From 433262a16364902dc7d76e62f4035d5f076c9730 Mon Sep 17 00:00:00 2001
From: Hu Ziang <hza2002@foxmail.com>
Date: Mon, 28 Oct 2024 04:39:11 +0800
Subject: [PATCH] Add posts breast-cancer-prediction

---
 .../breast-cancer-prediction/feature.jpg      | Bin 0 -> 81423 bytes
 .../breast-cancer-prediction/index.en.md      | 630 ++++++++++++++++++
 .../breast-cancer-prediction/index.zh-cn.md   | 618 +++++++++++++++++
 .../posts/breast-cancer-prediction/plot1.svg  |   1 +
 .../posts/breast-cancer-prediction/plot10.svg |   1 +
 .../posts/breast-cancer-prediction/plot11.svg |   1 +
 .../posts/breast-cancer-prediction/plot2.svg  |   9 +
 .../posts/breast-cancer-prediction/plot3.svg  |   9 +
 .../posts/breast-cancer-prediction/plot4.svg  |   9 +
 .../posts/breast-cancer-prediction/plot5.svg  |   9 +
 .../posts/breast-cancer-prediction/plot6.svg  |   9 +
 .../posts/breast-cancer-prediction/plot7.svg  |   9 +
 .../posts/breast-cancer-prediction/plot8.svg  |   1 +
 .../posts/breast-cancer-prediction/plot9.svg  |   1 +
 14 files changed, 1307 insertions(+)
 create mode 100644 content/posts/breast-cancer-prediction/feature.jpg
 create mode 100644 content/posts/breast-cancer-prediction/index.en.md
 create mode 100644 content/posts/breast-cancer-prediction/index.zh-cn.md
 create mode 100644 content/posts/breast-cancer-prediction/plot1.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot10.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot11.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot2.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot3.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot4.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot5.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot6.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot7.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot8.svg
 create mode 100644 content/posts/breast-cancer-prediction/plot9.svg

diff --git a/content/posts/breast-cancer-prediction/feature.jpg b/content/posts/breast-cancer-prediction/feature.jpg
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+---
+title: "Breast Cancer Prediction"
+date: 2022-06-22T01:23:48+08:00
+tags: ["Data Analysis", "R Language"]
+series: ["Data Analysis in R"]
+series_order: 4
+---
+
+> Data source: [Breast Cancer Prediction Dataset](https://www.kaggle.com/datasets/merishnasuwal/breast-cancer-prediction-dataset)
+
+## Introduction
+
+Worldwide, breast cancer is the most common type of cancer in women and the second highest in terms of mortality rates.Diagnosis of breast cancer is performed when an abnormal lump is found (from self-examination or x-ray) or a tiny speck of calcium is seen (on an x-ray). After a suspicious lump is found, the doctor will conduct a diagnosis to determine whether it is cancerous and, if so, whether it has spread to other parts of the body. 
+
+This breast cancer dataset was obtained from the University of Wisconsin Hospitals, Madison from Dr. William H. Wolberg.
+
+## Import
+
+The first step is import the raw data to the program code.
+
+```R
+data <- read.csv("Breast_cancer_data.csv")
+```
+
+Thanks to the selected raw data containing the header and the built-in function(`read.csv`) of importing *CSV files* in the R language, we only need a simple line of code to efficiently import files into our program for subsequent processing.
+
+Using the `head` function, we briefly view part of the data.
+
+```R
+head(data)
+```
+
+```text
+#   mean_radius mean_texture mean_perimeter mean_area mean_smoothness diagnosis
+# 1       17.99        10.38         122.80    1001.0         0.11840         0
+# 2       20.57        17.77         132.90    1326.0         0.08474         0
+# 3       19.69        21.25         130.00    1203.0         0.10960         0
+# 4       11.42        20.38          77.58     386.1         0.14250         0
+# 5       20.29        14.34         135.10    1297.0         0.10030         0
+# 6       12.45        15.70          82.57     477.1         0.12780         0
+```
+
+Obviously, each piece of data in the dataset contains 5 data related to breast cancer, and 0 and 1 are used in the last column to indicate whether the diagnosis is confirmed.
+
+## Tidy
+
+Generally speaking, in order to analyze the data, we need to **clean the data** to a certain extent, separate and merge some cell data, discard some unwanted data, and amplify important data, so as to make the data more **compact** for us to modeling and analyze.
+
+We expect to use data to build models. For this data set, every piece of information has its utilization value, so in order to ensure that the amount of data is sufficient, we do not need to process it too much.
+
+### Check for missing data
+
+We need to judge whether there is any data missing data in the data set to avoid unforeseen errors when building the model.
