\input{settings.sty}
\usepackage{Sweave}

 
\begin{document}
\vspace*{2cm}
\begin{center}
{\Large Modeling}\\
~\\
\today\\
~\\
Tim Bergsma\\
\end{center}
\newpage

\section{Purpose}
This script runs NONMEM models and diagnostics for sample phase1 data.
\section{Model Development}
\subsection{Set up for NONMEM run.}
\begin{Schunk}
\begin{Sinput}
> getwd()
\end{Sinput}
\begin{Soutput}
[1] "/home/timb/metrumrg/inst/sample/script"
\end{Soutput}
\begin{Sinput}
> library(metrumrg)
\end{Sinput}
\begin{Soutput}
metrumrg 5.0 
\end{Soutput}
\begin{Sinput}
> command <- '/opt/NONMEM/nm72/nmqual/autolog.pl'
> cat.cov='SEX'
> cont.cov=c('HEIGHT','WEIGHT','AGE')
> par.list=c('CL','Q','KA','V','V2','V3')
> eta.list=paste('ETA',1:10,sep='')
\end{Sinput}
\end{Schunk}
\subsection{Run NONMEM.}
\begin{Schunk}
\begin{Sinput}
> NONR72(
+      run=1005,
+      command=command,
+      project='/home/timb/metrumrg/inst/sample/nonmem',
+      grid=FALSE,
+      nice=TRUE,
+      checkrunno=FALSE,
+      cont.cov=cont.cov,
+      cat.cov=cat.cov,
+      par.list=par.list,
+      eta.list=eta.list,
+      plotfile='/home/timb/metrumrg/inst/sample/nonmem/*/diagnostics.pdf',
+      streams='/home/timb/metrumrg/inst/sample/nonmem/ctl',
+      checksum=FALSE
+ )
> getwd()
\end{Sinput}
\begin{Soutput}
[1] "/home/timb/metrumrg/inst/sample/script"
\end{Soutput}
\end{Schunk}
Covariance succeeded on model 1005.
\section{Predictive Check}
\subsection{Create a simulation control stream.}
Convert control stream to R object.
\begin{Schunk}
\begin{Sinput}
> ctl <- read.nmctl('../nonmem/ctl/1005.ctl')
\end{Sinput}
\end{Schunk}
Strip comments and view.
\begin{Schunk}
\begin{Sinput}
> ctl[] <- lapply(ctl,function(rec)sub(' *;.*','',rec))
> ctl
\end{Sinput}
\begin{Soutput}
 [1] "$PROB 1005 phase1 2 CMT like 1004 but diff. initial on V3"                                   
 [2] "$INPUT C ID TIME SEQ=DROP EVID AMT DV SUBJ HOUR TAFD TAD LDOS MDV HEIGHT WT SEX AGE DOSE FED"
 [3] "$DATA ../../data/derived/phase1.csv IGNORE=C"                                                
 [4] "$SUBROUTINE ADVAN4 TRANS4"                                                                   
 [5] "$PK"                                                                                         
 [6] " CL=THETA(1)*EXP(ETA(1)) * THETA(6)**SEX * (WT/70)**THETA(7)"                                
 [7] " V2 =THETA(2)*EXP(ETA(2))"                                                                   
 [8] " KA=THETA(3)*EXP(ETA(3))"                                                                    
 [9] " Q  =THETA(4)"                                                                               
[10] " V3=THETA(5)"                                                                                
[11] " S2=V2"                                                                                      
[12] " "                                                                                           
[13] "$ERROR"                                                                                      
[14] " Y=F*EXP(ERR(1))"                                                                            
[15] " IPRE=F"                                                                                     
[16] ""                                                                                            
[17] "$THETA"                                                                                      
[18] "(0,10,50)"                                                                                   
[19] "(0,10,100)"                                                                                  
[20] "(0,0.2, 5)"                                                                                  
[21] "(0,10,50)"                                                                                   
[22] "(0,100,1000)"                                                                                
[23] "(0,1,2)"                                                                                     
[24] "(0,0.75,3)"                                                                                  
[25] ""                                                                                            
