| title | author | date | bibliography | ||
|---|---|---|---|---|---|
Reversible Metabolism |
Sungpil Han |
2018-12-27 |
|
Keywords
Reversible metabolism, cisplatin, monohydrate, multiple compartment
본 모델링의 목적은 가역적 대사 (reversible metabolism, 혹은 가역적 상호전환, reversible interconversion)을 기술하는 미분방정식을 고안하여 모델링하고 이를 통한 시뮬레이션을 도출하는 것이다.
The aim of this exercise is to demonstrate how to implement a system of differential equations describing reversible metabolism. Data were taken from thε li〔eraturε on cisplatin kinetics (Andersson (1995]) and used [ O generate synthetic concentr따ion-time values for cisplatin p and its monohydrate m. This information was then used to obtain initial parameter estimates for a model of reversible metabolism. This exercise demonstrates how to implement the equations for this model into a program. In an infusion solution of cisplatin, equilibrium is established berween cisplatin and its monohydratε complex. Thus, the input rate can be split into cisplatin infusion ratε Iη and monohydra[ e infusion rate In,, We have also chosen to describe thε εquilibrium process in vivo berween cisplatin and its monohydrate complex by means of rwo clearance rates.
Objectives {@andersson1995stability}
- To implement a set of differential equations mimicking reversible metabolism
- To estimate the disposition and interconversion parameters of the two compounds
Pharmacokinetic and Pharmacodynamic Data Analysis PK34
Clpd and Cl,,,d. The exper that takes account of such a split inf] ut rate and clearance are shown in 「 Figure 34.1. See also Section 2.4. 638
6 Input, lnputm 5 /. 등 4 3- C ];I 2 Eliminat,。n Eliminati 。n ct, Cl., 0 0 20 40 60 80 100 120 140 160 180 Time (min) The equation for C뼈latin (p) is dC V - --ι= J.η - Cl · C - Cl J • C + Cl , · C dt p p P a P “ (341) Where VP' CP' Iη/μ Clp and Clpd are the volume, concentration, input rate, clearance and interthe concentration of [ he monohydratε. The conversion of cisplatin to the monohydrate occurs with a rate constant derived according to Equation 34:2 k12,pd = Cl pd . VP (34:2) The reversal rate for conversion of the monohydrate to cisplatin is k21 씨 = Cl111d · κ” (34 3) The equation for the monohydr따E (m) is dC V· -」뜨 = In111 -Cl111 · C” - Cl111r1 · C'" + Clpc1 · Cp (34:4) dt
Where κ,,, ζ’” Iη”” C/111 and Cl111d arε the volume, ζoncentration, input rate, clearance and inter-conversion clearancε of the monohydrate respectively. ζ” is the concentration of the monohydrate. Pharmac。kinetic Applications Figure 34.1 Left: Obse「ved (symb이s) and predicted (s이 id lines) concentration time data of cisplatin and its monohydrate The symbols correspond to cisplatin (upper curve) and the monohyd「ate (bottom curve) after infusion of cisplatin which also contains the monol1ydrate, and cisplalin (second f「om bottom) and monohyd「ate (second from top) after monohydrate infusion‘ Right: A two compaπment model mimicking reversible metabolism was used to model the data‘ 639
