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execute_all_methods.R
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# Author: Elizabeth Handorf
# Supplemental R code for
# "Analysis of survival data with non-proportional hazards:
# A comparison of propensity score weighted methods"
# 2020-07-07
# Function which runs every survival method on either the simulated data
# or the bootstrap sample
runAllMethods<-function(data,d) {
methods<-c("NUA","NCM","WKM","CTV_LT","CTV_LPW","AFT_GG","AFT_WBL_LS","PO")
dat<-data[d,]
last.obs.time<-min(c(max(dat$time[dat$trt==0&dat$fail==1]),max(dat$time[dat$trt==1&dat$fail==1])))
#Initalize tables of results of interest
res.median<-res.RMS<-res.2y<-res.5y<-res.10y<-matrix(rep(NA,2*length(methods)),ncol=2)
############# Estimate propensity score weights #########
ps.mod<-glm(trt~age+as.factor(charlson)+male+low.stage+high.grade+histology+white+hispanic+
as.factor(facility)+as.factor(income)+as.factor(education)+as.factor(insurance),
data=dat, family="binomial")
dat$ps.pred<-fitted.values(ps.mod)
pr.trt<-sum(dat$trt)/length(dat$trt)
#Variance-stabilized weights
#dat$ps.IPTW<-pr.trt*dat$trt*1/dat$ps.pred + (1-pr.trt)*(!dat$trt)*1/(1-dat$ps.pred)
#Standard weights
dat$ps.IPTW<-dat$trt*1/dat$ps.pred + (!dat$trt)*1/(1-dat$ps.pred)
########## 1. Naive (unadjusted) results from observed data only
########################
#start.time<-Sys.time()
i<-match("NUA",methods) #Index number of this method
#Unadjusted observed survival curves
S.obs<-survfit(Surv(time,fail)~trt, data=dat)
#medians
res.median[i,]<-as.numeric(summary(S.obs)$table[,'median'])
#RMS
res.RMS[i,]<-as.numeric(summary(S.obs,rmean=last.obs.time)$table[,'*rmean'])
#Survival
surv.prs<-matrix(as.numeric(summary(S.obs,times=c(2,5,10))$surv),nrow=3)
res.2y[i,]<-surv.prs[1,]
res.5y[i,]<-surv.prs[2,]
res.10y[i,]<-surv.prs[3,]
#end.time<-Sys.time()
#print(end.time-start.time)
############## 2. Naive cox model #########################
#start.time<-Sys.time()
i<-match("NCM",methods) #Index number of this method
NCM.mod<-coxph(Surv(time,fail)~trt, weights=ps.IPTW, data=dat, robust=TRUE)
s.NCM.trt0<-survfit(NCM.mod,newdata= data.frame(trt=0))
s.NCM.trt1<-survfit(NCM.mod,newdata= data.frame(trt=1))
#medians
res.median[i,1]<-as.numeric(summary(s.NCM.trt0)$table['median'])
res.median[i,2]<-as.numeric(summary(s.NCM.trt1)$table['median'])
#RMS
res.RMS[i,1]<-as.numeric(summary(s.NCM.trt0,rmean=last.obs.time)$table['*rmean'])
res.RMS[i,2]<-as.numeric(summary(s.NCM.trt1,rmean=last.obs.time)$table['*rmean'])
#Survival
surv0.prs<-matrix(as.numeric(summary(s.NCM.trt0,times=c(2,5,10))$surv),nrow=3)
surv1.prs<-matrix(as.numeric(summary(s.NCM.trt1,times=c(2,5,10))$surv),nrow=3)
res.2y[i,1]<-surv0.prs[1,]
res.5y[i,1]<-surv0.prs[2,]
res.10y[i,1]<-surv0.prs[3,]
res.2y[i,2]<-surv1.prs[1,]
res.5y[i,2]<-surv1.prs[2,]
res.10y[i,2]<-surv1.prs[3,]
#end.time<-Sys.time()
#print(end.time-start.time)
############## 3. Weighted Kaplan-Meier curves
#start.time<-Sys.time()
i<-match("WKM",methods) #Index number of this method