[26] "$OMEGA 0.09 0.09 0.09"                                                                       
[27] ""                                                                                            
[28] ""                                                                                            
[29] ""                                                                                            
[30] ""                                                                                            
[31] ""                                                                                            
[32] "$SIGMA 0.09"                                                                                 
[33] ""                                                                                            
[34] ""                                                                                            
[35] ""                                                                                            
[36] "$ESTIMATION MAXEVAL=9999 PRINT=5 NOABORT METHOD=1 INTER MSFO=./1005.msf"                     
[37] "$COV PRINT=E"                                                                                
[38] "$TABLE NOPRINT FILE=./1005.tab ONEHEADER ID AMT TIME EVID PRED IPRE CWRES"                   
[39] "$TABLE NOPRINT FILE=./1005par.tab ONEHEADER ID TIME CL Q V2 V3 KA ETA1 ETA2 ETA3"            
[40] ""                                                                                            
[41] ""                                                                                            
[42] ""                                                                                            
[43] ""                                                                                            
[44] ""                                                                                            
[45] ""                                                                                            
[46] ""                                                                                            
[47] ""                                                                                            
[48] ""                                                                                            
[49] ""                                                                                            
[50] ""                                                                                            
[51] ""                                                                                            
[52] ""                                                                                            
\end{Soutput}
\end{Schunk}
Fix records of interest.
\begin{Schunk}
\begin{Sinput}
> ctl$prob
\end{Sinput}
\begin{Soutput}
[1] "1005 phase1 2 CMT like 1004 but diff. initial on V3"
\end{Soutput}
\begin{Sinput}
> ctl$prob <- sub('1005','1105',ctl$prob)
> names(ctl)
\end{Sinput}
\begin{Soutput}
 [1] "prob"       "input"      "data"       "subroutine" "pk"        
 [6] "error"      "theta"      "omega"      "sigma"      "estimation"
[11] "cov"        "table"      "table"     
\end{Soutput}
\begin{Sinput}
> names(ctl)[names(ctl)=='theta'] <- 'msfi'
> ctl$msfi <- '=../1005/1005.msf'
> ctl$omega <- NULL
> ctl$sigma <- NULL
> names(ctl)[names(ctl)=='estimation'] <- 'simulation'
> ctl$simulation <- 'ONLYSIM (1968) SUBPROBLEMS=500'
> ctl$cov <- NULL
> ctl$table <- NULL
> ctl$table <- NULL
> ctl$table <- 'DV NOHEADER NOPRINT FILE=./1105.tab FORWARD NOAPPEND'
> write.nmctl(ctl,'../nonmem/ctl/1105.ctl')
\end{Sinput}
\end{Schunk}
\subsection{Run the simulation.}
This run makes the predictions (simulations).
\begin{Schunk}
\begin{Sinput}
> NONR72(
+      run=1105,
+      command=command,
+      project='../nonmem',
+      grid=FALSE,
+      nice=TRUE,
+      diag=FALSE,
+      streams='../nonmem/ctl',
+      checksum=FALSE
+ )
> getwd()
\end{Sinput}
\begin{Soutput}
[1] "/home/timb/metrumrg/inst/sample/script"
\end{Soutput}
\end{Schunk}
\subsection{Recover and format the original dataset.}
Now we fetch the results and integrate them with the other data.
\begin{Schunk}
\begin{Sinput}
> phase1 <- read.csv('../data/derived/phase1.csv',na.strings='.')