·‘ E」-- ·• ‘•·"'￥‘;-. -’--· ' - }T ~ Pharmac。kinetic and Pharmacodynamic Data Analys is ‘ ;」 Parameter κ(니 Clm (L·min·') ι,(μg·L· ') GIP (L· min-1) k12(min-1) k21 (min-1) WRSS 640 Initial parameter estimates Procedures involved in obtaining initial parameter estimates, AUC, MRT, and so on for a system of revεrsible processes are covered in depth in Ebling and Jusko [1986] . The initial parameter estimates selected diffcεred a little from the values used to gener따C the data. Interpretation of results and conclusions The observed and model-predicted plasma concentrations, and the final parameter estimates are shown in Figure 34.1 and Table 34. 1, respectively. WRSS in Table 34.1 denotes the weighted residual sum of squares. Table 34.1 Paramete「estimates of the micro-constant and interconversion clearance models Microconstant model Interconversion clearance model Estimate CV% Parameter Estimate CV% 14.1 3 κ(니 14.1 3 0.0085 22 C/m (L·min-1) 0.0084 22 2.96 2 Vm (μg·L-1) 2.97 2 0.446 2 GIP (L·min 1) 0.445 2 0.00021 34 Clpd (min-1) 0.0031 33 0.021 3 C/md (min-1) 0.063 5 0.0089 WRSS 0.0089
# setup ----
library(deSolve)
library(wnl)
library(ggplot2)
library(dplyr)
library(readr)
library(purrr)
round_df <- function(x, digits) {
# round all numeric variables
# x: data frame
# digits: number of digits to round
numeric_columns <- sapply(x, mode) == 'numeric'
x[numeric_columns] <- round(x[numeric_columns], digits)
x
}
raw_dPK34 <- read_csv('data-raw/PK34.csv', skip = 1) %>% # Unit: min NA umol/L NA
set_names(c("TIME", "MOL", "DV", "ID")) %>%
print()## Warning: Missing column names filled in: 'X2' [2], 'X4' [4]
## Parsed with column specification:
## cols(
## min = col_double(),
## X2 = col_character(),
## `umol/L` = col_double(),
## X4 = col_double()
## )
## # A tibble: 38 x 4
## TIME MOL DV ID
## <dbl> <chr> <dbl> <dbl>
## 1 20 Cp 2.90 1
## 2 30 Cp 3.80 1
## 3 40 Cp 4.35 1
## 4 60 Cp 5.08 1
## 5 65 Cp 5.11 1
## 6 80 Cp 3.22 1
## 7 95 Cp 2.11 1
## 8 120 Cp 0.950 1
## 9 150 Cp 0.453 1
## 10 180 Cp 0.200 1
## # ... with 28 more rows
# REQUIREMENT: dPK34
dPK34 <- raw_dPK34 %>%
as.data.frame() %>%
print()## TIME MOL DV ID
## 1 20 Cp 2.8980 1
## 2 30 Cp 3.7958 1
## 3 40 Cp 4.3491 1
## 4 60 Cp 5.0832 1
## 5 65 Cp 5.1105 1
## 6 80 Cp 3.2216 1
## 7 95 Cp 2.1134 1
## 8 120 Cp 0.9499 1
## 9 150 Cp 0.4529 1
## 10 180 Cp 0.1996 1
## 11 20 Cm 0.3432 1
## 12 30 Cm 0.4787 1
## 13 40 Cm 0.5655 1
## 14 60 Cm 0.6874 1
## 15 65 Cm 0.6351 1
## 16 80 Cm 0.4933 1
## 17 95 Cm 0.3230 1
## 18 120 Cm 0.1947 1
## 19 150 Cm 0.0873 1
## 20 5 Cp 0.1678 2
## 21 10 Cp 0.4507 2
## 22 15 Cp 0.5905 2
## 23 20 Cp 0.8120 2
## 24 30 Cp 0.9562 2
## 25 45 Cp 0.8809 2
## 26 60 Cp 0.8715 2
## 27 120 Cp 0.3371 2
## 28 150 Cp 0.1646 2
## 29 180 Cp 0.0965 2
## 30 5 Cm 3.3911 2
## 31 10 Cm 2.8098 2
## 32 15 Cm 2.3812 2
## 33 20 Cm 2.1331 2
## 34 30 Cm 1.8709 2
## 35 45 Cm 1.1224 2
## 36 60 Cm 0.8564 2
## 37 120 Cm 0.2119 2
## 38 180 Cm 0.0507 2
ggplot(data = raw_dPK34, aes(x = TIME, y = DV, group = interaction(ID, MOL), color = MOL, shape = factor(ID))) +
geom_line() +
geom_point()
# main ----
S1 = cbind(TIME=c(0, 60), RATE1=c(2.375,0), RATE2=c(0.065, 0))
S2 = cbind(TIME=c(0,5), RATE1=c(0, 0), RATE2=c(2, 0))
InfHist = list(S1, S2) ; InfHist## [[1]]
## TIME RATE1 RATE2
## [1,] 0 2.375 0.065
## [2,] 60 0.000 0.000
##
## [[2]]
## TIME RATE1 RATE2
## [1,] 0 0 2
## [2,] 5 0 0
PKde = function(t, y, p)
{
cInf = InfHist[[cID]]
Rate1 = cInf[findInterval(t, cInf[,"TIME"]),"RATE1"]
Rate2 = cInf[findInterval(t, cInf[,"TIME"]),"RATE2"]
Ke1 = p["CLp"]/p["Vc"]
Ke2 = p["CLm"]/p["Vm"]
K12 = p["CLd1"]/p["Vc"]
K21 = p["CLd2"]/p["Vm"]
dy1dt = Rate1/p["Vc"] - Ke1*y[1] - K12*y[1] + K21*y[2]
dy2dt = Rate2/p["Vm"] - Ke2*y[2] + K12*y[1] - K21*y[2]
return(list(c(dy1dt, dy2dt)))
}
# TIME = sort(unique(c(0, dPK34[,"TIME"]))) ; TIME
TIME <- dPK34 %>%
select(TIME) %>%
distinct %>%
arrange(TIME) %>%
.$TIME %>%
c(0, .)