S.WKM<-survfit(Surv(time,fail)~trt, data=dat, weights=ps.IPTW)
#medians
res.median[i,]<-as.numeric(summary(S.WKM)$table[,'median'])
#RMS
res.RMS[i,]<-as.numeric(summary(S.WKM,rmean=last.obs.time)$table[,'*rmean'])
#Survival
surv.prs<-matrix(as.numeric(summary(S.WKM,times=c(2,5,10))$surv),nrow=3)
res.2y[i,]<-surv.prs[1,]
res.5y[i,]<-surv.prs[2,]
res.10y[i,]<-surv.prs[3,]
#end.time<-Sys.time()
#print(end.time-start.time)
################## 4. Cox model with TV effect of log-time
#start.time<-Sys.time()
i<-match("CTV_LT",methods) #Index number of this method
#Split the dataset at the failure times - too computationally burdensome
#cut.points <- unique(dat$time[dat$fail == 1])
#Split at 1-month increments
cut.points<-seq(from=0,to=15,by=1/12)
SURV2 <- survSplit(data = dat, cut = cut.points, end = "time",
start = "time0", event = "fail")
SURV2$trtLT <-SURV2$trt*log(SURV2$time)
#Remove very small time differences - these cause errors
tdiff<-(SURV2$time-SURV2$time0)
SURV2<-SURV2[tdiff>10^-5,]
CTV.mod<-coxph(Surv(time0,time,fail)~trt+trtLT,data=SURV2, weights=ps.IPTW)
#Fitted curves from this cox model
#Get a list of all the time intervals (from the pt with longest follow-up)
last <- SURV2$ID[which.max(SURV2$time)]
intervals <- SURV2[SURV2$ID == last, c("time0", "time", "fail")]
#curve for control
covs<-data.frame(trt = 0, intervals)
covs$trtLT <- covs$trt * log(covs$time)
s.CTV.trt0<-survfit(CTV.mod, newdata = covs, individual = TRUE)
#redo for treated
covs<-data.frame(trt = 1, intervals)
covs$trtLT <- covs$trt * log(covs$time)
s.CTV.trt1<-survfit(CTV.mod, newdata = covs, individual = TRUE)
#medians
res.median[i,1]<-as.numeric(summary(s.CTV.trt0)$table['median'])
res.median[i,2]<-as.numeric(summary(s.CTV.trt1)$table['median'])
#RMS
res.RMS[i,1]<-as.numeric(summary(s.CTV.trt0,rmean=last.obs.time)$table['*rmean'])
res.RMS[i,2]<-as.numeric(summary(s.CTV.trt1,rmean=last.obs.time)$table['*rmean'])
#Survival
surv0.prs<-matrix(as.numeric(summary(s.CTV.trt0,times=c(2,5,10))$surv),nrow=3)
surv1.prs<-matrix(as.numeric(summary(s.CTV.trt1,times=c(2,5,10))$surv),nrow=3)
res.2y[i,1]<-surv0.prs[1,]
res.5y[i,1]<-surv0.prs[2,]
res.10y[i,1]<-surv0.prs[3,]
res.2y[i,2]<-surv1.prs[1,]
res.5y[i,2]<-surv1.prs[2,]
res.10y[i,2]<-surv1.prs[3,]
#end.time<-Sys.time()
#print(end.time-start.time)
################## 5. Cox model with piecewise TV effect
#start.time<-Sys.time()
i<-match("CTV_LPW",methods) #Index number of this method
#Split the dataset at times 2 and 5
cut.points <- c(2,5)
SURV2 <- survSplit(data = dat, cut = cut.points, end = "time",
start = "time0", event = "fail")
#Remove very small time differences - these cause errors
tdiff<-(SURV2$time-SURV2$time0)
SURV2<-SURV2[tdiff>10^-5,]
SURV2$trt_2y <-SURV2$trt*as.numeric(SURV2$time0==2)
SURV2$trt_5y <-SURV2$trt*as.numeric(SURV2$time0==5)
CTV.mod.LPW<-coxph(Surv(time0,time,fail)~trt+trt_2y+trt_5y,data=SURV2, weights=ps.IPTW)
#Fitted curves from this cox model
#Get a list of all the time intervals (from the pt with longest follow-up)
last <- SURV2$ID[which.max(SURV2$time)]