> head(phase1)
\end{Sinput}
\begin{Soutput}
     C ID TIME SEQ EVID  AMT    DV SUBJ HOUR TAFD  TAD LDOS MDV HEIGHT WEIGHT
1    C  1 0.00   0    0   NA 0.000    1 0.00 0.00   NA   NA   0    174   74.2
2 <NA>  1 0.00   1    1 1000    NA    1 0.00 0.00 0.00 1000   1    174   74.2
3 <NA>  1 0.25   0    0   NA 0.363    1 0.25 0.25 0.25 1000   0    174   74.2
4 <NA>  1 0.50   0    0   NA 0.914    1 0.50 0.50 0.50 1000   0    174   74.2
5 <NA>  1 1.00   0    0   NA 1.120    1 1.00 1.00 1.00 1000   0    174   74.2
6 <NA>  1 2.00   0    0   NA 2.280    1 2.00 2.00 2.00 1000   0    174   74.2
  SEX  AGE DOSE FED SMK DS CRCN predose zerodv
1   0 29.1 1000   1   0  0 83.5       1      0
2   0 29.1 1000   1   0  0 83.5       0      0
3   0 29.1 1000   1   0  0 83.5       0      0
4   0 29.1 1000   1   0  0 83.5       0      0
5   0 29.1 1000   1   0  0 83.5       0      0
6   0 29.1 1000   1   0  0 83.5       0      0
\end{Soutput}
\begin{Sinput}
> phase1 <- phase1[is.na(phase1$C),c('SUBJ','TIME','DV')]
> records <- nrow(phase1)
> records
\end{Sinput}
\begin{Soutput}
[1] 550
\end{Soutput}
\begin{Sinput}
> phase1 <- phase1[rep(1:records,500),]
> nrow(phase1)
\end{Sinput}
\begin{Soutput}
[1] 275000
\end{Soutput}
\begin{Sinput}
> phase1$SIM <- rep(1:500,each=records)
> #head(phase1,300)
> with(phase1,DV[SIM==1 & SUBJ==12])
\end{Sinput}
\begin{Soutput}
 [1]     NA  2.260  2.830  8.730 19.300 15.200 16.200  8.830 12.900 12.700
[11]  7.140  5.740  1.980  0.791
\end{Soutput}
\begin{Sinput}
> with(phase1,DV[SIM==2 & SUBJ==12])
\end{Sinput}
\begin{Soutput}
 [1]     NA  2.260  2.830  8.730 19.300 15.200 16.200  8.830 12.900 12.700
[11]  7.140  5.740  1.980  0.791
\end{Soutput}
\end{Schunk}
\subsection{Recover and format the simulation results.}
\begin{Schunk}
\begin{Sinput}
> pred <- scan('../nonmem/1105/1105.tab')
> nrow(phase1)
\end{Sinput}
\begin{Soutput}
[1] 275000
\end{Soutput}
\begin{Sinput}
> length(pred)
\end{Sinput}
\begin{Soutput}
[1] 275000
\end{Soutput}
\end{Schunk}
\subsection{Combine the original data and the simulation data.}
\begin{Schunk}
\begin{Sinput}
> phase1$PRED <- pred
> head(phase1)
\end{Sinput}
\begin{Soutput}
  SUBJ TIME    DV SIM    PRED
2    1 0.00    NA   1 0.00000
3    1 0.25 0.363   1 0.17932
4    1 0.50 0.914   1 0.53642
5    1 1.00 1.120   1 0.78983
6    1 2.00 2.280   1 1.84990
7    1 3.00 1.630   1 1.96530
\end{Soutput}
\begin{Sinput}
> phase1 <- phase1[!is.na(phase1$DV),]
> head(phase1)
\end{Sinput}
\begin{Soutput}
  SUBJ TIME    DV SIM    PRED
3    1 0.25 0.363   1 0.17932
4    1 0.50 0.914   1 0.53642
5    1 1.00 1.120   1 0.78983
6    1 2.00 2.280   1 1.84990
7    1 3.00 1.630   1 1.96530
8    1 4.00 2.040   1 2.01810
\end{Soutput}
\end{Schunk}
\subsection{Plot predictive checks.}
\subsubsection{Aggregate data within subject.}
Since subjects may contribute differing numbers of observations, it may
be useful to look at predictions from a subject-centric perspective.