iTime1 = TIME %in% dPK34[dPK34$ID==1 & dPK34$MOL == "Cp", "TIME"] ; iTime1 ; TIME[iTime1]## [1] FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## [12] TRUE TRUE TRUE TRUE
## [1] 20 30 40 60 65 80 95 120 150 180
iTime2 = TIME %in% dPK34[dPK34$ID==1 & dPK34$MOL == "Cm", "TIME"] ; iTime2 ; TIME[iTime2]## [1] FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## [12] TRUE TRUE TRUE FALSE
## [1] 20 30 40 60 65 80 95 120 150
iTime3 = TIME %in% dPK34[dPK34$ID==2 & dPK34$MOL == "Cp", "TIME"] ; iTime3 ; TIME[iTime3]## [1] FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE
## [12] FALSE TRUE TRUE TRUE
## [1] 5 10 15 20 30 45 60 120 150 180
iTime4 = TIME %in% dPK34[dPK34$ID==2 & dPK34$MOL == "Cm", "TIME"] ; iTime4 ; TIME[iTime4]## [1] FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE
## [12] FALSE TRUE FALSE TRUE
## [1] 5 10 15 20 30 45 60 120 180
## Figure 34.1, p 639
plot(0, 0, type="n", xlim=c(0, 180), ylim=c(0, 6), xlab="Time (min)", ylab="Concentration (uM)")
IDs = unique(dPK34[,"ID"])
nID = length(IDs)
y = vector()
for (i in 1:nID) {
cID <<- IDs[i] # referencing wihtin PKde
cy = lsoda(y=c(0, 0), times=TIME, func=PKde, parms=c(Vc=14.1169, Vm=2.96671, CLp=0.445693, CLm=0.00833429, CLd1=0.00308422, CLd2=0.0632217))
iTime1 = TIME %in% dPK34[dPK34$ID==cID & dPK34$MOL == "Cp", "TIME"]
iTime2 = TIME %in% dPK34[dPK34$ID==cID & dPK34$MOL == "Cm", "TIME"]
points(dPK34[dPK34$ID==cID & dPK34$MOL == "Cp", "TIME"], dPK34[dPK34$ID==cID & dPK34$MOL == "Cp", "DV"], pch=19, col=i)
points(dPK34[dPK34$ID==cID & dPK34$MOL == "Cm", "TIME"], dPK34[dPK34$ID==cID & dPK34$MOL == "Cm", "DV"], pch=15, col=i)
lines(TIME, cy[,"1"], col=i)
lines(TIME, cy[,"2"], lty=2, col=i)
y = c(y, cy[iTime1,"1"], cy[iTime2,"2"])
} ; y
## [1] 2.55552376 3.37761139 3.99610671 4.81441001 4.17378776 2.72732733
## [7] 1.78989627 0.89572921 0.39647380 0.17838586 0.35283682 0.47772517
## [13] 0.57722944 0.71947375 0.64234466 0.45657052 0.32400849 0.18240085
## [19] 0.09118321 0.16369918 0.43388961 0.63098688 0.76954597 0.91680743
## [25] 0.93544164 0.83643957 0.33047538 0.18391146 0.09863677 3.17547144
## [31] 2.81502383 2.49576460 2.21294735 1.74035083 1.21461251 0.84833055
## [37] 0.20307299 0.04893432
# REQUIREMENT: fPK34
fPK34 = function(THETA)
{
Vc = THETA[1]
Vm = THETA[2]
CLp = THETA[3]
CLm = THETA[4]
CLd1 = THETA[5]
CLd2 = THETA[6]
y = vector()
for (i in 1:nID) {
cID <<- IDs[i] # referencing wihtin PKde
cy = lsoda(y=c(0, 0), times=TIME, func=PKde, parms=c(Vc=Vc, Vm=Vm, CLp=CLp, CLm=CLm, CLd1=CLd1, CLd2=CLd2))
iTime1 = TIME %in% dPK34[dPK34$ID==cID & dPK34$MOL == "Cp", "TIME"]
iTime2 = TIME %in% dPK34[dPK34$ID==cID & dPK34$MOL == "Cm", "TIME"]
y = c(y, cy[iTime1,"1"], cy[iTime2,"2"])
}
return(y)
}
fPK34(c(14.1169, 2.96671, 0.445693, 0.00833429, 0.00308422, 0.0632217))## [1] 2.55552376 3.37761139 3.99610671 4.81441001 4.17378776 2.72732733
## [7] 1.78989627 0.89572921 0.39647380 0.17838586 0.35283682 0.47772517
## [13] 0.57722944 0.71947375 0.64234466 0.45657052 0.32400849 0.18240085
## [19] 0.09118321 0.16369918 0.43388961 0.63098688 0.76954597 0.91680743
## [25] 0.93544164 0.83643957 0.33047538 0.18391146 0.09863677 3.17547144
## [31] 2.81502383 2.49576460 2.21294735 1.74035083 1.21461251 0.84833055
## [37] 0.20307299 0.04893432
nlr(fPK34,
