies, a random-effects meta-analysis will award relatively more weight to smaller studies than such studies would receive in a fixed-effect meta-analysis. This is because small studies are more informative for learning about the distribution of effects across studies than for learning about an assumed common intervention effect.\n",
    "\n",
    "Note that a random-effects model does not 'take account' of the heterogeneity, in the sense that it is no longer an issue. It is always preferable to explore possible causes of heterogeneity, although there may be too few studies to do this adequately.\n",
    "\n",
    "If there is very little variation between trials then $I^2$ will be low and a fixed effects model might be appropriate. With fixed effects all of the studies that you are trying to examine as a whole are considered to have been conducted under similar conditions with similar subjects - in other words, the only difference between studies is their power to detect the outcome of interest. An alternative approach, 'random effects', allows the study outcomes to vary in a normal distribution between studies. Many investigators consider the random effects approach to be a more natural choice than fixed effects, for example in medical decision making contexts.\n",
    "\n",
    "More data are required for random effects models to achieve the same statistical power as fixed effects models, and there is no 'exact' way to handle studies with small numbers when assuming random effects. This should not be a problem with most meta-analyses, however do not use random effects models with sparse datasets without expert statistical guidance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meta-analysis for count data/proportions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "import io\n",
    "\n",
    "ss = \"\"\"\\\n",
    "    study,nei,nci,e1i,c1i,e2i,c2i,e3i,c3i,e4i,c4i\n",
    "    1,19,22,16.0,20.0,11,12,4.0,8.0,4,3\n",
    "    2,34,35,22.0,22.0,18,12,15.0,8.0,15,6\n",
    "    3,72,68,44.0,40.0,21,15,10.0,3.0,3,0\n",
    "    4,22,20,19.0,12.0,14,5,5.0,4.0,2,3\n",
    "    5,70,32,62.0,27.0,42,13,26.0,6.0,15,5\n",
    "    6,183,94,130.0,65.0,80,33,47.0,14.0,30,11\n",
    "    7,26,50,24.0,30.0,13,18,5.0,10.0,3,9\n",
    "    8,61,55,51.0,44.0,37,30,19.0,19.0,11,15\n",
    "    9,36,25,30.0,17.0,23,12,13.0,4.0,10,4\n",
    "    10,45,35,43.0,35.0,19,14,8.0,4.0,6,0\n",
    "    11,246,208,169.0,139.0,106,76,67.0,42.0,51,35\n",
    "    12,386,141,279.0,97.0,170,46,97.0,21.0,73,8\n",
    "    13,59,32,56.0,30.0,34,17,21.0,9.0,20,7\n",
    "    14,45,15,42.0,10.0,18,3,9.0,1.0,9,1\n",
    "    15,14,18,14.0,18.0,13,14,12.0,13.0,9,12\n",
    "    16,26,19,21.0,15.0,12,10,6.0,4.0,5,1\n",
    "    17,74,75,,,42,40,,,23,30\"\"\"\n",
    "df3 = pd.read_csv(io.StringIO(ss))\n",
    "df3_sub = df3[[\"e2i\", \"nei\", \"c2i\", \"nci\"]]\n",
    "\n",
    "count1_3, nobs1_3, count2_3, nobs2_3 = df3_sub.values.T\n",
    "dta = df3_sub.values.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>e2i</th>\n",
       "      <th>nei</th>\n",
       "      <th>c2i</th>\n",
       "      <th>nci</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11</td>\n",
       "      <td>19</td>\n",
       "      <td>12</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>34</td>\n",
       "      <td>12</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21</td>\n",
       "      <td>72</td>\n",
       "      <td>15</td>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14</td>\n",
       "      <td>22</td>\n",
       "      <td>5</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>42</td>\n",
       "      <td>70</td>\n",
       "      <td>13</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   e2i  nei  c2i  nci\n",
       "0   11   19   12   22\n",
       "1   18   34   12   35\n",
       "2   21   72   15   68\n",
       "3   14   22    5   20\n",
       "4   42   70   13   32"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3_sub.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "eff3, var_eff3 = effectsize_2proportions(*dta, statistic=\"rd\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: iterated\n",
      "                        eff    sd_eff    ci_low    ci_upp      w_fe      w_re\n",
      "0                  0.033493  0.155240 -0.270773  0.337758  0.017454  0.017454\n",
      "1                  0.186555  0.117324 -0.043395  0.416505  0.030559  0.030559\n",
      "2                  0.071078  0.073470 -0.072919  0.215076  0.077928  0.077928\n",
      "3                  0.386364  0.141044  0.109922  0.662805  0.021145  0.021145\n",
      "4                  0.193750  0.104721 -0.011499  0.398999  0.038357  0.038357\n",
      "5                  0.086095  0.061385 -0.034218  0.206407  0.111630  0.111630\n",
      "6                  0.140000  0.119262 -0.093749  0.373749  0.029574  0.029574\n",
      "7                  0.061103  0.091761 -0.118746  0.240951  0.049956  0.049956\n",
      "8                  0.158889  0.128034 -0.092052  0.409830  0.025660  0.025660\n",
      "9                  0.022222  0.110807 -0.194956  0.239401  0.034259  0.034259\n",
      "10                 0.065510  0.045953 -0.024556  0.155575  0.199199  0.199199\n",
      "11                 0.114173  0.046876  0.022297  0.206049  0.191426  0.191426\n",
      "12                 0.045021  0.109182 -0.168971  0.259014  0.035286  0.035286\n",
      "13                 0.200000  0.126491 -0.047918  0.447918  0.026290  0.026290\n",
      "14                 0.150794  0.119749 -0.083910  0.385497  0.029334  0.029334\n",
      "15                -0.064777  0.150599 -0.359945  0.230390  0.018547  0.018547\n",
      "16                 0.034234  0.081457 -0.125418  0.193887  0.063395  0.063395\n",
      "fixed effect       0.096212  0.020509  0.056014  0.136410  1.000000       NaN\n",
      "random effect      0.096212  0.020509  0.056014  0.136410       NaN  1.000000\n",
      "fixed effect wls   0.096212  0.016521  0.063831  0.128593  1.000000       NaN\n",
      "random effect wls  0.096212  0.016521  0.063831  0.128593       NaN  1.000000\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res5 = combine_effects(\n",
    "    eff3, var_eff3, method_re=\"iterated\", use_t=False\n",
    ")  # , row_names=rownames)\n",
    "\n",
    "res5_df = res5.summary_frame()\n",
    "\n",
    "print(\"method RE:\", res5.method_re)\n",
    "print(res5.summary_frame())\n",
    "\n",
    "fig = res5.plot_forest()\n",
    "fig.set_figheight(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example of the reboxetine study\n",
    "\n",
    "The analysis takes the data from the [article from Eyding et al. (2010)](https://www.bmj.com/content/341/bmj.c4737) discussed in page 455-456 and from which the forest plot in Figure 43.1 was derived."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: chi2\n",
      "RE variance tau2: 0.05605589416643271\n",
      "                        eff    sd_eff    ci_low    ci_upp  w_fe  w_re\n",
      "fixed effect       0.154119  0.089729 -0.021746  0.329984   1.0   NaN\n",
      "random effect      0.160783  0.129872 -0.093762  0.415328   NaN   1.0\n",
      "fixed effect wls   0.154119  0.125602 -0.092057  0.400295   1.0   NaN\n",
      "random effect wls  0.160783  0.136132 -0.106032  0.427598   NaN   1.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Odds ratio (95% CI)')"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_eyding = [\n",
    "    [\"014\",  60, 126,  34, 128],\n",
    "    [\"015\",  47, 110,  40, 111],\n",
    "    [\"046\", 132, 252, 124, 247],\n",
    "    [\"047\", 109, 238, 101, 239],\n",
    "    [\"050\",  48, 144,  54, 143],\n",
    "    [\"045\",  30,  88,  33,  86],\n",
    "    [\"049\",  29, 106,  27, 104],\n",
    "]\n",
    "colnames_eyding = [\"study\", \"count_t\", \"nobs_t\", \"count_c\", \"nobs_c\"]\n",
    "df_eyding = pd.DataFrame(data_eyding, columns=colnames_eyding).set_index('study')\n",
    "# sample 1 is treatment and sample 2 is control\n",
    "\n",
    "dta_eyding = df_eyding.values.T\n",
    "\n",
    "eff_eyding, var_eff_eyding = effectsize_2proportions(*dta_eyding, statistic=\"or\")\n",