Therefore, we wish to calculate summary statistics for each subject, 
(observed and predicted) and then make obspred comparisons therewith.
\begin{Schunk}
\begin{Sinput}
> head(phase1)
\end{Sinput}
\begin{Soutput}
  SUBJ TIME    DV SIM    PRED
3    1 0.25 0.363   1 0.17932
4    1 0.50 0.914   1 0.53642
5    1 1.00 1.120   1 0.78983
6    1 2.00 2.280   1 1.84990
7    1 3.00 1.630   1 1.96530
8    1 4.00 2.040   1 2.01810
\end{Soutput}
\begin{Sinput}
> subject <- melt(phase1,measure.var=c('DV','PRED'))
> head(subject)
\end{Sinput}
\begin{Soutput}
  SUBJ TIME SIM variable value
1    1 0.25   1       DV 0.363
2    1 0.50   1       DV 0.914
3    1 1.00   1       DV 1.120
4    1 2.00   1       DV 2.280
5    1 3.00   1       DV 1.630
6    1 4.00   1       DV 2.040
\end{Soutput}
\end{Schunk}
We are going to aggregate each subject's DV and PRED values using cast().
cast() likes an aggregation function that returns a list.
We write one that grabs min med max for each subject, sim, and variable.
\begin{Schunk}
\begin{Sinput}
> metrics <- function(x)list(min=min(x), med=median(x), max=max(x))
\end{Sinput}
\end{Schunk}
Now we cast, ignoring time.
\begin{Schunk}
\begin{Sinput}
> subject <- data.frame(cast(subject, SUBJ + SIM + variable ~ .,fun=metrics))
> head(subject)
\end{Sinput}
\begin{Soutput}
  SUBJ SIM variable      min    med    max
1    1   1       DV 0.363000 1.6100 3.0900
2    1   1     PRED 0.179320 1.9653 5.0314
3    1   2       DV 0.363000 1.6100 3.0900
4    1   2     PRED 0.096462 3.0448 7.4728
5    1   3       DV 0.363000 1.6100 3.0900
6    1   3     PRED 0.450430 5.5284 8.7665
\end{Soutput}
\end{Schunk}
Note that regardless of SIM, DV (observed) is constant.

Now we melt the metrics.
\begin{Schunk}
\begin{Sinput}
> metr <- melt(subject,measure.var=c('min','med','max'),variable_name='metric')
> head(metr)
\end{Sinput}
\begin{Soutput}
  SUBJ SIM variable metric    value
1    1   1       DV    min 0.363000
2    1   1     PRED    min 0.179320
3    1   2       DV    min 0.363000
4    1   2     PRED    min 0.096462
5    1   3       DV    min 0.363000
6    1   3     PRED    min 0.450430
\end{Soutput}
\begin{Sinput}
> metr$value <- reapply(
+ 	metr$value,
+ 	INDEX=metr[,c('SIM','variable','metric')],
+ 	FUN=sort,
+ 	na.last=FALSE
+ )
> metr <- data.frame(cast(metr))
> head(metr)
\end{Sinput}
\begin{Soutput}
  SUBJ SIM metric    DV     PRED
1    1   1    min 0.139 0.064213
2    1   1    med 1.025 1.943600
3    1   1    max 2.530 3.945400
4    1   2    min 0.139 0.016162
5    1   2    med 1.025 1.476300
6    1   2    max 2.530 3.463200
\end{Soutput}
\begin{Sinput}
> nrow(metr)
\end{Sinput}
\begin{Soutput}
[1] 60000
\end{Soutput}
\begin{Sinput}
> metr <- metr[!is.na(metr$DV),]#maybe no NA
> nrow(metr)
\end{Sinput}
\begin{Soutput}
[1] 60000
\end{Soutput}
\end{Schunk}
We plot using lattice.
\begin{Schunk}
\begin{Sinput}
> print(
+ 	xyplot(
+ 		PRED~DV|metric,
+ 		metr,
+ 		groups=SIM,
+ 		scales=list(relation='free'),
+ 		type='l',
+ 		panel=function(...){
+ 			panel.superpose(...)