dPK34,
pNames=c("Vc", "Vm", "CLp", "CLm", "CLd1", "CLd2"),
IE=c(15, 3, 0.5, 0.01, 0.003, 0.1),
Error="P") # different result## $Est
## Vc Vm CLp CLm CLd1
## PE 12.2632223 2.96922318 0.387163717 0.008286228 2.769220e-03
## SE 0.2976141 0.06429357 0.007053857 0.002297237 9.378015e-04
## RSE 2.4268835 2.16533300 1.821931206 27.723550725 3.386518e+01
## CLd2 PropErrVar PropErrSD
## PE 0.063359711 2.358498e-03 0.048564370
## SE 0.003403815 5.451718e-04 0.005612879
## RSE 5.372207654 2.311521e+01 11.557605967
##
## $Cov
## Vc Vm CLp CLm
## Vc 8.857416e-02 -4.059350e-03 1.763707e-03 2.384853e-04
## Vm -4.059350e-03 4.133663e-03 1.205204e-05 -1.215658e-04
## CLp 1.763707e-03 1.205204e-05 4.975689e-05 -4.102777e-07
## CLm 2.384853e-04 -1.215658e-04 -4.102777e-07 5.277296e-06
## CLd1 -1.234065e-06 3.361468e-05 9.578955e-07 -9.934532e-07
## CLd2 -2.907455e-04 2.006395e-04 8.793774e-07 -7.453596e-06
## PropErrVar 3.195370e-06 1.607169e-06 1.295802e-07 -2.241168e-08
## CLd1 CLd2 PropErrVar
## Vc -1.234065e-06 -2.907455e-04 3.195370e-06
## Vm 3.361468e-05 2.006395e-04 1.607169e-06
## CLp 9.578955e-07 8.793774e-07 1.295802e-07
## CLm -9.934532e-07 -7.453596e-06 -2.241168e-08
## CLd1 8.794717e-07 1.985034e-06 1.541532e-08
## CLd2 1.985034e-06 1.158596e-05 6.205444e-08
## PropErrVar 1.541532e-08 6.205444e-08 2.972123e-07
##
## $run
## $run$m
## [1] 18
##
## $run$n
## [1] 20
##
## $run$run
## [1] 20
##
## $run$p.value
## [1] 0.5601923
##
##
## $`Objective Function Value`
## [1] -214.8824
##
## $`-2LL`
## [1] -145.043
##
## $AIC
## [1] -131.043
##
## $AICc
## [1] -127.3097
##
## $BIC
## [1] -119.5799
##
## $Convergence
## NULL
##
## $Message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
##
## $Prediction
## [1] 2.93187136 3.86940128 4.57202567 5.49646370 4.75593120 3.08966796
## [7] 2.01582126 0.99900153 0.43718887 0.19461925 0.35348392 0.47910933
## [13] 0.57942649 0.72324174 0.64647820 0.46099030 0.32805038 0.18537752
## [19] 0.09299729 0.16377446 0.43407283 0.63122795 0.76981032 0.91705571
## [25] 0.93560330 0.83651042 0.33042301 0.18387134 0.09861319 3.17269773
## [31] 2.81243675 2.49336725 2.21073794 1.73849985 1.21323133 0.84732569
## [37] 0.20283544 0.04888868
##
## $Residual
## [1] -0.0338713646 -0.0736012783 -0.2229256654 -0.4132637050 0.3545687963
## [6] 0.1319320405 0.0975787355 -0.0491015264 0.0157111320 0.0049807500
## [11] -0.0102839209 -0.0004093298 -0.0139264874 -0.0358417357 -0.0113781976
## [16] 0.0323097019 -0.0050503797 0.0093224784 -0.0056972890 0.0040255415
## [21] 0.0166271687 -0.0407279536 0.0421896838 0.0391442919 -0.0547033032
## [26] 0.0349895756 0.0066769878 -0.0192713404 -0.0021131933 0.2184022677
## [31] -0.0026367526 -0.1121672536 -0.0776379380 0.1324001526 -0.0908313258
## [36] 0.0090743104 0.0090645616 0.0018113181
##
## $`Elapsed Time`
## Time difference of 21.49923 secs
# Vc 12.3 vs 14.1 (R vs WinNonlin, NONMEM)
# AIC -131.0377 vs -131.05554 (R vs WinNonlin)
e$r # -214.8824 vs -214.895 (R vs NONMEM)## $par