    "# log-odds-ratio and log-risk-ratio can be transformed back to or and rr using the exp function\n",
    "\n",
    "res_eyding = combine_effects(\n",
    "    eff_eyding, var_eff_eyding, method_re=\"chi2\", use_t=False, row_names=df_eyding.index,\n",
    ")\n",
    "\n",
    "print(\"method RE:\", res_eyding.method_re)\n",
    "print(\"RE variance tau2:\", res_eyding.tau2)\n",
    "print(res_eyding.summary_frame().iloc[-4:])\n",
    "\n",
    "fig = res_eyding.plot_forest(\n",
    "    use_exp=True, # to show OR instead of logOR\n",
    ")\n",
    "fig.set_figheight(7)\n",
    "plt.axvline(x=1, ls='--', color='blue')\n",
    "\n",
    "plt.xscale('log')\n",
    "\n",
    "ax = plt.gca()\n",
    "\n",
    "# By default, a logarithmic scale uses a LogFormatter\n",
    "from matplotlib.ticker import ScalarFormatter\n",
    "\n",
    "ax.xaxis.set_major_formatter(ScalarFormatter())\n",
    "ax.set_xticks([.33, .5, 1, 2, 3, 5])\n",
    "\n",
    "ax.set_title('Forest plot - reboxetine study')\n",
    "ax.set_xlabel('Odds ratio (95% CI)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9128399011196743, 0.2595352712298463)"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Total effect\n",
    "stats.fisher_exact([[413, 1058], [455, 1064]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.base.HolderTuple'>\n",
       "statistic = 11.756574010710532\n",
       "pvalue = 0.0676249431325276\n",
       "df = 6\n",
       "distr = 'chi2'\n",
       "tuple = (11.756574010710532, 0.0676249431325276)"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_eyding.test_homogeneity()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.0"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Total heterogeneity in %\n",
    "round(100 * res_eyding.i2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>eff</th>\n",
       "      <th>sd_eff</th>\n",
       "      <th>ci_low</th>\n",
       "      <th>ci_upp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>014</th>\n",
       "      <td>2.51</td>\n",
       "      <td>1.31</td>\n",
       "      <td>1.49</td>\n",
       "      <td>4.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>015</th>\n",
       "      <td>1.32</td>\n",
       "      <td>1.32</td>\n",
       "      <td>0.77</td>\n",
       "      <td>2.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>046</th>\n",
       "      <td>1.09</td>\n",
       "      <td>1.20</td>\n",
       "      <td>0.77</td>\n",
       "      <td>1.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>047</th>\n",
       "      <td>1.15</td>\n",
       "      <td>1.20</td>\n",
       "      <td>0.80</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>050</th>\n",
       "      <td>0.82</td>\n",
       "      <td>1.28</td>\n",
       "      <td>0.51</td>\n",
       "      <td>1.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>045</th>\n",
       "      <td>0.83</td>\n",
       "      <td>1.37</td>\n",
       "      <td>0.45</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>049</th>\n",
       "      <td>1.07</td>\n",
       "      <td>1.37</td>\n",
       "      <td>0.58</td>\n",
       "      <td>1.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fixed effect</th>\n",
       "      <td>1.17</td>\n",
       "      <td>1.09</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>random effect</th>\n",
       "      <td>1.17</td>\n",
       "      <td>1.14</td>\n",
       "      <td>0.91</td>\n",
       "      <td>1.51</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                eff  sd_eff  ci_low  ci_upp\n",
       "014            2.51    1.31    1.49    4.25\n",
       "015            1.32    1.32    0.77    2.27\n",
       "046            1.09    1.20    0.77    1.55\n",
       "047            1.15    1.20    0.80    1.66\n",
       "050            0.82    1.28    0.51    1.34\n",
       "045            0.83    1.37    0.45    1.54\n",
       "049            1.07    1.37    0.58    1.98\n",
       "fixed effect   1.17    1.09    0.98    1.39\n",
       "random effect  1.17    1.14    0.91    1.51"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# with with odds ratio instead of log odds ratio\n",
    "res_eyding_subframe = res_eyding.summary_frame().loc[\n",
    "    :'random effect',\n",
    "    ['eff', 'sd_eff', 'ci_low', 'ci_upp']\n",
    "]\n",
    "round(res_eyding_subframe.apply(np.exp), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.51336898, 1.32420635, 1.09112903, 1.1545015 , 0.82407407,\n",
       "       0.830721  , 1.07407407])"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Odds ratio\n",
    "np.exp(res_eyding.eff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.48615459, 0.7707871 , 0.76800148, 0.80402743, 0.50784043,\n",
       "        0.447326  , 0.58244518],\n",
       "       [4.25058316, 2.2749764 , 1.55020869, 1.65774656, 1.3372273 ,\n",
       "        1.5427169 , 1.98067586]])"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 95% CI of the odds ratio\n",
    "np.exp(res_eyding.conf_int_samples())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13.9143513 , 13.11748621, 31.1490689 , 29.34821992, 16.39224046,\n",
       "       10.0254981 , 10.25706022])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Weights for fixed effect situation\n",
    "1/var_eff_eyding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13.9143513 , 13.11748621, 31.1490689 , 29.34821992, 16.39224046,\n",
       "       10.0254981 , 10.25706022])"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_eyding.weights_fe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13185003, 0.12749867, 0.19132125, 0.18713961, 0.14408635,\n",
       "       0.10825823, 0.10984586])"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Relative weights for random effect situation\n",
    "res_eyding.weights_re / sum(res_eyding.weights_re)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13185003, 0.12749867, 0.19132125, 0.18713961, 0.14408635,\n",
       "       0.10825823, 0.10984586])"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_eyding.weights_rel_re"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step-by-step\n",
    "\n",
    "Similarly to the previous example with the Woolf method, we can calculate the different parameters using $ \\log\\mathrm(OR) = \\log(p_1) - \\log(1 - p_1) - \\log(p_2) + \\log(1 - p_2) $ and $ \\log(\\operatorname{SE})= \\sqrt{1/a + 1/b + 1/c + 1/d} $, with $ p_1 = a/n_1 $  and $ p_2 = c/n_2 $, and $ n_1 = a + b $ the total number of exposed to treatment (disease + no disease), and $ n_2 = c + d $ the total numner of not exposed to treatment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[60, 126, 34, 128]\n"
     ]
    }
   ],
   "source": [
    "# for example for stydy #014\n",
    "data014 = data_eyding[0][1:]\n",
    "print(data014)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "eff       0.921624\n",
       "sd_eff    0.268083\n",
       "ci_low    0.396192\n",
       "ci_upp    1.447056\n",
       "w_fe      0.112028\n",
       "w_re      0.131850\n",
       "Name: 014, dtype: float64"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_eyding.summary_frame().iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log(OR) for study `014` = 0.92162 with log(SE) = 0.26808\n",
      "Its 95% CI extends from 0.3962 to 1.4471\n",
      "OR for study `014` = 2.51 with SE = 1.31\n",
      "Its 95% CI extends from 1.49 to 4.25\n"
     ]
    }
   ],
   "source": [
    "a, n1, c, n2 = data014\n",
    "b, d = n1 - a, n2 - c\n",
    "p1, p2 = a/n1, c/n2\n",
    "\n",
    "log_or_014 = np.log(p1) - np.log(1-p1) - np.log(p2) + np.log(1-p2)\n",
    "log_se_014 = np.sqrt(1/a + 1/b + 1/c + 1/d)\n",
    "\n",
    "conf=0.95\n",
    "z = stats.norm.ppf((1 + conf) /2) # same as stats.norm.isf((1 - conf) /2)\n",
    "\n",
    "print(f\"Log(OR) for study `014` = {log_or_014:.5f} with log(SE) = {log_se_014:.5f}\")\n",
    "print(f\"Its 95% CI extends from {log_or_014 - z*log_se_014:.4f} to {log_or_014 + z*log_se_014:.4f}\")\n",
    "\n",
    "print(f\"OR for study `014` = {np.exp(log_or_014):.2f} with SE = {np.exp(log_se_014):.2f}\")\n",