+ 			panel.abline(0,1,col='white',lwd=2)
+ 		}
+ 	)
+ )
\end{Sinput}
\end{Schunk}
\includegraphics{model-qq}

For detail, we show one endpoint, tossing the outer 5 percent of values, and 
indicating quartiles.
\begin{Schunk}
\begin{Sinput}
> med <- metr[metr$metric=='med',]
> med$metric <- NULL
> head(med)
\end{Sinput}
\begin{Soutput}
   SUBJ SIM    DV     PRED
2     1   1 1.025 1.943600
5     1   2 1.025 1.476300
8     1   3 1.025 1.466300
11    1   4 1.025 1.342400
14    1   5 1.025 1.362350
17    1   6 1.025 0.625815
\end{Soutput}
\begin{Sinput}
> trim <- inner(med, id.var=c('SIM'),measure.var=c('PRED','DV'))
> head(trim)
\end{Sinput}
\begin{Soutput}
  SIM DV PRED
1   1 NA   NA
2   2 NA   NA
3   3 NA   NA
4   4 NA   NA
5   5 NA   NA
6   6 NA   NA
\end{Soutput}
\begin{Sinput}
> nrow(trim)
\end{Sinput}
\begin{Soutput}
[1] 20000
\end{Soutput}
\begin{Sinput}
> trim <- trim[!is.na(trim$DV),]
> nrow(trim)
\end{Sinput}
\begin{Soutput}
[1] 19000
\end{Soutput}
\begin{Sinput}
> head(trim)
\end{Sinput}
\begin{Soutput}
    SIM   DV   PRED
501   1 1.13 1.9653
502   2 1.13 1.5989
503   3 1.13 1.4754
504   4 1.13 1.4074
505   5 1.13 1.3787
506   6 1.13 1.4753
\end{Soutput}
\begin{Sinput}
> print(
+ 	xyplot(
+ 		PRED~DV,
+ 		trim,
+ 		groups=SIM,
+ 		type='l',
+ 		panel=function(x,y,...){
+ 			panel.xyplot(x=x,y=y,...)
+ 			panel.abline(0,1,col='white',lwd=2)
+ 			panel.abline(
+ 				v=quantile(x,probs=c(0.25,0.5,0.75)),
+ 				col='grey',
+ 				lty=2
+ 			)
+ 		}
+ 	)
+ )
\end{Sinput}
\end{Schunk}
\includegraphics{model-qqdetail}

We also show densityplots of predictions at those quartiles.
\begin{Schunk}
\begin{Sinput}
> head(trim)
\end{Sinput}
\begin{Soutput}
    SIM   DV   PRED
501   1 1.13 1.9653
502   2 1.13 1.5989
503   3 1.13 1.4754
504   4 1.13 1.4074
505   5 1.13 1.3787
506   6 1.13 1.4753
\end{Soutput}
\begin{Sinput}
> quantile(trim$DV)
\end{Sinput}
\begin{Soutput}
    0%    25%    50%    75%   100% 
  1.13   7.69  20.25 104.00 332.00 
\end{Soutput}
\begin{Sinput}
> molt <- melt(trim, id.var='SIM')
> head(molt)
\end{Sinput}
\begin{Soutput}
  SIM variable value
1   1       DV  1.13
2   2       DV  1.13
3   3       DV  1.13
4   4       DV  1.13
5   5       DV  1.13
6   6       DV  1.13
\end{Soutput}
\begin{Sinput}
> quart <- data.frame(cast(molt,SIM+variable~.,fun=quantile,probs=c(0.25,0.5,0.75)))
> head(quart)
\end{Sinput}
\begin{Soutput}
  SIM variable      X25.    X50.      X75.
1   1       DV  7.950000 20.2500 100.10000
2   1     PRED 10.329750 22.8675  91.61825
3   2       DV  7.950000 20.2500 100.10000
4   2     PRED 10.241500 23.4225  97.26175
5   3       DV  7.950000 20.2500 100.10000
6   3     PRED  8.081437 20.0330 106.59750
\end{Soutput}
\begin{Sinput}
> molt <- melt(quart,id.var='variable',measure.var=c('X25.','X50.','X75.'),variable_name='quartile')
> head(molt)
\end{Sinput}
\begin{Soutput}
  variable quartile     value
1       DV     X25.  7.950000
2     PRED     X25. 10.329750
3       DV     X25.  7.950000
4     PRED     X25. 10.241500
5       DV     X25.  7.950000
6     PRED     X25.  8.081437
\end{Soutput}
\begin{Sinput}
> levels(molt$quartile)
\end{Sinput}
\begin{Soutput}
[1] "X25." "X50." "X75."