+
+```R
+sum(is.na(data))
+```
+
+Fortunately, there is no data missing in our dataset, and each piece of data is complete and full of utilization value.
+
+### View redundant data
+
+First of all, we need to ensure that the data in the dataset is not duplicated to prevent interference with subsequent modeling.
+
+```R
+duplicated_count <- sum(duplicated(data))
+```
+
+Output 0, no duplicate data.
+
+## Analyze data
+
+Our goal is to establish a reasonable prediction model to achieve accurate prediction of breast cancer diagnosis through certain quantifiable data.
+
+### Analyze the distribution of variables
+
+In order to have a basic understanding of the distribution of parameters, we will map the distribution of each variable separately.
+
+In this case, the combination of histogram and density distribution map is the most intuitive and effective.
+
+Since the longitudinal axis of  `geom_density()` is density estimation, in order to be able to draw the histogram and the density estimation in the same coordinate system, it is necessary to change the longitudinal axis of the histogram to density estimation.
+
+```R
+rel_area <- ggplot(data, aes(x = mean_area, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_radius <- ggplot(data, aes(x = mean_radius, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_texture <- ggplot(data, aes(x = mean_texture, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_smooth <- ggplot(data, aes(x = mean_smoothness, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_perimeter <- ggplot(data, aes(x = mean_perimeter, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+```
+
+Finally, we use the `grid.arrange` function in the `gridExtra` library to arrange the charts together.
+
+```R
+grid.arrange(rel_area, rel_radius, rel_texture, rel_smooth, rel_perimeter,
+  nrow = 3,
+  ncol = 2
+)
+```
+
+![](plot1.svg)
+
+We note that the distribution of all data has two properties:
+
+1. All data is continuously distributed in a certain interval.
+2. Each data is distributed in large quantities near a value, and the farther away it is, the less distributed it will be.
+
+### Analysis of univariate diagnostic results
+
+> We analyze the correlation between each variable and the diagnostic results. Here we use the method of drawing a box pattern.
+
+#### mean_radius
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_radius)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_radius", x = "diagnosis")
+```
+
+![](plot2.svg)
+
+It can be seen that the average tumor radius of patients with breast cancer is mainly between 10 and 15, while the undiagnosed is mainly between 15 and 20.
+
+#### mean_texture
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_texture)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_texture", x = "diagnosis")
+```
+
+![](plot3.svg)
+
+It can be found that the average texture value of the patient's tumor is between 15 and 20, while that has not been diagnosed is between 20 and 25.
+
+#### mean_perimeter
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_perimeter)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_perimeter", x = "diagnosis")
+```
+
+![](plot4.svg)
+
+As can be seen from the figure, the average perimeter of tumors in confirmed patients is between 70 and 90, while those that have not been diagnosed is between 100 and 130.
+
+#### mean_area
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_area)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_area", x = "diagnosis")
+```
+
+![](plot5.svg)
+
+It can be found that the average tumor area of confirmed patients is about 500, while the main undiagnosed tumors are between 750 and 1250.
+
+#### mean_smoothness
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_smoothness)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_smoothness", x = "diagnosis")
+```
+
+![](plot6.svg)
+
+We have noticed that there is an intersection of tumor smoothness in patients with positive or negative confirmed results, but in general, the value of confirmed patients will be lower.
+
+### Relevance analysis
+
+According to the general process of modeling, we need to carry out correlation analysis of each variable.
+
+If the correlation between variables is significant, it will affect the predictive effect of the model.
+
+```R
+cor_analysis <- cor(data[c(1:5)])
+corrplot(cor_analysis, method = "number")
+```
+
+![](plot7.svg)
+
+Through correlation analysis, we found that the relationship between the three variables is very significant.
+
+They are **radius**, **perimeter** and **area**.
+
+These three values are obviously highly correlated, so we need to filter them.
+
+### Correlation between variables and diagnostic results
+
+Before the final accuracy of the qualitative analysis model, we want to use the image to see the relationship between variables and diagnostic results first. There are some intuitive impressions.
+
+We have a total of five variables:
+
+1. mean_radius
+2. mean_texture
+3. mean_perimeter
+4. mean_area
+5. mean_smoothness
+
+The correlation between them and diagnostic results is combined, and there are a total of 10 situations that need to be discussed and analyzed.
+
+> The red dot in the chart below indicates that the diagnostic result is undiagnosed.
+
+#### Weak correlation of variables
+
+> radius & texture, radius & smoothness, texture & perimeter, texture & area, texture & smoothness, perimeter & smoothness, area & smoothness
+
+![](plot8.svg)
+
+We can have an intuitive understanding of the relationship between the two variables through the scatter distribution in the chart.