## [1] -0.10144821 0.08968804 -0.15576057 -0.08799020 0.01995352 -0.35634204
## [7] -3.64714529
##
## $value
## [1] -214.8824
##
## $counts
## function gradient
## 114 114
##
## $convergence
## [1] 52
##
## $message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Edison Ack
$PROB GABRIELSSON PK34
$INPUT ID TIME AMT RATE CMT DV MDV
$DATA ../PK34NM.csv IGNORE=@
$SUBR ADVAN13 TOL6
$MODEL
COMP (PARENT)
COMP (METABOLITE)
$PK
Vc = THETA(1)*EXP(ETA(1))
Vm = THETA(2)
CLp = THETA(3)
CLm = THETA(4)
CLd1 = THETA(5)
CLd2 = THETA(6)
S1 = Vc
S2 = Vm
$DES
Ke1 = CLp/Vc
Ke2 = CLm/Vm
K12 = CLd1/Vc
K21 = CLd2/Vm
DADT(1) = -Ke1*A(1) - K12*A(1) + K21*A(2)*Vc/Vm
DADT(2) = -Ke2*A(2) + K12*A(1)*Vm/Vc - K21*A(2)
$ERROR
Y = F + F*ERR(1)
$THETA
(0, 15)
(0, 3)
(0, 0.5)
(0, 0.01)
(0, 0.003)
(0, 0.3)
$OMEGA 0 FIX
$SIGMA 0.1
$EST MAX=9999
$COV UNCOND PRINT=ERSNONLINEAR MIXED EFFECTS MODEL PROGRAM (NONMEM) VERSION 7.4.1
ORIGINALLY DEVELOPED BY STUART BEAL, LEWIS SHEINER, AND ALISON BOECKMANN
CURRENT DEVELOPERS ARE ROBERT BAUER, ICON DEVELOPMENT SOLUTIONS,
AND ALISON BOECKMANN. IMPLEMENTATION, EFFICIENCY, AND STANDARDIZATION
PERFORMED BY NOUS INFOSYSTEMS.
PROBLEM NO.: 1
GABRIELSSON PK34
DATA CHECKOUT RUN: NO
DATA SET LOCATED ON UNIT NO.: 2
THIS UNIT TO BE REWOUND: NO
NO. OF DATA RECS IN DATA SET: 41
NO. OF DATA ITEMS IN DATA SET: 8
ID DATA ITEM IS DATA ITEM NO.: 1
DEP VARIABLE IS DATA ITEM NO.: 6
MDV DATA ITEM IS DATA ITEM NO.: 7
INDICES PASSED TO SUBROUTINE PRED:
8 2 3 4 0 0 5 0 0 0 0
LABELS FOR DATA ITEMS:
ID TIME AMT RATE CMT DV MDV EVID
FORMAT FOR DATA:
(7E7.0,1F2.0)
TOT. NO. OF OBS RECS: 38
TOT. NO. OF INDIVIDUALS: 2
LENGTH OF THETA: 6
DEFAULT THETA BOUNDARY TEST OMITTED: NO
OMEGA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 1
DEFAULT OMEGA BOUNDARY TEST OMITTED: NO
SIGMA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 1
DEFAULT SIGMA BOUNDARY TEST OMITTED: NO
INITIAL ESTIMATE OF THETA:
LOWER BOUND INITIAL EST UPPER BOUND
0.0000E+00 0.1500E+02 0.1000E+07
0.0000E+00 0.3000E+01 0.1000E+07
0.0000E+00 0.5000E+00 0.1000E+07
0.0000E+00 0.1000E-01 0.1000E+07
0.0000E+00 0.3000E-02 0.1000E+07
0.0000E+00 0.3000E+00 0.1000E+07
INITIAL ESTIMATE OF OMEGA:
0.0000E+00
OMEGA CONSTRAINED TO BE THIS INITIAL ESTIMATE
INITIAL ESTIMATE OF SIGMA:
0.1000E+00
COVARIANCE STEP OMITTED: NO
R MATRIX PRINTED: YES
S MATRIX PRINTED: YES
EIGENVLS. PRINTED: YES
SPECIAL COMPUTATION: NO
COMPRESSED FORMAT: NO
GRADIENT METHOD USED: NOSLOW
SIGDIGITS ETAHAT (SIGLO): -1
SIGDIGITS GRADIENTS (SIGL): -1
EXCLUDE COV FOR FOCE (NOFCOV): NO
TURN OFF Cholesky Transposition of R Matrix (CHOLROFF): NO
KNUTHSUMOFF: -1
RESUME COV ANALYSIS (RESUME): NO
SIR SAMPLE SIZE (SIRSAMPLE): -1
NON-LINEARLY TRANSFORM THETAS DURING COV (THBND): 1
PRECONDTIONING CYCLES (PRECOND): 0
PRECONDTIONING TYPES (PRECONDS): TOS
FORCED PRECONDTIONING CYCLES (PFCOND):0
PRECONDTIONING TYPE (PRETYPE): 0
FORCED POS. DEFINITE SETTING: (FPOSDEF):0
WARNING: THE NUMBER OF PARAMETERS TO BE ESTIMATED
EXCEEDS THE NUMBER OF INDIVIDUALS WITH DATA.