    "print(f\"Its 95% CI extends from {np.exp(log_or_014 - z*log_se_014):.2f} to {np.exp(log_or_014 + z*log_se_014):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute Cochran's $Q$ with $ Q = \\sum w_i(E_i-E)^2 $ where $ E = \\frac{\\sum w_iE_i}{\\sum w_i} $, as discussed earlier.\n",
    "\n",
    "Also remember that $ I^2 = 100\\%  \\frac{Q - \\mathrm{Df}}{Q} $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cochrane Q = 11.757 and I² = 49.0%, with P value for homogeneity = 0.068\n"
     ]
    }
   ],
   "source": [
    "df_eyding = len(eff_eyding) - 1\n",
    "\n",
    "Q_eyding = sum(res_eyding.weights_fe * (res_eyding.effect - res_eyding.mean_effect_fe)**2)\n",
    "I_eyding = (Q_eyding - df_eyding)/Q_eyding\n",
    "pvalue_homogen_eyding = 1 - stats.chi2.cdf(x = Q_eyding, df=df_eyding)\n",
    "\n",
    "print(f\"Cochrane Q = {Q_eyding:.3f} and I² = {100*I_eyding:.1f}%, with P value for homogeneity = \\\n",
    "{pvalue_homogen_eyding:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the weight, in _fixed effect_ situation, $ \\mathrm{weight_{fe}} = \\frac{1}{\\operatorname{Var}} $ (see above). For the _random effect_ situation we needs to compute a $\\tau^2$ value that will serve as a correction.\n",
    "\n",
    "For the calculation of $\\tau^2$ using the $\\chi^2$ (also nammed DerSimonian and Laird) method, we need $ q = \\sum{w_iE_i^2} - \\frac{(\\sum{w_iE_i})^2}{\\sum{w_i}} $ and another constant  $ c = \\frac{\\sum{w_i} - \\sum{w_i^2}}{\\sum{w_i}} $.\n",
    "\n",
    "Thus, $ \\tau^2 = \\frac{q - \\mathrm{Df}}{c} $.\n",
    "\n",
    "Finally, the weights for the _random effect_ are obtained with $ \\mathrm{weight_{re}} = \\frac{1}{\\operatorname{Var} + \\tau^2} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau2 = 0.056\n",
      "relative weights for random effect: [0.13185003 0.12749867 0.19132125 0.18713961 0.14408635 0.10825823\n",
      " 0.10984586]\n"
     ]
    }
   ],
   "source": [
    "weights_eyding = 1/var_eff_eyding # weights fixed effect\n",
    "\n",
    "q_eyding = (weights_eyding * eff_eyding**2).sum() - ((weights_eyding * eff_eyding).sum())**2 / weights_eyding.sum()\n",
    "c_eyding = weights_eyding.sum() - (weights_eyding**2).sum() / weights_eyding.sum()\n",
    "tau_eyding = (q_eyding - df_eyding)/c_eyding\n",
    "weights_eyding_re = 1/(var_eff_eyding + tau_eyding) # weights random effect\n",
    "\n",
    "print(f\"tau2 = {tau_eyding:.3f}\")\n",
    "print(\"relative weights for random effect:\", weights_eyding_re/weights_eyding_re.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.756574010710532"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# of note q is same as Cochrane's Q\n",
    "q_eyding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Combined effect size = 0.16078 with SE = 0.12987 and the 95% CI ranging from -0.0938 to 0.4153\n",
      "The 95% CI of the total OR of 1.17 extends from 0.91 to 1.51\n"
     ]
    }
   ],
   "source": [
    "E_eyding_re = eff_eyding * weights_eyding_re\n",
    "E_bar_eyding_re = sum(E_eyding_re) / sum(weights_eyding_re)\n",
    "var_bar_eyding_re = 1 / sum(weights_eyding_re)\n",
    "SE_bar_eyding_re= var_bar_eyding_re**.5\n",
    "t_crit_eyding = stats.norm().ppf((1+.95)/2) # we didn't use t-distribution with combine_effect()\n",
    "\n",
    "# Z_eyding_re = E_bar_eyding_re/SE_bar_eyding_re\n",
    "# pvalue_eyding_re = 2 * (1 - stats.t.cdf(x = abs(Z_eyding_re), df=df_eyding))\n",
    "\n",
    "print(f\"Combined effect size = {E_bar_eyding_re:.5f} with SE = {SE_bar_eyding_re:.5f} and the 95% CI ranging from {E_bar_eyding_re - t_crit_eyding*SE_bar_eyding_re:.4f} to {E_bar_eyding_re + t_crit_eyding*SE_bar_eyding_re:.4f}\")\n",
    "print(f\"The 95% CI of the total OR of {np.exp(E_bar_eyding_re):.2f} extends from {np.exp(E_bar_eyding_re - t_crit_eyding*SE_bar_eyding_re):.2f} to {np.exp(E_bar_eyding_re + t_crit_eyding*SE_bar_eyding_re):.2f}\")\n",
    "# print(f\"Z statistic = {Z_eyding_re:.2f} with an associated P value = {pvalue_eyding_re:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Meta-analysis using flexible random-effects distribution models\n",
    "\n",
    "In meta-analysis in medical studies, random-effects models have been the primary statistical tools for quantitative evaluation of treatment effects that account for betweenstudies heterogeneity. Conventionally, the _normal distribution_ assumption has been adopted in most systematic reviews due to its computational and conceptual simplicity. However, the shape of the random-effects distribution reflects how the treatment effects parameters (e.g., mean difference, log relative risk) are distributed in the target population, and are directly associated with the fundamental heterogeneity of treatment effects. If the normal distribution assumption diverges drastically from the true heterogeneous structure, the overall results of the meta-analyses may be misleading.\n",
    "\n",
    "[New methods](https://arxiv.org/ftp/arxiv/papers/2003/2003.04598.pdf) propose the random-effects meta-analysis with flexible distribution models that can flexibly express skewness, kurtosis, and tailweight: (1) skew normal distribution, (2) skew t-distribution, (3) asymmetric Subbotin distribution, (4) Jones-Faddy distribution, and (5) sinh-arcsinh distribution.\n",
    "\n",
    "The overall conclusions and interpretations of meta-analyses can be dramatically altered if the normal distribution assumption is not suitable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mantel-Hanszel odds-ratio using contingency tables\n",
    "\n",
    "the meta-analysis functions currently do not include the Mantel-Hanszel method. However, the fixed effects results can be computed directly using StratifiedTable as illustrated later. Here we use the `catheter` dataset from the R package `R meta`, with `n.trt` and `n.ctrl` the number of subjects , and `col.trt` and `col.ctrl` the number of events in the _treatment_ and _control_ groups respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>n.trt</th>\n",
       "      <th>n.ctrl</th>\n",
       "      <th>col.trt</th>\n",
       "      <th>col.ctrl</th>\n",
       "      <th>inf.trt</th>\n",
       "      <th>inf.ctrl</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Ciresi</td>\n",
       "      <td>124</td>\n",
       "      <td>127</td>\n",
       "      <td>15.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>George</td>\n",
       "      <td>44</td>\n",
       "      <td>35</td>\n",
       "      <td>10.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hannan</td>\n",
       "      <td>68</td>\n",
       "      <td>60</td>\n",
       "      <td>22.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Heard</td>\n",
       "      <td>151</td>\n",
       "      <td>157</td>\n",
       "      <td>60.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>vanHeerden</td>\n",
       "      <td>28</td>\n",
       "      <td>26</td>\n",
       "      <td>4.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Name  n.trt  n.ctrl  col.trt  col.ctrl  inf.trt  inf.ctrl\n",
       "1      Ciresi    124     127     15.0      21.0     13.0      14.0\n",
       "2      George     44      35     10.0      25.0      1.0       3.0\n",
       "3      Hannan     68      60     22.0      22.0      5.0       7.0\n",
       "4       Heard    151     157     60.0      82.0      5.0       6.0\n",
       "5  vanHeerden     28      26      4.0      10.0      NaN       NaN"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "catheter = pd.read_csv(\"https://raw.githubusercontent.com/sbwiecko/intro_statistique_R/master/data/catheter.csv\", index_col=0)\n",
    "\n",
    "catheter.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>col.trt</th>\n",
       "      <th>n.trt</th>\n",
       "      <th>col.ctrl</th>\n",
       "      <th>n.ctrl</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Tennenberg</th>\n",
       "      <td>8.0</td>\n",
       "      <td>137</td>\n",
       "      <td>32.0</td>\n",
       "      <td>145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maki</th>\n",
       "      <td>28.0</td>\n",
       "      <td>208</td>\n",
       "      <td>47.0</td>\n",
       "      <td>195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vanHeerden</th>\n",
       "      <td>4.0</td>\n",
       "      <td>28</td>\n",