+
+#### Strong correlation of variables
+
+> radius & perimeter, radius & area, perimeter & area
+
+```R
+# radius & perimeter
+rpPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & area
+raPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & area
+paPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rpPlot, raPlot, paPlot,
+  nrow = 1,
+  ncol = 3
+)
+```
+
+![](plot9.svg)
+
+As previously expected, they are quite relevant, and their analysis can be carried out at the same time.
+
+Obviously, from the chart, patients with an average tumor radius of 10 to 15 have a higher probability of being diagnosed with breast cancer.
+
+## Model
+
+### Dataset segmentation
+
+For subsequent modeling, we need to randomly divide the data set into two parts, one to train the prediction model, and the other to test the accuracy of the model.
+
+```R
+set.seed(123) # Set the repeatability set.seed() to ensure that it is repeatable
+train <- sample(nrow(data), 0.7 * nrow(data))
+train_data <- data[train, ]
+test_data <- data[-train, ]
+```
+
+*train_ data* means training data, *validate_ data* stands for inspection data
+
+### Logistic regression modeling
+
+> Since the final prediction results are 0 and 1, it is not suitable to use linear regression.
+>
+> Here we choose to use the idea of logical regression to build a model.
+
+The connection function used in logical regression is the best representative of the Sigmoid function, that is, the logistic function.
+
+From the above analysis, we select *radius* among *radius*, *perimeter* and *area* for modeling.
+
+```R
+model <- glm(
+  data = train_data,
+  formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+  family = binomial(link = "logit")
+)
+model <- step(model) # Carry out the step-by-step regression method for data analysis
+summary(model)
+```
+
+Use `summary (model)` to view the model.
+
+```text
+Call:
+glm(formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+    family = binomial(link = "logit"), data = train_data)
+
+Deviance Residuals:
+     Min        1Q    Median        3Q       Max
+-2.91948  -0.03436   0.04781   0.21133   2.01672
+
+Coefficients:
+                  Estimate Std. Error z value Pr(>|z|)
+(Intercept)       40.52957    5.09828   7.950 1.87e-15 ***
+mean_texture      -0.34187    0.06622  -5.163 2.44e-07 ***
+mean_smoothness -140.35265   21.54005  -6.516 7.23e-11 ***
+mean_radius       -1.36821    0.17827  -7.675 1.65e-14 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+
+(Dispersion parameter for binomial family taken to be 1)
+
+    Null deviance: 515.0  on 397  degrees of freedom
+Residual deviance: 134.9  on 394  degrees of freedom
+AIC: 142.9
+
+Number of Fisher Scoring iterations: 8
+```
+
+From the results of `summary`, it can be seen that the three variables we selected contribute significantly to the results.
+
+### Calculate the fitting threshold
+
+Here we use `roc` from `pRoc` to find the optimal threshold.
+
+```R
+pre <- predict(model, type = "response", train_data)
+modelroc <- roc(train_data$diagnosis, pre)
+plot(modelroc,
+  print.auc = TRUE, auc.polygon = TRUE,
+  grid = c(0.1, 0.2), grid.col = c("green", "red"),
+  max.auc.polygon = TRUE,
+  auc.polygon.col = "skyblue", print.thres = TRUE
+)
+```
+
+![](plot10.svg)
+
+It can be seen that 0.588 is the threshold we need. Considering it, we choose 0.6 as the threshold of the model.
+
+### Test Set Data Validation
+
+After successfully using the training set data to build a model, we should also use the check data set to check the accuracy of model prediction.
+
+Since the forecast is a number, and what we ultimately want is a confirmed or undiagnosed result, we need a threshold to classify the predicted value to get a numerical result of 1 or 0.
+
+```R
+test_data$prob <- model %>%
+  predict(type = "response", newdata = test_data)
+test_data$prob <- ifelse(test_data$prob > 0.6, 1, 0)
+test_data$diff <- ifelse(test_data$diagnosis == test_data$prob, 1, 0)
+```
+
+### Evaluate the predictive effect of the model
+
+We can draw a pie chart to visualize the accuracy of the model.
+
+```R
+diff_count <- test_data %>%
+  count(diff, name = "count")
+diff_count$diff <- ifelse(diff_count$diff == 0, "False", "True")
+
+diff_plot <- diff_count %>%
+  ggplot(mapping = aes(
+    x = 1,
+    y = count,
+    fill = factor(diff),
+  ))
+
+diff_plot +
+  geom_bar(stat = "identity") +
+  coord_polar(theta = "y") +
+  scale_x_continuous(name = NULL, breaks = NULL) +
+  scale_y_continuous(name = NULL, breaks = NULL) +
+  labs(
+    x = "", y = "",
+    fill = "",
+    title = "Model prediction accuracy",
+  ) +
+  theme(
+    legend.position = "top",
+    plot.title = element_text(hjust = 0.5, size = 14), # title position
+  )
+```
+
+![](plot11.svg)
+
+```R
+paste(
+  round(100 * diff_count$count[2] / (diff_count$count[1] + diff_count$count[2]), 2),
+  "%"
+)
+```
+
+```text
+[1] "93.57 %"
+```
+
+The result was very surprising. The prediction accuracy of our model was extremely high. In order to avoid errors and remove preset random values, I tried many times and got better results of more than 90%, which shows that our model is stable and accurate.