DOUBLE PRECISION PREDPP VERSION 7.4.1
GENERAL NONLINEAR KINETICS MODEL WITH STIFF/NONSTIFF EQUATIONS (LSODA, ADVAN13)
MODEL SUBROUTINE USER-SUPPLIED - ID NO. 9999
MAXIMUM NO. OF BASIC PK PARAMETERS: 6
COMPARTMENT ATTRIBUTES
COMPT. NO. FUNCTION INITIAL ON/OFF DOSE DEFAULT DEFAULT
STATUS ALLOWED ALLOWED FOR DOSE FOR OBS.
1 PARENT ON YES YES YES YES
2 METABOLITE ON YES YES NO NO
3 OUTPUT OFF YES NO NO NO
INITIAL (BASE) TOLERANCE SETTINGS:
NRD (RELATIVE) VALUE(S) OF TOLERANCE: 6
ANRD (ABSOLUTE) VALUE(S) OF TOLERANCE: 12
ADDITIONAL PK PARAMETERS - ASSIGNMENT OF ROWS IN GG
COMPT. NO. INDICES
SCALE BIOAVAIL. ZERO-ORDER ZERO-ORDER ABSORB
FRACTION RATE DURATION LAG
1 7 * * * *
2 8 * * * *
3 * - - - -
- PARAMETER IS NOT ALLOWED FOR THIS MODEL
* PARAMETER IS NOT SUPPLIED BY PK SUBROUTINE;
WILL DEFAULT TO ONE IF APPLICABLE
ERROR IN LOG Y IS MODELED
DATA ITEM INDICES USED BY PRED ARE:
EVENT ID DATA ITEM IS DATA ITEM NO.: 8
TIME DATA ITEM IS DATA ITEM NO.: 2
DOSE AMOUNT DATA ITEM IS DATA ITEM NO.: 3
DOSE RATE DATA ITEM IS DATA ITEM NO.: 4
COMPT. NO. DATA ITEM IS DATA ITEM NO.: 5
PK SUBROUTINE CALLED WITH EVERY EVENT RECORD.
PK SUBROUTINE NOT CALLED AT NONEVENT (ADDITIONAL OR LAGGED) DOSE TIMES.
DURING SIMULATION, ERROR SUBROUTINE CALLED WITH EVERY EVENT RECORD.
OTHERWISE, ERROR SUBROUTINE CALLED ONCE IN THIS PROBLEM.
DES SUBROUTINE USES COMPACT STORAGE MODE.
#TBLN: 1
#METH: First Order
ESTIMATION STEP OMITTED: NO
ANALYSIS TYPE: POPULATION
NUMBER OF SADDLE POINT RESET ITERATIONS: 0
GRADIENT METHOD USED: NOSLOW
EPS-ETA INTERACTION: NO
NO. OF FUNCT. EVALS. ALLOWED: 9999
NO. OF SIG. FIGURES REQUIRED: 3
INTERMEDIATE PRINTOUT: YES
ESTIMATE OUTPUT TO MSF: NO
IND. OBJ. FUNC. VALUES SORTED: NO
NUMERICAL DERIVATIVE
FILE REQUEST (NUMDER): NONE
MAP (ETAHAT) ESTIMATION METHOD (OPTMAP): 0
ETA HESSIAN EVALUATION METHOD (ETADER): 0
INITIAL ETA FOR MAP ESTIMATION (MCETA): 0
SIGDIGITS FOR MAP ESTIMATION (SIGLO): 100
GRADIENT SIGDIGITS OF
FIXED EFFECTS PARAMETERS (SIGL): 100
NOPRIOR SETTING (NOPRIOR): OFF
NOCOV SETTING (NOCOV): OFF
DERCONT SETTING (DERCONT): OFF
FINAL ETA RE-EVALUATION (FNLETA): ON
EXCLUDE NON-INFLUENTIAL (NON-INFL.) ETAS
IN SHRINKAGE (ETASTYPE): NO
NON-INFL. ETA CORRECTION (NONINFETA): OFF
RAW OUTPUT FILE (FILE): PK34.ext
EXCLUDE TITLE (NOTITLE): NO
EXCLUDE COLUMN LABELS (NOLABEL): NO
FORMAT FOR ADDITIONAL FILES (FORMAT): S1PE12.5
PARAMETER ORDER FOR OUTPUTS (ORDER): TSOL
WISHART PRIOR DF INTERPRETATION (WISHTYPE):0
KNUTHSUMOFF: 0
INCLUDE LNTWOPI: NO
INCLUDE CONSTANT TERM TO PRIOR (PRIORC): NO
INCLUDE CONSTANT TERM TO OMEGA (ETA) (OLNTWOPI):NO
ADDITIONAL CONVERGENCE TEST (CTYPE=4)?: NO
EM OR BAYESIAN METHOD USED: NONE
TOLERANCES FOR ESTIMATION/EVALUATION STEP:
NRD (RELATIVE) VALUE(S) OF TOLERANCE: 6
ANRD (ABSOLUTE) VALUE(S) OF TOLERANCE: 12
TOLERANCES FOR COVARIANCE STEP:
NRD (RELATIVE) VALUE(S) OF TOLERANCE: 6
ANRD (ABSOLUTE) VALUE(S) OF TOLERANCE: 12
THE FOLLOWING LABELS ARE EQUIVALENT
PRED=NPRED
RES=NRES
WRES=NWRES
IWRS=NIWRES
IPRD=NIPRED
IRS=NIRES
MONITORING OF SEARCH:
ITERATION NO.: 0 OBJECTIVE VALUE: 24295395.2609277 NO. OF FUNC. EVALS.: 8
CUMULATIVE NO. OF FUNC. EVALS.: 8