       "      <td>10.0</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hannan</th>\n",
       "      <td>22.0</td>\n",
       "      <td>68</td>\n",
       "      <td>22.0</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bach(b)</th>\n",
       "      <td>2.0</td>\n",
       "      <td>116</td>\n",
       "      <td>16.0</td>\n",
       "      <td>117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Heard</th>\n",
       "      <td>60.0</td>\n",
       "      <td>151</td>\n",
       "      <td>82.0</td>\n",
       "      <td>157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Collins</th>\n",
       "      <td>2.0</td>\n",
       "      <td>98</td>\n",
       "      <td>25.0</td>\n",
       "      <td>139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ciresi</th>\n",
       "      <td>15.0</td>\n",
       "      <td>124</td>\n",
       "      <td>21.0</td>\n",
       "      <td>127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ramsay</th>\n",
       "      <td>45.0</td>\n",
       "      <td>199</td>\n",
       "      <td>63.0</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Trazzera</th>\n",
       "      <td>16.0</td>\n",
       "      <td>123</td>\n",
       "      <td>24.0</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>George</th>\n",
       "      <td>10.0</td>\n",
       "      <td>44</td>\n",
       "      <td>25.0</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            col.trt  n.trt  col.ctrl  n.ctrl\n",
       "Name                                        \n",
       "Tennenberg      8.0    137      32.0     145\n",
       "Maki           28.0    208      47.0     195\n",
       "vanHeerden      4.0     28      10.0      26\n",
       "Hannan         22.0     68      22.0      60\n",
       "Bach(b)         2.0    116      16.0     117\n",
       "Heard          60.0    151      82.0     157\n",
       "Collins         2.0     98      25.0     139\n",
       "Ciresi         15.0    124      21.0     127\n",
       "Ramsay         45.0    199      63.0     189\n",
       "Trazzera       16.0    123      24.0      99\n",
       "George         10.0     44      25.0      35"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_catheter = catheter[[\"Name\", \"col.trt\", \"n.trt\",  \"col.ctrl\", \"n.ctrl\"]].set_index(\"Name\")\n",
    "df_catheter = df_catheter.iloc[[12,5,4,2,11,3,10,0,7,9,1]]\n",
    "df_catheter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    eff  sd_eff  ci_low  ci_upp  w_fe  w_re\n",
      "Tennenberg         0.22    1.52    0.10    0.49  1.07  1.10\n",
      "Maki               0.49    1.30    0.29    0.82  1.17  1.12\n",
      "vanHeerden         0.27    1.96    0.07    1.00  1.02  1.06\n",
      "Hannan             0.83    1.45    0.40    1.72  1.08  1.10\n",
      "Bach(b)            0.11    2.14    0.02    0.49  1.02  1.05\n",
      "Heard              0.60    1.26    0.38    0.95  1.23  1.13\n",
      "Collins            0.09    2.11    0.02    0.41  1.02  1.05\n",
      "Ciresi             0.69    1.44    0.34    1.42  1.09  1.11\n",
      "Ramsay             0.58    1.26    0.37    0.92  1.24  1.13\n",
      "Trazzera           0.47    1.43    0.23    0.94  1.09  1.11\n",
      "George             0.12    1.68    0.04    0.33  1.04  1.08\n",
      "fixed effect       0.47    1.11    0.38    0.58  2.72   NaN\n",
      "random effect      0.38    1.25    0.25    0.58   NaN  2.72\n",
      "fixed effect wls   0.47    1.18    0.34    0.65  2.72   NaN\n",
      "random effect wls  0.38    1.25    0.25    0.58   NaN  2.72\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Forest plot - Catheter dataset')"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcoAAAHwCAYAAAAmfS8XAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAA/TUlEQVR4nO3df5xcdX33/dd7JpmkgCvxB8UUCKWEttAuqEizAdpova1rROrdJLXS22u9a9eyN6JXa63Wy8aVlkvuWsSilz8o3lvtdVk2e1UKaqTYIEI3EcKPDAEsSYQgIgKuyI8oO85+7j/OWZxsdr47s9md2d28n4/HeezO93zP93xmzmTf8z1zZqKIwMzMzCZXaHcBZmZmc5mD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZguIpA9K+qd21zFdknok3dzuOuqRdLykkLSo3bVY6zgozWpIekDSjyU9XbMsb+H+vy7pbS3a1wOSXn2QY0jShZJ2SnpG0kOSNkn69Qa2ndHQmWshK2mNpIcWyn4OZQ5KswOdExFH1CwPN7PxITbb+BjwTuBC4AXAScDVwNo21jQth9hxsyY4KM0aIGmJpMskPZwvl0lakq9bk8+k/kLSI8D/J6kg6b2S9kj6gaRBSS/I+y+V9E95+xOSbpX085L+Bjgb+Hg+k/34JHWMz8J68zq+J+ndibrfIOnufD9fl/SrefvngeOAa/N9vWcaj8lK4P8B/iAitkTEsxGxLyL+Z0R8OO+zVtIdkp6U9B1JH6wZ4hv5zyfyGrpqxv6IpB9Kul9Sd0378yVdmd/v70r6a0nF/H59CujKx3oi778kH+tBSd+X9ClJP5evO+C4TXIfi/n2j0v6NhNeAEh6q6R7JT0l6duS3p63Hw5sBpbXnpmQdIakrfnx+J6kj0sq5dtI0kclPZo/XndJ+rXU/ai3n2aPpU0hIrx48ZIvwAPAqydp/xCwDTgKeDEwDFyUr1sD/BS4BFgC/BzZLGsbcEze9mngC3n/twPXAocBReDlQEe+7uvA2xL1HQ8E8AXgcODXgcfGawY+CPxT/vtJwDPA/wEsBt4D7AZKqfvaxGP1J8DeKfqsyWssAJ3A94HfnXBfFtX07wEqwB/nj835wMOA8vVfzB/Lw/NjcQvw9pptb56w/48C15DNdp+XP+7/vd5xq3MfvwUcm49xQ23NZMH5S4CA3wL2AS+rGf+hCeO9HFgFLMrv/73Au/J1vwPcBhyZj/erwEsavB8PpY6Dl4P8u9DuArx4mUtLHh5PA0/ky9V5+x7gdTX9fgd4IP99DTAKLK1Zfy/w2zW3X5IHwCLg/yYL2s5J9v91GgvKX6lp+3+BK/PfP8jPgvIDwGBNvwLwXWBNzX09mKB8P7CtyW0uAz464b5MDMrdNbcPy/scDfw88GxtoAF/ANxQs+3NNetE9kLhl2rauoD76x23SerdAvxJze3XTKx5Qv+rgXfWjJ8MMOBdwBfz318F3EcWpIUm74eDchYXn5M3O9DvRsTXJrQtB/bW3N6bt417LCJ+UnN7BfBFSWM1bVWyP/afJ5uh/LOkI4F/At4fEZUmavzOhFomu3hmv5ojYkzSd4BfaGQHkjaTnQqGbNb2Pyd0+QHZC4DUGL8BfBj4NaBENnPbNMWuH6mpeZ8kgCPIZlOLge/lbZCF/3cmDpB7MVnQ3lbTX2Qz1XETj9tEyznwsX5Oflp4I9nsvZDv7656g0k6CbgUOD3vu4hsFklEbMlPt38CWCHpX4B3A0sbuB82i/wepVljHiYLv3HH5W3jJv43PN8BuiPiyJplaUR8NyIqEdEfEScDq4HXA2+pM049xyZqmbRmZX9ljyWbVU65r4jojp9d0DQxJAH+HThG0umJYf4X2SnDYyPi+WTvI47/tW/2vy76DtmM8kU1j2lHRJxSZ7zHgR8Dp9T0f35EHFF7N6fY5/c48LEGsvcNgf8NfAT4+Yg4EvgK6fv3SbJTuSsjogP4y5r+RMTfR8TLgZPJwvfPG7gf/i+gZpmD0qwxXwD+m6QXS3oR8FdkM8F6PgX8jaQVAPl25+a/v1LSr0sqAk+SnZIdn3l+HzihgXo+IOkwSacAbwWumqTPILBW0m9LWgz8GVnQDDe5r0lFxC7gfwBfyC+MKeUXKr1J0nvzbs8DRiLiJ5LOAN5cM8RjZPe7oRoi4nvAvwF/J6lD2QVTvyTpt2ruzzHjF8dExBhwBfBRSUcBSPoFSb/TxN0cBC6UdIykZcB7a9aNz5AfA36azy5fU7P++8ALJT2/pu15ZMf8aUm/QvYeLHltr5D0G/mxegb4CTDWwP2YbD82gxyUZo35a2A7UCY7tXZ73lbPx8hmUv8m6SmyC3t+I193NDBE9gfzXuBGstOx49uty6/4/PvE+DeSXZjz78BHIuLfJnaIiP8E/hC4nGxWcg7ZR19G8y7/nSz8n1DiytkpXAiMny58guy93DeSXWwC0Ad8KH8M/ooseMbr2wf8DfAfeQ2rGtjfW8gC6h7gh2SP4/jp3y3A3cAjkh7P2/6C7HHaJulJ4GvALzdx/64ArgN2kB3zf6mp/ymy+z+Y1/JmsmM+vv5bZC+wvp3fv+Vkp1LfDDyVj137Aqcjb/sh2SneHwB/O9X9qLMfm0HjV5KZ2Twg6XjgfmBxRPy0zeWYHRI8ozQzM0twUJqZmSX41KuZmVmCZ5RmZmYJDkozM7MEfzPPwuNz6WZmzVO9FZ5RmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFBa6+3ZA3190NEBhUL2s68vazczm2MWxJeiS/oc0En2H+JWyf7H8W0R8SdtqufpiDiiHftmBr6Zp7+/fybqmNSJu3axfnCQYrVKcWzsufZqoUC1WGTThg3sXrly1vbfDhs3bmx3CWY2tYX9zTwR8ZaIOA34FPDRiDitXSFp9S0bGWH94CClSmW/kAQojo1RqlRYPzjIspGRNlVoZnagBRGU9Ug6R9ItknZIurSm/WlJl0u6T9IVDbQ3NU62SldI2inpYw2Ms0bS9ZKG8m0uy9v/XNK3JF0jaU/+v9vPW13DwxSr1WSfYrXKqq1bW1SRmdnUFuyXoks6CvgAsCYi9knaJOlVEbEFOBz4AvCnwB5JyyPi4cnagZ9OY5zDgCHg7cA3JJ0N/GdiHIAzgTMiYqekIyUdl29/KnAscE8j93tgYOCgHrfZ1FkuHzCTnKg4NkZnuczmtWtbVNXsm8vHxMwyPT09ddct2KAEVgEnAMOSAI7Ib28BRiNiGEDS/WTvbT5cp/2YaYxTBa6PiDFJ1wOnA8sS4wDcFhE7ASLiCUmvBG6KiGeAb0naOxsPUiuVRkdntJ+ZWSss5KAEuC4izpukvVLze/CzU9D12psdZ6LxC2zqjQPwozrtTUm9KmrUbF3MM1oqsaSBEBwtlWZl/+0yE8fEzNpnIb9HuQ04W9IxAJJWSDq6ReMUgd+WVABeDdw6jXFuA86SdJikXwFWTKP2OaXc2Um1kH7KVQsFyp2dLarIzGxqCzYoI+JR4HzgWkl3AVeRvafYinH2AX8AlIHbI+I/mh0nIh4EPgPcDlwM3A8822z9c8nW1aupFovJPtVikW1dXS2qyMxsagvic5QLlaTnRcRTkl5ENsM8PqY+YHP7gG7eDOvWQaWSLeMWL86WoSHo7m5ffWZ2qFrYn6NcwD4qqUx2wc+FDYTk3NfdDeUy9Pbu/808vb1Zu0PSzOYYzygXHh9QM7PmeUZpZmY2HQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSrODtWcP9PVBRwcUCtnPvr6s3czmPUVEu2tYkCQNAK+MiBWSisAjwFURcUGd/g8Ap0fE45OsewNwckR8uIFdL8gD2t/f3+4SJnXirl2sHxykWK1SHBt7rr1aKFAtFtm0YQO7V65sY4Xts3HjxnaXYNYM1VvhGeXselrSqcCZwPenO0hEXNNgSFoLLRsZYf3gIKVKZb+QBCiOjVGqVFg/OMiykZE2VWhmM8FBObuuAd6QL9cASLpW0g5J2yUdMLuU9EuSbpe0Mr/9OUkPSvp4Syu3KXUND1OsVpN9itUqq7ZubVFFZjYbFrW7gAXuNuDNZI/zvwCnA+dHxEOSFgN3SxqKiEfy/scC/wD8l4jYBRARb5HUk287pYGBgZm9B1ZXZ7l8wExyouLYGJ3lMpvXrm1RVXOHn4s2n/T09NRd56CcfY8AT9fcfpukc8nOhy/Pl/GgvBr4ckTc1dIKbVpKo6Mz2s/M5iYH5ez7S2AM+D+BNcCTwJkRsU/SdvY//d0L/K2kMyLilunsLPWqaD6bixfzjJZKLGkgBEdLpRZUM/cs1OeiHXr8HuUsi4gnIuLJ/OZhwON5SJ4CnDqh+23A24ErJS1pZZ3WvHJnJ9VC+p9QtVCg3NnZoorMbDY4KFvrq0BB0j3ARcDtEztExFbga8BFko6XdCfwIeD3Jd0p6XWtLNjq27p6NdViMdmnWiyyraurRRWZ2Wzw5ygXHh/QVtq8Gdatg0olW8YtXpwtQ0PQ3d2++sysUf4cpdms6O6Gchl6e/f/Zp7e3qzdIWk273lGufD4gJqZNc8zSjMzs+lwUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFDa3LRnD/T1QUcHFArZz76+rN3MrIUUEe2uYc6Q1AOcHhEX5Le/BHwkIr4+S/vbCbw+Ih6YwWGbOqD9/f0zuOuZceKuXawfHKRYrVIcG3uuvVooUC0W2bRhA7tXrmxjhTafbNy4sd0l2Pygeis8o7Q5ZdnICOsHBylVKvuFJEBxbIxSpcL6wUGWjYy0qUIzO9QsmKCU9GZJH6+5fZmkt0i6VtIOSdslXVCz/mlJl0u6T9IVDYx/jqRb8rEubaB9jaTrJQ1J2inpsrz9PZLulbQJWNrAOE3VOd91DQ9TrFaTfYrVKqu2bm1RRWZ2qFswp14ldQB3ACdGREi6DzgDOCIiHpK0GLgb+M2IeERSAGcCtwJ7gFXAa4C/Bb6bD/uLwLnAPcCXgDURsS8PuU8COydrj4gtktYAXwHOiIidko4EjgSuBzqBE4C78p/7EuMcUGdEPFzvcRgYGGjqgO7du7eZ7rPuvRdfzJLR0Sn7/WTJEi553/taUJHNdytWrGh3CTYP9PT01D31uqiVhcymiHhS0r3AKyRVgPsj4glJ75J0Ltn55+X58ggwGhHDAJLuB47Oh7pqwnuUkIXoCcCwJIAj8ttH1Gnfkm93W0TszOt7QtKrgJsj4sfA3ZL2TjH+ljp11g3K+a7UQEg208/M7GAtmKDMDQFvBEaB/53P6l4DnJnP1Lbzs9PNlZrtgqlPQ18XEefVNkh6w2TtNX404XZqtldvnKbq7OnpSa0+wFy7mGe0VGpoRjlaKrWgGlsImv03YTbRgnmPMncN8HrgDcDVQAfweB6SpwCnTnPcbcDZko4BkLRC0tGJ9npuB1ZLWirpZGD8nFCz4yxY5c5OqoX007JaKFDu7GxRRWZ2qFtQM8qIGJH0PaAUEY9K+irQK+ke4FtkQTWdcR+VdD5wraRFwDPAeRGxZ7L2xDh7JV1J9l7qPcD9qfGnU+t8t3X1ak7dseOAK15rVYtFtnV1tbAqMzuULZiLeew58/+Abt4M69ZBpZIt4xYvzpahIejubl99ZrYQ+XOUNo90d0O5DL29+38zT29v1u6QNLMW8oxy4fEBNTNrnmeUZmZm0+GgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDSzg7NnD/T1QUcHFArZz76+rN1sAVBEtLuGeUFSD3B6RFyQ3/4S8JGI+Ho765qED2gD+vv7213CgnDirl2sHxykWK1SHBt7rr1aKFAtFtm0YQO7V65sY4VmaRs3bhz/VfX6eEZpZtOybGSE9YODlCqV/UISoDg2RqlSYf3gIMtGRtpUodnMcFAeJEnXStohabukC2ran5Z0uaT7JF3RQHtT45i1W9fwMMVqNdmnWK2yauvWFlVkNjt86rVB+anXvwW+mzf9InAusDsiHpK0GLgb+M2IeERSAGcCtwJ7gFUR8XCi/ZhmxqlX58DAgA9oA/bu3dvuEua99158MUtGR6fs95MlS7jkfe9rQUVmzVuxYgUAPT09PvU6Q66KiNMi4jTgprztbZLuIAuy5fkCMBoRwxFRAe4Hjp6ivdlxzNqq1EBINtPPbK5a1O4CFoDXAGdGxD5J2/nZi49KTZ9ItUtaM41xJtXT0zONu3Do8cU8B2+0VGpoRjlaKrWgGrPpaeRvpmeUB6cDeDwPt1OAU9s8jlnLlDs7qRbSf0KqhQLlzs4WVWQ2OxyUB+cnZDPCe4CLgNunOc5XZ2gcs5bZuno11WIx2adaLLKtq6tFFZnNDl/Ms/D4gFrrbN4M69ZBpZIt4xYvzpahIejubl99Zo3zxTxmNgu6u6Fcht7e/b+Zp7c3a3dI2gLgGeXC4wNqZtY8zyjNzMymw0FpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaVPbswf6+qCjAwqF7GdfX9ZuZrbAKSLaXcOcImkN8K/A/cAi4AsR8TfTGOfpiDgisf4q4L9FxK5Uf0kvBv4pIn6nwV0/d0D7+/ubrPpAJ+7axfrBQYrVKsWxsefaq4UC1WKRTRs2sHvlyoPez0K1cePGdpdgZo1RvRWeUU7upog4DTgN+C+SVszk4JJOAZaOh2RKRDwGPCzpN2eyhkYsGxlh/eAgpUplv5AEKI6NUapUWD84yLKRkVaXZmbWMg7KtMOAEvCspGsl7ZC0XdIF4x0kHS3pmnzdbZJOqll3uaT7JF0xYdzzgC9OaJOkKyTtlPSxCeuuBv5w5u5WY7qGhylWq8k+xWqVVVu3tqgiM7PWW9TuAuaosyXdCZwIXBoRj0g6PyIekrQYuFvSUEQ8AlwObI6IT0rqAJbmYxwOfAH4U2CPpOUR8XC+7sx8Xa3DgCHg7cA3JJ0dETfl67YDDZ3+HRgYmM79nVRnuXzATHKi4tgYneUym9eunbH9LiQzeTzMbPb09PTUXecZ5eTGT72+BHitpE7gbZLuAG4FlucLwBrgSoCIeDIiHs3bRyNiOCIqZO93Hl0z/kuAxybsswpcHxFjwPXA6TXrHs23aanS6OiM9jMzm488o0yIiKckbQHOAl4DnBkR+yRtZ+oXGZXaoSb0/zE/m3nW3X3N70vzbaZU+6roYC/mGS2VWNJACI6WSge1n4Us9SrVzOYHzygTJBXILuh5CHg8D8lTgFNrut0AvDXvf3h+lepU7iE7rVurCPx2vs9Xk81cx52Ub9NS5c5OqoX0U6RaKFDu7GxRRWZmreegnNz4e5Rl4D7gOqAg6R7gIuD2mr4XAmsl7QBuBJY1MP6XgFdOaNsH/EG+z9sj4j9q1r0S+PI07sdB2bp6NdViMdmnWiyyraurRRWZmbWeP0fZBpJ+jmwmelZE/LSB/jcB50ZEI5/DmNkDunkzrFsHlUq2jFu8OFuGhqC7e0Z3aWbWBv4c5VwSET8GPgAcM1Xf/FTu3zUYkjOvuxvKZejt3f+beXp7s3aHpJktcJ5RLjw+oGZmzfOM0szMbDoclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmc9GePdDXBx0dUChkP/v6snYzaylFRLtrmNck9QCnR8QF+e0vAR+JiK/Pwr52Aq+PiAcS3XxAE/r7+9tdwpRO3LWL9YODFKtVimNjz7VXCwWqxSKbNmxg98qVbaxwbti4cWO7S7CFRfVWeEZpNocsGxlh/eAgpUplv5AEKI6NUapUWD84yLKRkTZVaHbocVDOEknnSLpF0g5Jl9a0X5u3bZd0QU37GknXSxqStFPSZXn7eyTdK2kTsLT198RaqWt4mGK1muxTrFZZtXVriyoys0XtLmCB+H1JZ+W//yLwOeDdwJqI2Cdpk6RXRcQW4PyIeEjSYuBuSUMR8Ui+7ZnAGRGxU9KRko4H/hjoBE4A7pqqkIGBgZm9Z9ZSneXyATPJiYpjY3SWy2xeu7ZFVc1Nfq7bTOrp6am7zjPKmXFVRJwWEacBNwE/IQu2YUl3Ai/NbwO8TdIdwK3A8nwZd1tE7ASIiCeAlwE3R8SPI+JuYG8L7ou1UWl0dEb7mdnB84xy9lwXEefVNkhaA7wGODOfaW5n/xcrP5owRtMX5qReFdncv5hntFRiSQMhOFoqtaCauc3PdWsVzyhnx1LgbEnHAEhaIelooAN4PA/JU4BTpxjndmC1pKWSTgZWzGrV1nblzk6qhfQ/y2qhQLmzs0UVmZmDcnY8CpwPXCvpLuAq4HDgq0BB0j3ARWRBWFdE7AWuBO7I+98/m0Vb+21dvZpqsZjsUy0W2dbV1aKKzMyfo1x4fEDnu82bYd06qFSyZdzixdkyNATd3e2rz2xh8ucozeaN7m4ol6G3d/9v5untzdodkmYt5RnlwuMDambWPM8ozczMpsNBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWmT27MH+vqgowMKhexnX1/WbmZ2CFFEtLuGOUfSScCVwAuBZ4FzI+LBSfr9MnAVcCKwJiK2p9prtnsDcHJEfHgWyn/ugPb3909rgBN37WL94CDFapXi2Nhz7dVCgWqxyKYNG9i9cuXBVzpPbNy4sd0lmNnsU70VnlFO7vPA+yLiZGAt8MxknSLiPyPiNGB7I+0166+ZpZA8aMtGRlg/OEipUtkvJAGKY2OUKhXWDw6ybGSkTRWambWWg3ICSacCz0bEzQAR8XBE/EDShZJ25stbD2L8z0l6UNLHJ7Q/LelySfdJuqKm/Z2S7pVUlnTJtO9Yg7qGhylWq8k+xWqVVVu3znYpZmZzwqJ2FzAHnQDs90acpOOBC4HTgMXADklfjohHmx08It4iqQc4fcKqw4EvAH8K7JG0PCIeBvqBYyPiKUlHTTX+wMBAsyXtp7NcPmAmOVFxbIzOcpnNa9ce1L7mi4N9TM1s7uvp6am7zjPKA012nvqlwE0R8XRE/BC4Beic4f2ORsRwRFSA+4Gj8/Zbgc/m4frsDO/zAKXR0RntZ2Y233lGeaBvA7/U5Db1rohq5kqpyoTtxl/EvBY4C3gT8A7g5alBal8VTedintFSiSUNhOBoqdT02PNV6pWmmS18nlFOEBF3AkdIOgtA0kuAB4GzJB0u6UjgFUC5ZrMfAMdMMly99oZIEnBcRNwIvB9YMd2xGlXu7KRaSD8tqoUC5c6ZnlCbmc1NDsrJ/SFwiaR7geuAx4DLgW8CNwP9E96fvDTvf6ek5fXaJR0v6U7gQ8Dv5+2vS9Qh4POSysBNwLtn6g7Ws3X1aqrFYrJPtVhkW1fXbJdiZjYn+HOUC8/BH9DNm2HdOqhUsmXc4sXZMjQE3d0HvRszsznEn6O0JnR3Q7kMvb37fzNPb2/W7pA0s0OIZ5QLjw+omVnzPKM0MzObDgelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpdlCtmcP9PVBRwcUCtnPvr6s3cwaoohodw3zhqSTgCuBFwLPAudGxIOS3gCcHBEfnqX9NjP+IXtA+/v7213CnHLirl2sHxykWK1SHBt7rr1aKFAtFtm0YQO7V65sY4U2123cuLHdJbSS6q3wjLI5nwfeFxEnA2uBZwAi4prZCslWjG8Lz7KREdYPDlKqVPYLSYDi2BilSoX1g4MsGxlpU4Vm84eDskGSTgWejYibASLi4Yj4gaTPSXpQ0scn9F8j6XpJQ5J2Srosbz9H0i2Sdki6tKb/OyXdK6ks6ZKa9knHN0vpGh6mWK0m+xSrVVZt3dqiiszmr0XtLmAeOQE44I2diHiLpB7g9Em2ORM4IyJ2SjpS0lHAB4A1EbFP0iZJr4qILUA/cGxEPJX3a2T8AwwMDDR7v2wB6iyXD5hJTlQcG6OzXGbz2rUtqsrmm0Pp70lPT0/ddZ5RNq7u+euE2yJiJ0BEPAGsIgvcYUl3Ai/NbwPcCnw2D8VnD7ZYO7SVRkdntJ/ZocwzysZ9G/ilJrf50SRt10XEeZO0vxY4C3gT8A7g5U3uC0i/KlrofDHPz4yWSixpIARHS6UWVGPz1aH896SWZ5QNiog7gSMknQUg6SWSXtjkMNuAsyUdk4+xQtLRkgQcFxE3Au8HVsxg6XYIKnd2Ui2k/3lXCwXKnZ0tqshs/vKMsjl/CFwh6QVABbhA0t8DLwB+Lg/Rv4yIr0y2cUQ8Kul84FpJi8iumj2P7LTu5yV1AEXg3QCSjgeubnR8s3FbV6/m1B07ku9TVotFtnV1tbAqs/nJn6NceHxALbN5M6xbB5VKtoxbvDhbhoagu7t99ZnNLf4cpdkhp7sbymXo7d3/m3l6e7N2h6RZQzyjXHh8QM3MmucZpZmZ2XQ4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjN5oo9e6CvDzo6oFDIfvb1Ze1m1jaKiHbXMC9IWgP8K3A/sAT4WER8qp011eEDOon+/v52l5B04q5drB8cpFitUhwbe669WihQLRbZtGEDu1eubGOF7bNx48Z2l2CHBtVb4Rllc26KiNOA3wT+WtLyNtdjC8CykRHWDw5SqlT2C0mA4tgYpUqF9YODLBsZaVOFZoc2B+U0RMRjwG7gFyRdK2mHpO2SLgCQ9EFJN0raLekTku6T9OJ83Tsl3SupLOmS8THrjHOOpP9Z06df0n9t7b212dY1PEyxWk32KVarrNq6tUUVmVmtRe0uYD6SdGz+axk4PyIekrQYuFvSUL7uGuA44EHgq0BX3tYPHBsRT0k6qmbYycbZDHxM0uER8QywAViTqm1gYGBG7qO1Tme5fMBMcqLi2Bid5TKb165tUVVzh5/T1go9PT111zkom3O2pLuBFcAbI+JZSW+TdC7Z+e3l+QIwAnTU/Hx+3n4r8FlJXwa+WDP2AeNExCOS/hX4XUm7gG9HxPdn+T5ai5VGR2e0n5nNLAdlc26KiNfngXalpD8CXgOcGRH7JG3nZ6ezY8JSzNtfC5wFvAl4B/Dy/EKheuP8I3AxsAv43FQFpl4VHcrm8sU8o6USSxoIwdFSqQXVzD1+Tlu7+T3KaYiIfwXuIpv5PZ6H2ynAqantJAk4LiJuBN5PNjOFbMY56TgRcSfw88A5ZKdubYEpd3ZSLaT/KVYLBcqdnS2qyMxqeUY5fX8DXAl8W9I9wLeA26fYRsDnJXWQzTDfnbd/FehNjPMvwC9HxI9nqnibO7auXs2pO3Yk36esFots6+pqYVVmNs6fo5wHJH0FuDQivtZAdx/Q+WjzZli3DiqVbBm3eHG2DA1Bd3f76jNb+Pw5yvlI0gsl3Qc8Bvx7u+uxWdTdDeUy9Pbu/808vb1Zu0PSrG08o1x4fEDNzJrnGaWZmdl0OCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozZq1Zw/09UFHBxQK2c++vqzdzBYcRUS7a2g5SZ8DOoGjgSrwGLAtIv6krYXNjHlzQPv7+9tdQtNO3LWL9YODFKtVimNjz7VXCwWqxSKbNmxg98qVbaxw4du4cWO7S7CFSfVWHJIzyoh4S0ScBnwK+GhEnLZAQtJm0bKREdYPDlKqVPYLSYDi2BilSoX1g4MsGxlpU4VmNhsOyaCsR9IaSddLGpK0U9Jlefu1knZI2i7pgpr+X5F0Z75UJT1/ivZzJN2Sj3XpdPdr7dE1PEyxWk32KVarrNq6tUUVmVkrLGp3AXPQmcAZEbFT0pF52/kR8ZCkxcDdkoYi4pGIeB2ApLcCr4qIHwFM1i7pKOADwJqI2Cdpk6RXRcSWZvebKn5gYGCmHgeboLNcPmAmOVFxbIzOcpnNa9e2qKpDj5/jNht6enrqrnNQHui2iNgJEBFP5G1vk3Qu2Tns5fnyCICkXwEuBM6uHWSS9lXACcCwJIAj8tvjQdnUfq31SqOjM9rPzOYHB+WBflR7Q9Ia4DXAmflMcDv5KWtJS4B/BP4oIp6u2WbSduC6iDjvYPebknpVNNfMt4t5RkslljQQgqOlUguqOXTNp+e4LQx+j3JqHcDjeVidApxas+7vgC9ExO0TtpmsfRtwtqRjACStkHT0NPdrbVDu7KRaSP+TqRYKlDs7W1SRmbWCg3JqXwUKku4BLgJqw68PeGvNhTvPq9ceEY8C5wPXSroLuAo4fJr7tTbYuno11WIx2adaLLKtq6tFFZlZKxySn6Nc4HxAZ9PmzbBuHVQq2TJu8eJsGRqC7u721Wdm0+XPUZrNiO5uKJeht3f/b+bp7c3aHZJmC45nlAuPD6iZWfM8ozQzM5sOB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelNWbPHujrg44OKBSyn319WbuZ2QKmiGh3DfOGpFXA/wCWAt8HfjciftTeqg5Q94D29/dPa8ATd+1i/eAgxWqV4tjYc+3VQoFqscimDRvYvXLltMZuhY0bN7a7BDOb+1RvhWeUDZJUAv4J6ImIk4E/Axa1t6rZt2xkhPWDg5Qqlf1CEqA4NkapUmH94CDLRkbaVKGZ2exyUDauGyhHRBkgIm6PiB9IOkfSLZJ2SLp0vLOkCyXtzJe31rSvkXS9pKF83WV5+59L+pakayTtkXR83j7p+K3SNTxMsVpN9ilWq6zaurVFFZmZtdaCnxHNoBOA/d6Qk3QU8AFgTUTsk7RJ0quAbwMXAqcBi4Edkr4cEY/mm54JnBEROyUdKek44O3AqcCxwD2p8SNiS70iBwYGZu4eA53l8gEzyYmKY2N0lstsXrt2Rvc9U2b6MTGzhaenp6fuOs8omxMAkv5G0h6yWeYJwLCkO4GX5rdfCtwUEU9HxA+BW4DOmnFui4idABHxBPDyvP8zEfEtYG/eb1Wd8VumNDo6o/3MzOYbzygbdz+wGiAi3i/p+cDzgesi4rzajpLeOMVYzVwAdMD4KalXRdO5mGe0VGJJAyE4Wio1PXarpB4TM7OpeEbZuM3AyyT9an67SHb169mSjgGQtELS0cAdwFmSDpd0JPAKoJwY+7a8/2GSfgVYkbdvqzN+y5Q7O6kW0k+TaqFAubMz2cfMbL7yjLJBEfGspB7gC5IEPA58BLgbuFbSIuAZ4LyI2CPpcuCb+eb9Ne9PTjb2g5I+A9xO9v7k/cCzEfGopPMnjj9Ld3FSW1ev5tQdO5LvU1aLRbZ1dbWwKjOz1vHnKOcISc+LiKckvYhshnl8TO/gzPwB3bwZ1q2DSiVbxi1enC1DQ9DdPeO7NTNrIX+Och74qKQysAW4cJohOTu6u6Fcht7e/b+Zp7c3a3dImtkC5hnlwuMDambWPM8ozczMpsNBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWnWrD17oK8POjqgUMh+9vVl7Wa24Cgi2l1DXZLOBj4NjAJvjoh78vY3ACdHxIdnaD87gddHxAMzXOek7dMY/13AZyJiXwPd5+4BnQP6+/sPavsTd+1i/eAgxWqV4tjYc+3VQoFqscimDRvYvXLlwZa5n40bN87oeGY2KdVbMddnlOcBF0fEabUhExHXzFRIzpBJ60y0N+tdwGEHU6AdvGUjI6wfHKRUqewXkgDFsTFKlQrrBwdZNjLSpgrNbDbMyaCUdKSkO4ENwEWS7pR0cr7uc5IelPTxmv4n5n0Ok7RU0u2STsrXnSPpFkk7JF1as817JN0raROwtIGaDhinXp1T1F+vnqMlXZO33ybpJEmvzsdZDtyQj7P8oB5cm7au4WGK1WqyT7FaZdXWrS2qyMxaYa6feh0AvhQRQxPae4DTI+KCmrYLgBPJTnN+NyI+Juko4EvAmojYl4fiJ4FvA9cDncAJwF3ACfVOvdYbJyK2TFHnfu2pcfLft0TEJyV1AEsj4tF8uwfy+/v4VI/ZwMDA3D2gc8DevXunve17L76YJaOjU/b7yZIlXPK+9017PxOtWLFixsYys8n19PTUPfW6qJWFzLJPAF8jmyX/Rd62iiwIhyUBHJHfPhK4OSJ+DNwtaaq/nvXG2dJkjalx1pCdqiUingSebHJsm2WlBkKymX5mNj8spKA8HHhh/vsRwFP579dFxHm1HSW9cRrjHzDONM3UOJPq6emZraEXhIO5mGe0VGpoRjlaKk17H5PxMTVrrzn5HuU0/R3wKeBy4GN52zbgbEnHAEhaIelo4HZgdf5+5snAVOe26o3TrNQ4NwBvzdsPl/Timu2eBF4wjf3ZDCp3dlItpP/JVAsFyp2dLarIzFphXs0oJR0PXE0WGj8n6SzgL8k+EnEC8CcREZLWSzo3Iv5V0vnAtZIWAc8A50XEHklXAncA9wD3p/YbEY9ONk6z9U8xzoXAZyT1ARXgzcBj+brLgasljQDrIuKRZvdtB2/r6tWcumPHAVe81qoWi2zr6mphVWY22+b0xTw2LT6gs2nzZli3DiqVbBm3eHG2DA1Bd3f76jOz6Zq3n6M0m1u6u6Fcht7e/b+Zp7c3a3dImi04nlEuPD6gZmbN84zSzMxsOhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclHbo2LMH+vqgowMKhexnX1/WbmZWhyKi3TXMOEk7gddHxAMt2t/ZwKeBUeDNEXFPqn0a478L+ExE7Gug+7w7oP39/bO+jxN37WL94CDFapXi2Nhz7dVCgWqxyKYNG9i9cuWs1zEdGzdubHcJZocC1VvhGeXMOA+4OCJOmxCG9dqb9S7gsIMp8FC2bGSE9YODlCqV/UISoDg2RqlSYf3gIMtGRtpUoZnNZW0PSklrJF0vaUjSTkmX5e3XStohabukC2r6Py3pckn3Sbqipv09ku6VtAlYWtN+YT7uTklvzds+KOlGSbslfSIf68VT1HmOpFvymi7N246UdCewAbhI0p2STq7XXm+cvP1oSdfk7bdJOknSq/NxlgM35OMsP6gH/BDUNTxMsVpN9ilWq6zaurVFFZnZfNL2U6+S1gBfAc6IiJ2SjoyIJyQdExEPSVoM3A38ZkQ8IimAM4FbgT3AKqAEXA90AicAd+U/Ab4GnAYsBnYApwN9wFPAccCDwArgaxFxTZ0ajwK+BKyJiH15GH8yIrbk6weAL0XE0ITt9mtPjZP/viUiPimpA1gaEY/m2z0AnB4Rj0/1eA4MDMy7U6979+6d1fHfe/HFLBkdnbLfT5Ys4ZL3vW9Wa5mOFStWtLsEswWvp6en7qnXRa0sJOG2iNgJEBFP5G1vk3Qu2Xnj5fnyCDAaEcMAku4HjgaOB26OiB8Dd0sa/8v7UuCmiHg6738LWZgCjAAdNT+fn6hvFVnwDksCOCK/vaXJ+5kaZw3ZqVoi4kngySbHtjpKDYRkM/3M7NAyV4LyR7U38lnma4Az85nXdn52mrhS0zXy9unMomLCUpyi/3URcd409jNb40yqp6dntoaeNbN9Mc9oqdTQjHK0VJrVOqZrPh5Ts4Wk7e9R1tEBPJ6H5CnAqVP0vx1YLWlp/l7g+LmqO4CzJB0u6UjgFUB5GvVsA86WdAyApBWSjp7hcW4Axt9DPXzCe6ZPAi+Yxv4MKHd2Ui2kn+rVQoFyZ2eyj5kdmuZqUH4VKEi6B7iILAjrioi9wJVkwXgRcH/e/gBwOfBN4Gagf/x9v2bk25wPXCvpLuAq4PAZHudCYK2kHcCNwLKaTS8HrpZ08zQD+pC2dfVqqsX0CYNqsci2rq4WVWRm80nbL+axGecDOpnNm2HdOqhUsmXc4sXZMjQE3d3tq8/M2s2fo7RDXHc3lMvQ27v/N/P09mbtDkkzq8MzyoXHB9TMrHmeUZqZmU2Hg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgkOSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSrFl79kBfH3R0QKGQ/ezry9rNbMFRREx/Y+ls4NPAKPDmiLgnb38DcHJEfHhGipR2Aq+PiAdmuM5J26cx/ruAz0TEvmlu/8vAVcCJwJqI2D6dcXLTP6DzXH9//6zv48Rdu1g/OEixWqU4NvZce7VQoFossmnDBnavXDnrdTRi48aN7S7BbD5RvRUHO6M8D7g4Ik6rDZmIuGamQnKGTFpnor1Z7wIOm+7GEfGfEXEacDABabNs2cgI6wcHKVUq+4UkQHFsjFKlwvrBQZaNjLSpQjObDdMKSklHSroT2ABcJOlOSSfn6z4n6UFJH6/pf2Le5zBJSyXdLumkfN05km6RtEPSpTXbvEfSvZI2AUsbqOmAcerVOUX99eo5WtI1efttkk6S9Op8nOXADfk4yxM17pG0qOZ2QdLuKe7XO/PHoSzpkqkeB5s9XcPDFKvVZJ9itcqqrVtbVJGZtcKiqbscKCKeAE6TNAB8KSKGata9RVIPcHpN225J/wBcTHaa8x8j4j5JRwEfIDvduE/SJkmvAr4N/DHQCZwA3JWqp944EbGlXp2TtU8xzuXA5oj4pKQOYGlE3JeP8wDwyoh4fIqHbgdwiqTHyKb5zwPunWKbfuDYiHgqry9pYGBgqi42TZ3l8gEzyYmKY2N0lstsXru2RVXV5+eCWeN6enrqrptWUE7TJ4Cvkc1i/yJvW0UWhMOSAI7Ibx8J3BwRPwbulrR3irHrjbOlyRpT46whO1VLRDwJPNnk2ADfBF4G/DrZ43BLvqTcCnxW0peBL05jnzZDSqOjM9rPzOaHVgbl4cAL89+PAJ7Kf78uIs6r7SjpjdMY/4BxpmmmxpnMLcDvkb2fGcDLgX+rWT/ZhTivBc4C3gS8I9+mrtSrooVuti/mGS2VWNJACI6WSrNaR6MO5eeC2Uxq5cdD/g74FNkpzI/lbduAsyUdAyBphaSjgduB1fn7mScDK6YYu944zUqNcwPw1rz9cEkvrtnuSeAFDYy/HXgl8H3gIaCb/WeUPwCOGb+hbFp7XETcCLyfqR8Hm0Xlzk6qhfQ/mWqhQLmzs0UVmVkrzGhQSjo+v7jlQ8Dv5xe3vE5SN9kpzE9HxJXAcknnRsSjwPnAtZLuIvuIxOERsRe4ErgDuAi4P7XfeuM0W/8U41wIrJW0A7gRWFaz6eXA1ZJuTgV0RDwFjJGdyv13YHFE/LCmy6XAJTUXBQn4vKQycBPw7mbvk82cratXUy0Wk32qxSLburpaVJGZtcJBfY7S5iQf0Nm0eTOsWweVSraMW7w4W4aGoLu7ffWZ2XTN2ucozQ4t3d1QLkNv7/7fzNPbm7U7JM0WHM8oFx4fUDOz5nlGaWZmNh0OSjMzswQHpZmZWYKD0szMLMFBaWZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDko7dOzZA3190NEBhUL2s68vazczq0MR0fqdSjuB10fEAy3a39nAp4FR4M0RcU+qfRrjvwv4TETsm+b2vwxcBZwIrImI7dMZJ9f6A3qQ+vv7Z30fJ+7axfrBQYrVKsWxsefaq4UC1WKRTRs2sHvlylmvYzo2btzY7hLMDgWqt+JQmVGeB1wcEadNCMN67c16F3DYdDeOiP+MiNOAgwlIq2PZyAjrBwcpVSr7hSRAcWyMUqXC+sFBlo2MtKlCM5vLpgxKSWskXS9pSNJOSZfl7ddK2iFpu6QLavo/LelySfdJuqKm/T2S7pW0CVha035hPu5OSW/N2z4o6UZJuyV9Ih/rxVPUeY6kW/KaLs3bjpR0J7ABuEjSnZJOrtdeb5y8/WhJ1+Ttt0k6SdKr83GWAzfk4yxP1LhH0qKa2wVJu6e4X+/MH7eypEtSfW1yXcPDFKvVZJ9itcqqrVtbVJGZzSeLpu4CwJnAGRGxU9KRedv5EfGQpMXA3ZKGIuIR4HDgC8CfAnvy4CgBfwx0AicAdwFIOh64EDgNWAzskPTlfPxrgOOAB4GvAl152wEkHQV8gOy05T5JmyS9KiK2AKdJGgC+FBFDNZsd0D7FOJcDmyPik5I6gKURcV8+zgPAKyPi8Skexx3AKZIeI5vmPw+4d4pt+oFjI+KpvL6kgYGBqboccjrL5QNmkhMVx8boLJfZvHZti6pqnI+p2ezr6empu67RoLwtInYCRMQTedvbJJ1L9gd/eb48AoxGxDCApPuBo4HjgZsj4sdkobo3H+OlwE0R8XTe/xayMAUYATpqfj4/Ud8qsgAelgRwRH57S4P3r5Fx1pCdqiUingSebHJsgG8CLwN+nWw2f0u+pNwKfDZ/AfHFaezzkFcaHZ3RfmZ2aGk0KH9Ue0PSGuA1wJn5zGs7PzuNW6npGnn7dC4wiQlLcYr+10XEedPYz2yNM5lbgN8jez8zgJcD/1azfrLH6bXAWcCbgHfk29SVelU0V832xTyjpRJLGgjB0VJpVuuYrvl4TM0WkulezNMBPJ6H5CnAqVP0vx1YLWlp/l7girz9DuAsSYfnp3RfAZSnUc824GxJxwBIWiHp6Bke5wZg/D3Uwye8Z/ok8IIGxt8OvBL4PvAQ0M3+M8ofAMeM31A2rT0uIm4E3s/PHjdrQrmzk2oh/VSvFgqUOzuTfczs0DTdoPwqUJB0D3ARWRDWFRF7gSvJgvEi4P68/QGy9/6+CdwM9EfEo80Wk29zPnCtpLvIPmpx+AyPcyGwVtIO4EZgWc2mlwNXS7o5FdAR8RQwRnYq99+BxRHxw5oulwKX1FwUJODzksrATcC7m71PBltXr6ZaTJ+QqBaLbOvqalFFZjaftOVzlDarfEAns3kzrFsHlUq2jFu8OFuGhqC7u331mVm7HfKfo7RDXXc3lMvQ27v/N/P09mbtDkkzq8MzyoXHB9TMrHmeUZqZmU2Hg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgmNfim6zR91PwtkZmbN84zSzMwswUFpZmaW4KA0MzNLcFCamZklOCjNzMwSHJRmZmYJDkozM7MEB6WZmVmCg9LMzCzBQWlmZpbgoDQzM0twUJqZmSU4KM3MzBIclGZmZgn+b7YWGElfBV6U33wR8Hgby6nHdTXHdTXHdTXHdWUej4jXTrZCEdHCOqyVJG2PiNPbXcdErqs5rqs5rqs5rmtqPvVqZmaW4KA0MzNLcFAubJ9pdwF1uK7muK7muK7muK4p+D1KMzOzBM8ozczMEhyU85yk10r6T0m7Jb13kvVLJF2Vr/+mpOPnSF1/KukeSWVJ/y5pxVyoq6bf70kKSS256q6RuiRtyB+zuyX9r1bU1Uhtko6TdIOkO/Lj+boW1PRZSY9K2llnvST9fV5zWdLLZrumBus6L6/nLknDkk6dC3XV9HuFpJ9KWjdX6pK0RtKd+fP+xlbUdYCI8DJPF6AI7AFOAErADuDkCX36gE/lv78JuGqO1PVK4LD89/PnSl15v+cB3wC2AafPhbqAlcAdwLL89lFz6Dn2GeD8/PeTgQdaUNdvAi8DdtZZ/zpgMyBgFfDNFj1eU9W1uuYYds+VumqO9RbgK8C6uVAXcCRwD3Bcfrslz/uJi2eU89sZwO6I+HZEjAL/DJw7oc+5wD/mvw8Bvy1J7a4rIm6IiH35zW3AMbNcU0N15S4CLgF+0oKaGq3rj4FPRMQPASLi0TlUWwAd+e/PBx6e7aIi4hvASKLLucDnIrMNOFLSS9pdV0QMjx9DWve8b+TxAngH8L+BVj23GqnrzcC/RMSDef+W1VbLQTm//QLwnZrbD+Vtk/aJiJ8CPwJeOAfqqvVHZK/+Z9uUdeWn6I6NiC+3oJ6G6wJOAk6S9B+Stkma9BtE2lTbB4E/lPQQ2WzkHa0pLanZ52A7tOp5PyVJvwC8Efhku2uZ4CRgmaSvS7pN0lvaUYS/ws7aStIfAqcDvzUHaikAlwI9bS5lMovITr+uIZuFfEPSr0fEE+0sKvcHwEBE/J2kLuDzkn4tIsbaXdhcJemVZEF5VrtryV0G/EVEjM3+CaemLAJeDvw28HPAVknbIuK+Vhdh89d3gWNrbh+Tt03W5yFJi8hOjf1gDtSFpFcD7wd+KyKeneWaGqnrecCvAV/P/1gcDVwj6Q0Rsb2NdUE2I/pmRFSA+yXdRxact85iXY3W9kfAawEiYqukpWTf09mW02S5hp6D7SCpE/gHoDsiZvvfYqNOB/45f96/CHidpJ9GxNVtrSp73v8gIp4BnpH0DeBUoKVB6VOv89utwEpJvyipRHaxzjUT+lwD/Jf893XAlsjfFW9nXZJeCnwaeEML33dI1hURP4qIF0XE8RFxPNl7SLMdklPWlbuabDaJpBeRnZL69izX1WhtD5K94kfSrwJLgcdaUFvKNcBb8qtfVwE/iojvtbkmJB0H/Avwf7V6VpQSEb9Y87wfAvrmQEgC/CtwlqRFkg4DfgO4t9VFeEY5j0XETyVdAFxHdsXaZyPibkkfArZHxDXAlWSnwnaTvWn+pjlS198CRwCb8lexD0bEG+ZAXS3XYF3XAa+RdA9QBf68FbORBmv7M+AKSf+V7MKentl+MSbpC2QvHF6Uvze6EVic1/wpsvdKXwfsBvYBb53Nepqo66/IrhH4H/nz/qfRgi/+bqCutpiqroi4V9n/iFQGxoB/iIjkR1xmpc7Zn1yYmZnNXz71amZmluCgNDMzS3BQmpmZJTgozczMEhyUZmZmCQ5KMzOzBAelmZlZgoPSzMws4f8Hvg3ah8vg1hsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_catheter = combine_effects(\n",
    "     *effectsize_2proportions(*df_catheter.values.T, statistic=\"or\"),\n",
    "     use_t=False,\n",
    "     row_names=df_catheter.index,\n",