+
+{{%details summary="Full code"%}}
+```R
+library(tidyverse)
+library(ggplot2)
+library(corrplot)
+library(pROC)
+library(gridExtra)
+
+# Import the original data
+data <- read.csv("Breast_cancer_data.csv")
+head(data)
+
+# Check for missing data
+sum(is.na(data))
+
+# Redundant data view
+duplicated_count <- sum(duplicated(data))
+
+# Analyze the distribution of each variable
+rel_area <- ggplot(data, aes(x = mean_area, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_radius <- ggplot(data, aes(x = mean_radius, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_texture <- ggplot(data, aes(x = mean_texture, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_smooth <- ggplot(data, aes(x = mean_smoothness, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_perimeter <- ggplot(data, aes(x = mean_perimeter, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+grid.arrange(rel_area, rel_radius, rel_texture, rel_smooth, rel_perimeter,
+  nrow = 3,
+  ncol = 2
+)
+
+# Univariate box pattern analysis
+# mean_radius
+ggplot(data, aes(x = factor(diagnosis), y = mean_radius)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_radius", x = "diagnosis")
+# mean_texture
+ggplot(data, aes(x = factor(diagnosis), y = mean_texture)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_texture", x = "diagnosis")
+# mean_perimeter
+ggplot(data, aes(x = factor(diagnosis), y = mean_perimeter)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_perimeter", x = "diagnosis")
+# mean_area
+ggplot(data, aes(x = factor(diagnosis), y = mean_area)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_area", x = "diagnosis")
+# mean_smoothness
+ggplot(data, aes(x = factor(diagnosis), y = mean_smoothness)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_smoothness", x = "diagnosis")
+
+# Correlation analysis between variables
+cor_analysis <- cor(data[c(1:5)])
+corrplot(cor_analysis, method = "number")
+
+# Relevance between variables and results
+# ----------------------------Related variables------------------------------ #
+# radius & texture
+rtPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_texture,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & smoothness
+rsPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & perimeter
+tpPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & area
+taPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & smoothness
+tsPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & smoothness
+psPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# area & smoothness
+asPlot <- ggplot(data, aes(
+  x = mean_area, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rtPlot, rsPlot, tpPlot, taPlot, tsPlot, psPlot, asPlot,
+  nrow = 3,
+  ncol = 3
+)
+# ---------------------------Strong related variable---------------------------- #
+# radius & perimeter
+rpPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & area
+raPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & area
+paPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rpPlot, raPlot, paPlot,
+  nrow = 1,
+  ncol = 3
+)
+
+# Dataset segmentation
+set.seed(123) # Set the repeatable set.seed() to ensure that it is repeatable
+train <- sample(nrow(data), 0.7 * nrow(data))
+train_data <- data[train, ]
+test_data <- data[-train, ]
+
+# Logical regression modeling
+model <- glm(
+  data = train_data,
+  formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+  family = binomial(link = "logit")
+)
+model <- step(model) # step-by-step regression method
+summary(model) # Export all results
+
+# Calculate the fitting threshold
+pre <- predict(model, type = "response", train_data)