NPARAMETR: 1.5000E+01 3.0000E+00 5.0000E-01 1.0000E-02 3.0000E-03 3.0000E-01 1.0000E-01
PARAMETER: 1.0000E-01 1.0000E-01 1.0000E-01 1.0000E-01 1.0000E-01 1.0000E-01 1.0000E-01
GRADIENT: -1.6717E+08 -5.4465E+07 2.1578E+08 4.9026E+06 -4.8134E+07 9.7933E+07 -4.8586E+07
ITERATION NO.: 39 OBJECTIVE VALUE: -214.894944711757 NO. OF FUNC. EVALS.: 414
CUMULATIVE NO. OF FUNC. EVALS.: 422
NPARAMETR: 1.4118E+01 2.9669E+00 4.4572E-01 8.3276E-03 3.0861E-03 6.3233E-02 2.3467E-03
PARAMETER: 3.9363E-02 8.8922E-02 -1.4925E-02 -8.3110E-02 1.2829E-01 -1.4569E+00 -1.7761E+00
GRADIENT: 6.1245E-02 5.4563E-02 -6.6534E-02 -2.9759E-02 1.1708E-03 -9.9369E-02 8.2812E-03
#TERM:
MINIMIZATION SUCCESSFUL
HOWEVER, PROBLEMS OCCURRED WITH THE MINIMIZATION.
REGARD THE RESULTS OF THE ESTIMATION STEP CAREFULLY, AND ACCEPT THEM ONLY
AFTER CHECKING THAT THE COVARIANCE STEP PRODUCES REASONABLE OUTPUT.
NO. OF FUNCTION EVALUATIONS USED: 422
NO. OF SIG. DIGITS IN FINAL EST.: 3.4
TOTAL DATA POINTS NORMALLY DISTRIBUTED (N): 38
N*LOG(2PI) CONSTANT TO OBJECTIVE FUNCTION: 69.839328523555125
OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT: -214.89494471175738
OBJECTIVE FUNCTION VALUE WITH CONSTANT: -145.05561618820224
REPORTED OBJECTIVE FUNCTION DOES NOT CONTAIN CONSTANT
TOTAL EFFECTIVE ETAS (NIND*NETA): 0
#TERE:
Elapsed estimation time in seconds: 0.09
S MATRIX ALGORITHMICALLY SINGULAR
INVERSE COVARIANCE MATRIX SET TO RS*RMAT, WHERE S* IS A PSEUDO INVERSE OF S
Elapsed covariance time in seconds: 0.02
Elapsed postprocess time in seconds: 0.00
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
#OBJT:************** MINIMUM VALUE OF OBJECTIVE FUNCTION ********************
******************** ********************
************************************************************************************************************************
#OBJV:******************************************** -214.895 **************************************************
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** FINAL PARAMETER ESTIMATE ********************
******************** ********************
************************************************************************************************************************
THETA - VECTOR OF FIXED EFFECTS PARAMETERS *********
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6
1.41E+01 2.97E+00 4.46E-01 8.33E-03 3.09E-03 6.32E-02
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
ETA1
ETA1 0.00E+00
SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
EPS1
EPS1 2.35E-03
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
ETA1
ETA1 0.00E+00
SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
EPS1
EPS1 4.84E-02
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** STANDARD ERROR OF ESTIMATE ********************
******************** ********************
************************************************************************************************************************
THETA - VECTOR OF FIXED EFFECTS PARAMETERS *********
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6
2.50E-01 1.34E-02 2.03E-03 3.80E-04 7.34E-05 3.17E-05
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
ETA1
ETA1 .........
SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
EPS1
EPS1 2.26E-04
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
ETA1
ETA1 .........
SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
EPS1
EPS1 2.33E-03
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** COVARIANCE MATRIX OF ESTIMATE ********************
******************** ********************
************************************************************************************************************************
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6 OM11 SG11
TH 1 6.26E-02
TH 2 3.36E-03 1.80E-04
TH 3 5.07E-04 2.72E-05 4.10E-06
TH 4 9.50E-05 5.10E-06 7.69E-07 1.44E-07
TH 5 1.84E-05 9.85E-07 1.49E-07 2.79E-08 5.38E-09
TH 6 7.93E-06 4.25E-07 6.42E-08 1.20E-08 2.32E-09 1.01E-09
OM11 ......... ......... ......... ......... ......... ......... .........
SG11 -5.66E-05 -3.03E-06 -4.58E-07 -8.58E-08 -1.66E-08 -7.16E-09 ......... 5.11E-08
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** CORRELATION MATRIX OF ESTIMATE ********************
******************** ********************
************************************************************************************************************************
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6 OM11 SG11
TH 1 2.50E-01
TH 2 1.00E+00 1.34E-02
TH 3 1.00E+00 1.00E+00 2.03E-03
TH 4 1.00E+00 1.00E+00 1.00E+00 3.80E-04
TH 5 1.00E+00 1.00E+00 1.00E+00 1.00E+00 7.34E-05
TH 6 9.99E-01 9.99E-01 9.99E-01 9.98E-01 9.98E-01 3.17E-05
OM11 ......... ......... ......... ......... ......... ......... .........
SG11 -1.00E+00 -1.00E+00 -1.00E+00 -1.00E+00 -1.00E+00 -9.99E-01 ......... 2.26E-04
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** INVERSE COVARIANCE MATRIX OF ESTIMATE ********************
******************** ********************
************************************************************************************************************************
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6 OM11 SG11
TH 1 2.60E+00
TH 2 6.64E+01 1.70E+03
TH 3 -1.31E+02 -3.35E+03 6.61E+03
TH 4 -5.05E+03 -1.29E+05 2.55E+05 9.81E+06
TH 5 3.40E+03 8.68E+04 -1.71E+05 -6.60E+06 4.44E+06
TH 6 -4.94E+03 -1.26E+05 2.49E+05 9.60E+06 -6.46E+06 9.39E+06
OM11 ......... ......... ......... ......... ......... ......... .........
SG11 4.71E+03 1.20E+05 -2.37E+05 -9.15E+06 6.15E+06 -8.95E+06 ......... 8.53E+06
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** EIGENVALUES OF COR MATRIX OF ESTIMATE ********************
******************** ********************
************************************************************************************************************************
1 2 3 4 5 6 7
-1.91E-16 2.25E-15 -3.56E-15 1.05E-14 -1.51E-14 2.54E-03 7.00E+00
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** R MATRIX ********************
******************** ********************
************************************************************************************************************************
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6 OM11 SG11
TH 1 6.09E+01
TH 2 -4.10E+01 2.17E+03
TH 3 -2.19E+03 1.31E+03 9.44E+04
TH 4 -6.57E+03 -4.78E+04 2.53E+05 5.04E+06
TH 5 7.35E+02 2.58E+04 -5.77E+04 -2.30E+06 2.47E+06
TH 6 -1.69E+03 -7.40E+04 8.00E+04 4.20E+06 -2.26E+06 4.47E+06
OM11 ......... ......... ......... ......... ......... ......... .........
SG11 3.93E+02 -1.45E+03 -2.19E+04 -1.80E+05 9.30E+04 -1.02E+05 ......... 3.45E+06
************************************************************************************************************************
******************** ********************
******************** FIRST ORDER ********************
******************** S MATRIX ********************
******************** ********************
************************************************************************************************************************
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6 OM11 SG11
TH 1 5.89E+01
TH 2 2.51E+01 1.07E+01
TH 3 -1.85E+03 -7.85E+02 5.79E+04
TH 4 1.12E+03 4.75E+02 -3.50E+04 2.12E+04
TH 5 -2.85E+03 -1.21E+03 8.94E+04 -5.41E+04 1.38E+05
TH 6 2.59E+03 1.10E+03 -8.13E+04 4.92E+04 -1.26E+05 1.14E+05
OM11 ......... ......... ......... ......... ......... ......... .........
SG11 -6.22E+03 -2.64E+03 1.95E+05 -1.18E+05 3.01E+05 -2.74E+05 ......... 6.56E+05
Elapsed finaloutput time in seconds: 0.01
#CPUT: Total CPU Time in Seconds, 0.172