    ")\n",
    "\n",
    "print(round(res_catheter.summary_frame().apply(np.exp), 2))\n",
    "\n",
    "fig = res_catheter.plot_forest(use_exp=True)\n",
    "fig.set_figheight(8)\n",
    "plt.gca().set_title('Forest plot - Catheter dataset')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.base.HolderTuple'>\n",
       "statistic = 24.90220481352818\n",
       "pvalue = 0.005533987983273774\n",
       "df = 10\n",
       "distr = 'chi2'\n",
       "tuple = (24.90220481352818, 0.005533987983273774)"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_catheter.test_homogeneity()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  8., 129.],\n",
       "       [ 32., 113.]])"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we need to create a 2 x 2 x k contingency table to be used with StratifiedTable.\n",
    "t, nt, c, nc = df_catheter.values.T\n",
    "counts = np.column_stack([t, nt - t, c, nc - c])\n",
    "ctables = counts.T.reshape(2, 2, -1)\n",
    "ctables[:, :, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  8., 129.,  32., 113.])"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  8., 137.,  32., 145.])"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_catheter.values.T.T[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0102672315383547, -0.6084890097914877)"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.api as smstats\n",
    "\n",
    "st = smstats.StratifiedTable(ctables.astype(np.float64))\n",
    "\n",
    "st.logodds_pooled_confint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue      0.00266808399022056\n",
      "statistic   26.93358948598208\n"
     ]
    }
   ],
   "source": [
    "print(st.test_equal_odds())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue      1.2212453270876722e-15\n",
      "statistic   64.11077206665642\n"
     ]
    }
   ],
   "source": [
    "# MHtest\n",
    "print(st.test_null_odds())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   Estimate   LCB    UCB  \n",
      "------------------------------------------\n",
      "Pooled odds           0.445   0.364  0.544\n",
      "Pooled log odds      -0.809  -1.010 -0.608\n",
      "Pooled risk ratio     0.560               \n",
      "                                          \n",
      "                 Statistic P-value \n",
      "-----------------------------------\n",
      "Test of OR=1        64.111   0.000 \n",
      "Test constant OR    26.934   0.003 \n",
      "                       \n",
      "-----------------------\n",
      "Number of tables   11  \n",
      "Min n              54  \n",
      "Max n             403  \n",
      "Avg n             235  \n",
      "Total n          2585  \n",
      "-----------------------\n"
     ]
    }
   ],
   "source": [
    "print(st.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               eff  ci_low  ci_upp\n",
      "fixed effect  0.47    0.38    0.58\n"
     ]
    }
   ],
   "source": [
    "print(round(res_catheter.summary_frame().apply(np.exp).iloc[-4:-3][['eff', 'ci_low', 'ci_upp']], 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are not totally identical between the _Woolf and inverse variance_ (previous section), that can be used to estimate the pooled odds ratio with fixed effects, and the _Mantel-Haenszel_ method, which is generally the _most robust_ (see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5287121/).\n",
    "\n",
    "A confidence interval for the Mantel-Haenszel odds ratio in StatsDirect is calculated using the Robins, Breslow and Greenland variance formula (Robins et al., 1986) or by the method of Sato (1990) if the estimate of the odds ratio can not be determined. A chi-square test statistic is given with its associated probability that the pooled odds ratio is equal to one.\n",
    "\n",
    "There are at least two other ways to do a fixed effects meta-analysis of binary data. _Peto's method_ is a computationally simpler approximation to the Mantel-Haenszel approach. It is also possible to weight the individual odds ratios according to their estimated variances. The Mantel-Haenszel method is superior if there are trials with small numbers of events (less than 5 or so in either group)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funnel plots\n",
    "\n",
    "A [funnel plot](https://psmu.improvement.nhs.uk/psc-shared-library/measurement-evidence-base/16-funnel-plots-for-comparing-institutional-performance/file) is a scatterplot of treatment effect against a measure of study precision. It is used primarily as a visual aid for detecting bias or systematic heterogeneity. A symmetric inverted funnel shape arises from a 'well-behaved' data set, in which publication bias is unlikely. An asymmetric funnel indicates a relationship between treatment effect estimate and study precision. This suggests the possibility of either publication bias or a systematic difference between studies of higher and lower precision (typically 'small study effects'). Asymmetry can also arise from use of an inappropriate effect measure. Whatever the cause, an asymmetric funnel plot leads to doubts over the appropriateness of a simple meta-analysis and suggests that there needs to be investigation of possible causes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distcod</th>\n",
       "      <th>county</th>\n",
       "      <th>district</th>\n",
       "      <th>grspan</th>\n",
       "      <th>enrltot</th>\n",
       "      <th>teachers</th>\n",
       "      <th>calwpct</th>\n",
       "      <th>mealpct</th>\n",
       "      <th>computer</th>\n",
       "      <th>testscr</th>\n",
       "      <th>compstu</th>\n",
       "      <th>expnstu</th>\n",
       "      <th>str</th>\n",
       "      <th>avginc</th>\n",
       "      <th>elpct</th>\n",
       "      <th>readscr</th>\n",
       "      <th>mathscr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>75119</td>\n",
       "      <td>Alameda</td>\n",
       "      <td>Sunol Glen Unified</td>\n",
       "      <td>KK-08</td>\n",
       "      <td>195</td>\n",
       "      <td>10.900000</td>\n",
       "      <td>0.510200</td>\n",
       "      <td>2.040800</td>\n",
       "      <td>67</td>\n",
       "      <td>690.799988</td>\n",
       "      <td>0.343590</td>\n",
       "      <td>6384.911133</td>\n",
       "      <td>17.889910</td>\n",
       "      <td>22.690001</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>691.599976</td>\n",
       "      <td>690.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>61499</td>\n",
       "      <td>Butte</td>\n",
       "      <td>Manzanita Elementary</td>\n",
       "      <td>KK-08</td>\n",
       "      <td>240</td>\n",
       "      <td>11.150000</td>\n",
       "      <td>15.416700</td>\n",
       "      <td>47.916698</td>\n",
       "      <td>101</td>\n",
       "      <td>661.200012</td>\n",
       "      <td>0.420833</td>\n",
       "      <td>5099.380859</td>\n",
       "      <td>21.524664</td>\n",
       "      <td>9.824000</td>\n",
       "      <td>4.583333</td>\n",
       "      <td>660.500000</td>\n",
       "      <td>661.900024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>61549</td>\n",
       "      <td>Butte</td>\n",
       "      <td>Thermalito Union Elementary</td>\n",
       "      <td>KK-08</td>\n",
       "      <td>1550</td>\n",
       "      <td>82.900002</td>\n",
       "      <td>55.032299</td>\n",
       "      <td>76.322601</td>\n",
       "      <td>169</td>\n",
       "      <td>643.599976</td>\n",
       "      <td>0.109032</td>\n",
       "      <td>5501.954590</td>\n",
       "      <td>18.697226</td>\n",
       "      <td>8.978000</td>\n",
       "      <td>30.000002</td>\n",
       "      <td>636.299988</td>\n",
       "      <td>650.900024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>61457</td>\n",
       "      <td>Butte</td>\n",
       "      <td>Golden Feather Union Elementary</td>\n",
       "      <td>KK-08</td>\n",
       "      <td>243</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>36.475399</td>\n",
       "      <td>77.049202</td>\n",
       "      <td>85</td>\n",
       "      <td>647.700012</td>\n",
       "      <td>0.349794</td>\n",
       "      <td>7101.831055</td>\n",