+modelroc <- roc(train_data$diagnosis, pre)
+plot(modelroc,
+  print.auc = TRUE, auc.polygon = TRUE,
+  grid = c(0.1, 0.2), grid.col = c("green", "red"),
+  max.auc.polygon = TRUE,
+  auc.polygon.col = "skyblue", print.thres = TRUE
+)
+
+# Test set data verification
+test_data$prob <- model %>%
+  predict(type = "response", newdata = test_data)
+test_data$prob <- ifelse(test_data$prob > 0.6, 1, 0)
+test_data$diff <- ifelse(test_data$diagnosis == test_data$prob, 1, 0)
+
+# Test set data forecast statistics percentage
+diff_count <- test_data %>%
+  count(diff, name = "count")
+diff_count$diff <- ifelse(diff_count$diff == 0, "False", "True")
+
+diff_plot <- diff_count %>%
+  ggplot(mapping = aes(
+    x = 1,
+    y = count,
+    fill = factor(diff),
+  ))
+
+diff_plot +
+  geom_bar(stat = "identity") +
+  coord_polar(theta = "y") +
+  scale_x_continuous(name = NULL, breaks = NULL) +
+  scale_y_continuous(name = NULL, breaks = NULL) +
+  labs(
+    x = "", y = "",
+    fill = "",
+    title = "Model prediction accuracy",
+  ) +
+  theme(
+    legend.position = "top",
+    plot.title = element_text(hjust = 0.5, size = 14),
+  )
+
+paste(
+  round(100 * diff_count$count[2] / (diff_count$count[1] + diff_count$count[2]), 2),
+  "%"
+)
+```
+{{%/details%}}
\ No newline at end of file
diff --git a/content/posts/breast-cancer-prediction/index.zh-cn.md b/content/posts/breast-cancer-prediction/index.zh-cn.md
new file mode 100644
index 0000000..26ec3bb
--- /dev/null
+++ b/content/posts/breast-cancer-prediction/index.zh-cn.md
@@ -0,0 +1,618 @@
+---
+title: "乳腺癌预测模型"
+date: 2022-06-22T01:23:48+08:00
+tags: ["数据分析", "R语言"]
+series: ["R语言数据分析"]
+series_order: 4
+---
+
+> 数据来源：[乳腺癌预测数据集](https://www.kaggle.com/datasets/merishnasuwal/breast-cancer-prediction-dataset)
+
+## 简介
+
+全球范围内，乳腺癌是女性最常见的癌症类型，在死亡率方面排名第二。当发现异常肿块（来自自我检查或X光）或看到钙质小点（在X光片上）时，就会进行乳腺癌的诊断。在发现可疑肿块后，医生将进行诊断以确定是否为癌症，如果是，是否已扩散到身体的其他部位。
+
+此乳腺癌数据集是从威斯康星大学麦迪逊分校的威廉·H·沃尔伯格博士处获得的。
+
+## 导入
+
+第一步是将原始数据导入程序代码。
+
+```R
+data <- read.csv("Breast_cancer_data.csv")
+```
+
+原始数据包含标题，使用R语言中导入*CSV文件*的内置函数(`read.csv`)，只需一行简单的代码即可高效地将文件导入我们的程序进行后续处理。
+
+使用`head`函数，我们可以简要查看数据的一部分。
+
+```R
+head(data)
+```
+
+```text
+#   mean_radius mean_texture mean_perimeter mean_area mean_smoothness diagnosis
+# 1       17.99        10.38         122.80    1001.0         0.11840         0
+# 2       20.57        17.77         132.90    1326.0         0.08474         0
+# 3       19.69        21.25         130.00    1203.0         0.10960         0
+# 4       11.42        20.38          77.58     386.1         0.14250         0
+# 5       20.29        14.34         135.10    1297.0         0.10030         0
+# 6       12.45        15.70          82.57     477.1         0.12780         0
+```
+
+显然，数据集中每条数据包含5个与乳腺癌相关的数据，最后列使用0和1来表示是否确诊。
+
+## 清洗数据
+
+一般来说，为了分析数据，我们需要在一定程度上**清洗数据**，分离和合并一些单元格数据，丢弃一些不需要的数据，并放大重要数据，以便使数据对我们建模和分析更加**紧凑**。
+
+我们期望使用数据来构建模型。对这个数据集，每条信息都有其利用价值，因此为了确保数据量充足，我们不需要对其进行过多处理。
+
+### 检查缺失数据
+
+我们需要判断数据集中是否存在缺失数据，以避免在构建模型时出现未预见的错误。
+
+```R
+sum(is.na(data))
+```
+
+幸运的是，我们的数据集中没有缺失数据，每一份数据都是完整且充满利用价值的。
+
+### 查看冗余数据
+
+首先，我们需要确保数据集中的数据没有重复，以防止对后续建模造成干扰。
+
+```R
+duplicated_count <- sum(duplicated(data))
+```
+
+输出 0，无重复数据。
+
+## 分析数据
+
+我们的目标是建立一个合理的预测模型，通过某些可量化数据实现乳腺癌诊断的准确预测。
+
+### 分析变量分布
+
+为了对参数分布有一个基本了解，我们将分别映射每个变量的分布。在这种情况下，直方图和密度分布图的组合是最直观和有效的。由于`geom_density()`的纵向轴是密度估计，为了能够在同一坐标系中绘制直方图和密度估计，有必要将直方图的纵向轴改为密度估计。
+
+```R
+rel_area <- ggplot(data, aes(x = mean_area, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_radius <- ggplot(data, aes(x = mean_radius, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_texture <- ggplot(data, aes(x = mean_texture, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_smooth <- ggplot(data, aes(x = mean_smoothness, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+rel_perimeter <- ggplot(data, aes(x = mean_perimeter, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) +