\end{Soutput}
\begin{Sinput}
> levels(molt$quartile) <- c('first quartile','second quartile','third quartile')
> head(molt)
\end{Sinput}
\begin{Soutput}
  variable       quartile     value
1       DV first quartile  7.950000
2     PRED first quartile 10.329750
3       DV first quartile  7.950000
4     PRED first quartile 10.241500
5       DV first quartile  7.950000
6     PRED first quartile  8.081437
\end{Soutput}
\begin{Sinput}
> levels(molt$variable)
\end{Sinput}
\begin{Soutput}
[1] "DV"   "PRED"
\end{Soutput}
\begin{Sinput}
> molt$variable <- factor(molt$variable,levels=c('PRED','DV'))
> print(
+ 	densityplot(
+ 		~value|quartile,
+ 		molt,
+ 		groups=variable,
+ 		layout=c(3,1),
+ 		scales=list(relation='free'),
+ 		aspect=1,
+ 		panel=panel.superpose,
+ 		panel.groups=function(x,...,group.number){
+ 			if(group.number==1)panel.densityplot(x,...)
+ 			if(group.number==2)panel.abline(v=unique(x),...)
+ 		},
+ 		auto.key=TRUE
+ 	)
+ )
\end{Sinput}
\end{Schunk}
\includegraphics{model-qqdensity}
\section{Bootstrap Estimates of Parameter Uncertainty}
\subsection{Create directories.}
\begin{Schunk}
\begin{Sinput}
> getwd()
\end{Sinput}
\begin{Soutput}
[1] "/home/timb/metrumrg/inst/sample/script"
\end{Soutput}
\begin{Sinput}
> dir.create('../nonmem/1005.boot')
> dir.create('../nonmem/1005.boot/data')
> dir.create('../nonmem/1005.boot/ctl')
\end{Sinput}
\end{Schunk}
\subsection{Create replicate control streams.}
\begin{Schunk}
\begin{Sinput}
> t <- metaSub(
+      clear(readLines('../nonmem/ctl/1005.ctl'),';.+',fixed=FALSE),
+      names=1:300,
+      pattern=c(
+          '1005',
+          '../../data/derived/phase1.csv',
+          '$COV',
+          '$TABLE'
+      ),
+      replacement=c(
+          '*',
+          '../data/*.csv',
+          ';$COV',
+          ';$TABLE'
+     ),
+     fixed=TRUE,
+     out='../nonmem/1005.boot/ctl',
+     suffix='.ctl'
+  )
\end{Sinput}
\end{Schunk}
\subsection{Create replicate data sets by resampling original.}
\begin{Schunk}
\begin{Sinput}
>  bootset <- read.csv('../data/derived/phase1.csv')
>  r <- resample(
+  	bootset,
+  	names=1:300,
+  	key='ID',
+  	rekey=TRUE,
+  	out='../nonmem/1005.boot/data',
+  	stratify='SEX'
+  )
\end{Sinput}
\end{Schunk}
\subsection{Run bootstrap models.}
\begin{Schunk}
\begin{Sinput}
> NONR72(
+      run=1:300,
+      command=command,
+      project='../nonmem/1005.boot/',
+      boot=TRUE,
+      nice=TRUE,
+      #grid=TRUE,
+      #concurrent=TRUE,
+      streams='../nonmem/1005.boot/ctl',
+      checksum=FALSE
+ )
\end{Sinput}
\begin{Soutput}
Installing SIGCHLD signal handler...Done.
\end{Soutput}
\begin{Sinput}
> nms <- paste('../nonmem/1005.boot/',1:300,'.boot/',1:300,'.log.xml',sep='')
> while(!(all(file.exists(nms))))Sys.sleep(10)
> boot <- rlog(
+ 	run=1:300,
+ 	project='../nonmem/1005.boot',
+ 	boot=TRUE,
+ 	append=FALSE,
+ 	tool='nm7'
+ )
> write.csv(boot, '../nonmem/1005.boot/log.csv')  
\end{Sinput}
\end{Schunk}
\end{document}