       "      <td>17.357143</td>\n",
       "      <td>8.978000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>651.900024</td>\n",
       "      <td>643.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>61523</td>\n",
       "      <td>Butte</td>\n",
       "      <td>Palermo Union Elementary</td>\n",
       "      <td>KK-08</td>\n",
       "      <td>1335</td>\n",
       "      <td>71.500000</td>\n",
       "      <td>33.108601</td>\n",
       "      <td>78.427002</td>\n",
       "      <td>171</td>\n",
       "      <td>640.849976</td>\n",
       "      <td>0.128090</td>\n",
       "      <td>5235.987793</td>\n",
       "      <td>18.671329</td>\n",
       "      <td>9.080333</td>\n",
       "      <td>13.857677</td>\n",
       "      <td>641.799988</td>\n",
       "      <td>639.900024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   distcod   county                         district grspan  enrltot  \\\n",
       "1    75119  Alameda               Sunol Glen Unified  KK-08      195   \n",
       "2    61499    Butte             Manzanita Elementary  KK-08      240   \n",
       "3    61549    Butte      Thermalito Union Elementary  KK-08     1550   \n",
       "4    61457    Butte  Golden Feather Union Elementary  KK-08      243   \n",
       "5    61523    Butte         Palermo Union Elementary  KK-08     1335   \n",
       "\n",
       "    teachers    calwpct    mealpct  computer     testscr   compstu  \\\n",
       "1  10.900000   0.510200   2.040800        67  690.799988  0.343590   \n",
       "2  11.150000  15.416700  47.916698       101  661.200012  0.420833   \n",
       "3  82.900002  55.032299  76.322601       169  643.599976  0.109032   \n",
       "4  14.000000  36.475399  77.049202        85  647.700012  0.349794   \n",
       "5  71.500000  33.108601  78.427002       171  640.849976  0.128090   \n",
       "\n",
       "       expnstu        str     avginc      elpct     readscr     mathscr  \n",
       "1  6384.911133  17.889910  22.690001   0.000000  691.599976  690.000000  \n",
       "2  5099.380859  21.524664   9.824000   4.583333  660.500000  661.900024  \n",
       "3  5501.954590  18.697226   8.978000  30.000002  636.299988  650.900024  \n",
       "4  7101.831055  17.357143   8.978000   0.000000  651.900024  643.500000  \n",
       "5  5235.987793  18.671329   9.080333  13.857677  641.799988  639.900024  "
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from funnelplot.core import funnel\n",
    "from pydataset import data\n",
    "\n",
    "dataset=data('Caschool')\n",
    "dataset.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: invalid value encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n",
      "C:\\Users\\Sébastien\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\funnelplot\\core.py:14: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return band / np.sqrt(group_size)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "funnel(df=data(\"Caschool\"), x=\"testscr\", group=\"county\", error_mode=\"data\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However options are missing in Python to plot comprehensive visualizations of forest plots, subgroups and funnel plots, compared to R."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation in R using rmeta and meta packages\n",
    "\n",
    "```r\n",
    "library('rmeta') # for meta.MH and meta.DSL; see https://www.rdocumentation.org/packages/rmeta/versions/3.0\n",
    "library('meta') # for metabin\n",
    "\n",
    "# preparing the data\n",
    "data_yepes <- list(\n",
    "    EUCTR2005 = c(21,  76, 25, 76),\n",
    "    Glover = c(6,  13,  5, 11),\n",
    "    Kaufman = c(9,  16,  3, 10),\n",
    "    Leroy = c(5,  11,  3, 10),\n",
    "    Novak = c(64, 107,  9, 55),\n",
    "    Sanchez = c(5,  31,  2, 29),\n",
    "    Silny = c(5,  10,  1, 10),\n",
    "    Wen = c(23, 38,  6, 18),\n",
    "    Werfel = c(19, 53,  5, 26)\n",
    ")\n",
    "\n",
    "df <- t(as.data.frame(data_yepes))\n",
    "colnames(df) <- c(\"count_ait\", \"nobs_ait\", \"count_control\", \"nobs_control\")\n",
    "\n",
    "df = data.frame(name=row.names(df), df, row.names = NULL)\n",
    "\n",
    "# MH analysis\n",
    "a <- meta.MH( # Fixed effects (Mantel-Haenszel) meta-analysis\n",
    "    ntrt = nobs_ait,\n",
    "    nctrl = nobs_control,\n",
    "    ptrt = count_ait,\n",
    "    pctrl = count_control,\n",
    "    names = name,\n",
    "    data = df,\n",
    "    conf.level = .95,\n",
    "    statistic = 'RR')\n",
    "\n",
    "summary(a)\n",
    "print(a)\n",
    "plot(a, colors=meta.colors(NULL))\n",
    "\n",
    "# same as above with some customization\n",
    "metaplot(\n",
    "    a$logRR,\n",
    "    a$selogRR,\n",
    "    nn=a$selogRR^-2,\n",
    "    a$names,\n",
    "    xlab=\"Relative Rate\",\n",
    "    summn=a$logMH,\n",
    "    sumse=a$selogMH,\n",
    "    sumnn=a$selogMH^-2,\n",
    "    logeffect=TRUE,\n",
    "    colors=meta.colors(\n",
    "        box=\"black\",\n",
    "        lines=\"royalblue\",\n",
    "        zero=\"darkred\",\n",
    "        summary=\"orangered\",\n",
    "        text=\"forestgreen\")\n",
    ")\n",
    "\n",
    "# forest plot together with a table of text\n",
    "tabletext<-cbind(\n",
    "    c(\"\", \"Study\", a$names, NA, \"Summary\"),\n",
    "    c(\"Decreased severity\", \"(AIT)\", df$count_ait, NA, NA),\n",
    "    c(\"Decreased severity\", \"(control)\", df$count_control, NA, NA),\n",
    "    c(\"\", \"AR\", format(exp(a$logRR), digits=2), NA, format(exp(a$logMH), digits=2))\n",
    ")\n",
    "\n",
    "m<-     c(NA, NA, a$logRR, NA, a$logMH)\n",
    "l<- m - c(NA, NA, a$selogRR, NA, a$selogMH)*2\n",
    "u<- m + c(NA, NA, a$selogRR, NA, a$selogMH)*2\n",
    "\n",
    "forestplot(\n",
    "    tabletext,\n",
    "    m, l, u,\n",
    "    is.summary=c(TRUE, TRUE, rep(FALSE, 9), TRUE),\n",
    "    xlog=TRUE,\n",
    "    zero = 0,\n",
    "    xticks = c(0.1, 0.5, 1, 2, 5, 10),\n",
    "    clip = c(-Inf, 10),\n",
    "    boxsize=0.75,\n",
    "    col = meta.colors(\n",
    "        box=\"black\",\n",
    "        line=\"darkblue\",\n",
    "        summary=\"royalblue\"\n",
    "    )\n",
    ")\n",
    "\n",
    "# funnel plot\n",
    "funnelplot(\n",
    "    a$logRR,\n",
    "    a$selogRR,\n",
    "    plot.conf = FALSE,\n",
    "    summ=a$logMH,\n",
    "    mirror = FALSE\n",
    ")\n",
    "\n",
    "# DerSimonian-Laird analysis\n",
    "meta.DSL( # Fixed effects (Mantel-Haenszel) meta-analysis\n",
    "    ntrt = nobs_ait,\n",
    "    nctrl = nobs_control,\n",
    "    ptrt = count_ait,\n",
    "    pctrl = count_control,\n",
    "    names = name,\n",
    "    data=df,\n",
    "    conf.level = .95,\n",
    "    statistic = 'RR')\n",
    "\n",
    "\n",
    "# using the meta package\n",
    "mb <- metabin(\n",
    "    event.e = count_ait, # Number of events in experimental group\n",
    "    n.e = nobs_ait,   # Number of observations in experimental group\n",
    "    event.c = count_control,# Number of events in control group\n",
    "    n.c = nobs_control,  # Number of observations in control group\n",
    "    data=df,\n",
    "    studlab = df$name,\n",
    "    sm=\"RR\", # summary measure\n",
    "    method=\"MH\", # use 'Inverse' for inverse variance method\n",
    "    backtransf=TRUE)\n",
    "\n",
    "print(summary(mb))\n",
    "\n",
    "forest(\n",
    "    mb,\n",
    "    comb.random = FALSE,\n",
    "    hetstats = FALSE,\n",
    "    text.fixed = \"MH estimate\"\n",
    ")\n",
    "\n",
    "funnel(\n",
    "    mb,\n",
    "    pch=16,\n",
    "    contour = c(0.9, 0.95, 0.99),\n",
    "    col.contour = c(\"darkgray\", \"gray\", \"lightgray\")\n",
    ")\n",
    "\n",
    "legend(\n",
    "    x = .35, y=.9,\n",
    "    c(\"0.1 > p > 0.05\", \"0.05 > p > 0.01\", \"< 0.01\"),\n",
    "    fill=c(\"darkgray\", \"gray\",\"lightgray\"),\n",
    "    bty=\"n\"\n",
    ")\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6 (tags/v3.10.6:9c7b4bd, Aug  1 2022, 21:53:49) [MSC v.1932 64 bit (AMD64)]"
  },
  "vscode": {
   "interpreter": {
    "hash": "7a8885463334bb42cd7c3bcf20e1ded52aa84aae23a765b2062c0c7846a4299a"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}