+  geom_density()
+```
+
+最后，我们使用`gridExtra`库中的`grid.arrange`函数将图表排列在一起。
+
+```R
+grid.arrange(rel_area, rel_radius, rel_texture, rel_smooth, rel_perimeter,
+  nrow = 3,
+  ncol = 2
+)
+```
+
+![](plot1.svg)
+
+我们注意到所有数据的分布有两个特性：
+
+1. 所有数据在某个区间内连续分布。
+2. 每个数据在某个值附近大量分布，距离越远，分布越少。
+
+### 单变量诊断结果分析
+
+> 分析每个变量与诊断结果之间的相关性，使用绘制箱形图的方法
+
+#### 平均半径
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_radius)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_radius", x = "diagnosis")
+```
+
+![](plot2.svg)
+
+乳腺癌患者的平均肿瘤半径主要在10至15之间，而未诊断的患者主要在15至20之间。
+
+#### 平均纹理
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_texture)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_texture", x = "diagnosis")
+```
+
+![](plot3.svg)
+
+可以发现在患者的肿瘤中，平均纹理值介于15到20之间，而尚未被诊断的肿瘤则介于20到25之间。
+
+#### 平均周长
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_perimeter)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_perimeter", x = "diagnosis")
+```
+
+![](plot4.svg)
+
+如图所示，确诊患者肿瘤的平均周长在70至90之间，而未诊断的患者在100至130之间。
+
+#### 平均面积
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_area)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_area", x = "diagnosis")
+```
+
+![](plot5.svg)
+
+可以发现在确诊患者的平均肿瘤面积约为500，而主要未诊断的肿瘤在750到1250之间。
+
+#### 平均平滑度
+
+```R
+ggplot(data, aes(x = factor(diagnosis), y = mean_smoothness)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_smoothness", x = "diagnosis")
+```
+
+![](plot6.svg)
+
+我们注意到，在阳性或阴性确认结果的病人中存在肿瘤平滑度的交集，但总体而言，确认病人的数值将会更低。
+
+### 相关性分析
+
+根据建模的一般过程，我们需要对每个变量进行相关性分析。如果变量之间的相关性显著，它将影响模型的预测效果。
+
+```R
+cor_analysis <- cor(data[c(1:5)])
+corrplot(cor_analysis, method = "number")
+```
+
+![](plot7.svg)
+
+通过相关性分析，我们发现这三个变量之间的关系非常显著。它们是**半径**、**周长**和**面积**。这三个值显然高度相关，因此我们需要对它们进行筛选。
+
+### 变量与诊断结果的相关性
+
+在定性分析模型最终精度之前，我们想先通过图像看看变量和诊断结果之间的关系。有一些直观的印象。
+
+我们有总共五个变量：
+
+1. mean_radius
+2. mean_texture
+3. mean_perimeter
+4. mean_area
+5. mean_smoothness
+
+它们与诊断结果之间的相关性被结合，总共有10种情况需要讨论和分析。
+
+> 下图中红色圆点表示诊断结果为未诊断
+
+#### 变量之间的弱相关性
+
+> radius & texture, radius & smoothness, texture & perimeter, texture & area, texture & smoothness, perimeter & smoothness, area & smoothness
+
+![](plot8.svg)
+
+我们可以通过图表中的散点分布直观地理解两个变量之间的关系。
+
+#### 变量之间强相关性
+
+> radius & perimeter, radius & area, perimeter & area
+
+```R
+# radius & perimeter
+rpPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & area
+raPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & area
+paPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rpPlot, raPlot, paPlot,
+  nrow = 1,
+  ncol = 3
+)
+```
+
+![](plot9.svg)
+
+如先前预期的那样，它们相当相关，并且可以同时进行分析。
+
+显然，从图表中可以看出，平均肿瘤半径为10至15毫米的患者被诊断为乳腺癌的概率更高。
+
+## 模型
+
+### 数据集分割
+
+对于后续建模，我们需要将数据集随机分为两部分，一部分用于训练预测模型，另一部分用于测试模型的准确性。
+
+```R
+set.seed(123) # Set the repeatability set.seed() to ensure that it is repeatable
+train <- sample(nrow(data), 0.7 * nrow(data))
+train_data <- data[train, ]
+test_data <- data[-train, ]
+```
+
+*train_data* 表示训练数据，*validate_data* 代表验证数据
+
+### 逻辑回归建模
+
+> 由于最终预测结果是0和1，因此不适宜使用线性回归
+>
+> 这里我们选择使用逻辑回归的思想来构建模型
+
+逻辑回归中使用的连接函数是Sigmoid函数的最佳代表，即逻辑函数。
+
+从上述分析中，我们选择 *radius* 在 *radius*、*perimeter* 和 *area* 中用于建模。
+
+```R
+model <- glm(
+  data = train_data,
+  formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+  family = binomial(link = "logit")
+)
+model <- step(model) # Carry out the step-by-step regression method for data analysis
+summary(model)
+```
+
+Use `summary (model)` to view the model.
+
+```text
+Call:
+glm(formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+    family = binomial(link = "logit"), data = train_data)
+
+Deviance Residuals:
+     Min        1Q    Median        3Q       Max
+-2.91948  -0.03436   0.04781   0.21133   2.01672
+
+Coefficients:
+                  Estimate Std. Error z value Pr(>|z|)
+(Intercept)       40.52957    5.09828   7.950 1.87e-15 ***
+mean_texture      -0.34187    0.06622  -5.163 2.44e-07 ***
+mean_smoothness -140.35265   21.54005  -6.516 7.23e-11 ***
+mean_radius       -1.36821    0.17827  -7.675 1.65e-14 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+
+(Dispersion parameter for binomial family taken to be 1)
+
+    Null deviance: 515.0  on 397  degrees of freedom
+Residual deviance: 134.9  on 394  degrees of freedom
+AIC: 142.9
+
+Number of Fisher Scoring iterations: 8
+```
+
+From the results of `summary`, it can be seen that the three variables we selected contribute significantly to the results.
+
+### Calculate the fitting threshold
+
+Here we use `roc` from `pRoc` to find the optimal threshold.
+
+```R
+pre <- predict(model, type = "response", train_data)
+modelroc <- roc(train_data$diagnosis, pre)
+plot(modelroc,
+  print.auc = TRUE, auc.polygon = TRUE,
+  grid = c(0.1, 0.2), grid.col = c("green", "red"),
+  max.auc.polygon = TRUE,
+  auc.polygon.col = "skyblue", print.thres = TRUE
+)
+```
+
+![](plot10.svg)
+
+可以看出0.588是我们需要的阈值。考虑到这一点，我们选择0.6作为模型的阈值。
+
+### 测试集数据验证
+
+在成功使用训练集数据构建模型后，我们还应该使用检查数据集来检查模型预测的准确性。由于预测是一个数字，而我们最终想要的是一个已确认或未诊断的结果，我们需要一个阈值来将预测值分类，以获得1或0的数值结果。
+
+```R
+test_data$prob <- model %>%
+  predict(type = "response", newdata = test_data)
+test_data$prob <- ifelse(test_data$prob > 0.6, 1, 0)
+test_data$diff <- ifelse(test_data$diagnosis == test_data$prob, 1, 0)
+```
+
+### 评估模型的预测效果
+
+我们可以绘制饼图来可视化模型的准确率。
+
+```R
+diff_count <- test_data %>%
+  count(diff, name = "count")
+diff_count$diff <- ifelse(diff_count$diff == 0, "False", "True")
+
+diff_plot <- diff_count %>%
+  ggplot(mapping = aes(
+    x = 1,
+    y = count,
+    fill = factor(diff),
+  ))
+
+diff_plot +
+  geom_bar(stat = "identity") +
+  coord_polar(theta = "y") +
+  scale_x_continuous(name = NULL, breaks = NULL) +
+  scale_y_continuous(name = NULL, breaks = NULL) +
+  labs(
+    x = "", y = "",
+    fill = "",
+    title = "Model prediction accuracy",
+  ) +
+  theme(
+    legend.position = "top",
+    plot.title = element_text(hjust = 0.5, size = 14), # title position
+  )
+```
+
+![](plot11.svg)
+
+```R
+paste(
+  round(100 * diff_count$count[2] / (diff_count$count[1] + diff_count$count[2]), 2),
+  "%"
+)
+```
+
+```text
+[1] "93.57 %"
+```
+
+结果非常令人惊讶。我们模型的预测准确度极高。为了避免错误和移除预设的随机值，我尝试了许多次，并得到了超过90%的更好结果，这表明我们的模型稳定且准确。
+
+{{%details summary="Full code"%}}
+```R
+library(tidyverse)
+library(ggplot2)
+library(corrplot)
+library(pROC)
+library(gridExtra)
+
+# Import the original data
+data <- read.csv("Breast_cancer_data.csv")
+head(data)
+
+# Check for missing data
+sum(is.na(data))
+
+# Redundant data view
+duplicated_count <- sum(duplicated(data))
+
+# Analyze the distribution of each variable
+rel_area <- ggplot(data, aes(x = mean_area, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_radius <- ggplot(data, aes(x = mean_radius, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_texture <- ggplot(data, aes(x = mean_texture, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_smooth <- ggplot(data, aes(x = mean_smoothness, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+rel_perimeter <- ggplot(data, aes(x = mean_perimeter, y = ..density..)) +
+  geom_histogram(fill = "blue", color = "black", size = 0.2, alpha = 0.2, bins = 30) + # nolint
+  geom_density()
+grid.arrange(rel_area, rel_radius, rel_texture, rel_smooth, rel_perimeter,
+  nrow = 3,
+  ncol = 2
+)
+
+# Univariate box pattern analysis
+# mean_radius
+ggplot(data, aes(x = factor(diagnosis), y = mean_radius)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_radius", x = "diagnosis")
+# mean_texture
+ggplot(data, aes(x = factor(diagnosis), y = mean_texture)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_texture", x = "diagnosis")
+# mean_perimeter
+ggplot(data, aes(x = factor(diagnosis), y = mean_perimeter)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_perimeter", x = "diagnosis")
+# mean_area
+ggplot(data, aes(x = factor(diagnosis), y = mean_area)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_area", x = "diagnosis")
+# mean_smoothness
+ggplot(data, aes(x = factor(diagnosis), y = mean_smoothness)) +
+  geom_boxplot(outlier.colour = "blue", outlier.shape = 5, outlier.size = 4) +
+  labs(title = "Plot of mean_smoothness", x = "diagnosis")
+
+# Correlation analysis between variables
+cor_analysis <- cor(data[c(1:5)])
+corrplot(cor_analysis, method = "number")
+
+# Relevance between variables and results
+# ----------------------------Related variables------------------------------ #
+# radius & texture
+rtPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_texture,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & smoothness
+rsPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & perimeter
+tpPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & area
+taPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# texture & smoothness
+tsPlot <- ggplot(data, aes(
+  x = mean_texture, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & smoothness
+psPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# area & smoothness
+asPlot <- ggplot(data, aes(
+  x = mean_area, y = mean_smoothness,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rtPlot, rsPlot, tpPlot, taPlot, tsPlot, psPlot, asPlot,
+  nrow = 3,
+  ncol = 3
+)
+# ---------------------------Strong related variable---------------------------- #
+# radius & perimeter
+rpPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_perimeter,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# radius & area
+raPlot <- ggplot(data, aes(
+  x = mean_radius, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+# perimeter & area
+paPlot <- ggplot(data, aes(
+  x = mean_perimeter, y = mean_area,
+  color = as.factor(diagnosis)
+)) +
+  geom_point() +
+  theme_minimal() +
+  theme(legend.position = "none")
+grid.arrange(rpPlot, raPlot, paPlot,
+  nrow = 1,
+  ncol = 3
+)
+
+# Dataset segmentation
+set.seed(123) # Set the repeatable set.seed() to ensure that it is repeatable
+train <- sample(nrow(data), 0.7 * nrow(data))
+train_data <- data[train, ]
+test_data <- data[-train, ]
+
+# Logical regression modeling
+model <- glm(
+  data = train_data,
+  formula = diagnosis ~ mean_texture + mean_smoothness + mean_radius,
+  family = binomial(link = "logit")
+)
+model <- step(model) # step-by-step regression method
+summary(model) # Export all results
+
+# Calculate the fitting threshold
+pre <- predict(model, type = "response", train_data)
+modelroc <- roc(train_data$diagnosis, pre)
+plot(modelroc,
+  print.auc = TRUE, auc.polygon = TRUE,
+  grid = c(0.1, 0.2), grid.col = c("green", "red"),
+  max.auc.polygon = TRUE,
+  auc.polygon.col = "skyblue", print.thres = TRUE
+)
+
+# Test set data verification
+test_data$prob <- model %>%
+  predict(type = "response", newdata = test_data)
+test_data$prob <- ifelse(test_data$prob > 0.6, 1, 0)
+test_data$diff <- ifelse(test_data$diagnosis == test_data$prob, 1, 0)
+
+# Test set data forecast statistics percentage
+diff_count <- test_data %>%
+  count(diff, name = "count")
+diff_count$diff <- ifelse(diff_count$diff == 0, "False", "True")
+
+diff_plot <- diff_count %>%
+  ggplot(mapping = aes(
+    x = 1,
+    y = count,
+    fill = factor(diff),
+  ))
+
+diff_plot +
+  geom_bar(stat = "identity") +
+  coord_polar(theta = "y") +
+  scale_x_continuous(name = NULL, breaks = NULL) +
+  scale_y_continuous(name = NULL, breaks = NULL) +
+  labs(
+    x = "", y = "",
+    fill = "",
+    title = "Model prediction accuracy",
+  ) +
+  theme(
+    legend.position = "top",
+    plot.title = element_text(hjust = 0.5, size = 14),
+  )
+
+paste(
+  round(100 * diff_count$count[2] / (diff_count$count[1] + diff_count$count[2]), 2),
+  "%"
+)
+```
+{{%/details%}}
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