intervals <- SURV2[SURV2$ID == last, c("time0", "time", "fail")]
#curve for control
covs<-data.frame(trt = 0, intervals)
covs$trt_2y <- covs$trt * as.numeric(covs$time0==2)
covs$trt_5y <- covs$trt * as.numeric(covs$time0==5)
s.CTV.trt0<-survfit(CTV.mod.LPW, newdata = covs, individual = TRUE)
#redo for treated
covs<-data.frame(trt = 1, intervals)
covs$trt_2y <- covs$trt * as.numeric(covs$time0==2)
covs$trt_5y <- covs$trt * as.numeric(covs$time0==5)
s.CTV.trt1<-survfit(CTV.mod.LPW, newdata = covs, individual = TRUE)
#medians
res.median[i,1]<-as.numeric(summary(s.CTV.trt0)$table['median'])
res.median[i,2]<-as.numeric(summary(s.CTV.trt1)$table['median'])
#RMS
res.RMS[i,1]<-as.numeric(summary(s.CTV.trt0,rmean=last.obs.time)$table['*rmean'])
res.RMS[i,2]<-as.numeric(summary(s.CTV.trt1,rmean=last.obs.time)$table['*rmean'])
#Survival
surv0.prs<-matrix(as.numeric(summary(s.CTV.trt0,times=c(2,5,10))$surv),nrow=3)
surv1.prs<-matrix(as.numeric(summary(s.CTV.trt1,times=c(2,5,10))$surv),nrow=3)
res.2y[i,1]<-surv0.prs[1,]
res.5y[i,1]<-surv0.prs[2,]
res.10y[i,1]<-surv0.prs[3,]
res.2y[i,2]<-surv1.prs[1,]
res.5y[i,2]<-surv1.prs[2,]
res.10y[i,2]<-surv1.prs[3,]
#end.time<-Sys.time()
#print(end.time-start.time)
################## 6. parametric AFT model - Generalized Gamma
#start.time<-Sys.time()
i<-match("AFT_GG",methods) #Index number of this method
aft.ggam.mod<-flexsurvreg(Surv(time,fail)~as.factor(trt), data=dat, weights = ps.IPTW, dist="gengamma")
#Median
medians<-summary(aft.ggam.mod, fn = median.ggam, t = 1, B = 10000) #Helper function defined above
res.median[i,1]<-medians[['as.factor(trt)=0']]$est
res.median[i,2]<-medians[['as.factor(trt)=1']]$est
#Mean restricted survival time
rmst<-summary(aft.ggam.mod, fn = rmst_gengamma, t = last.obs.time, B = 10000)
res.RMS[i,1]<-rmst[['as.factor(trt)=0']]$est
res.RMS[i,2]<-rmst[['as.factor(trt)=1']]$est
#predicted survival function
sum.ggam<-summary(aft.ggam.mod, t=c(2,5,10))
res.2y[i,1]<-sum.ggam[['as.factor(trt)=0']]$est[1]
res.5y[i,1]<-sum.ggam[['as.factor(trt)=0']]$est[2]
res.10y[i,1]<-sum.ggam[['as.factor(trt)=0']]$est[3]
res.2y[i,2]<-sum.ggam[['as.factor(trt)=1']]$est[1]
res.5y[i,2]<-sum.ggam[['as.factor(trt)=1']]$est[2]
res.10y[i,2]<-sum.ggam[['as.factor(trt)=1']]$est[3]
#end.time<-Sys.time()
#print(end.time-start.time)
################## 7. parametric AFT model - Weibull allowing location and scale to vary
#start.time<-Sys.time()
i<-match("AFT_WBL_LS",methods) #Index number of this method
aft.wbl.mod.L.S<-flexsurvreg(Surv(time,fail)~as.factor(trt),anc = list(shape = ~ as.factor(trt)),
data=dat, weights = ps.IPTW, dist="weibull")
medians<-summary(aft.wbl.mod.L.S, fn = median.weibull, t = 1, B = 10000)
res.median[i,1]<-medians[['as.factor(trt)=0']]$est
res.median[i,2]<-medians[['as.factor(trt)=1']]$est
#Mean restricted survival time
rmst<-summary(aft.wbl.mod.L.S, fn = rmst_weibull, t = last.obs.time, B = 10000)
res.RMS[i,1]<-rmst[['as.factor(trt)=0']]$est
res.RMS[i,2]<-rmst[['as.factor(trt)=1']]$est
sum.wbl<-summary(aft.wbl.mod.L.S, t=c(2,5,10))
res.2y[i,1]<-sum.wbl[['as.factor(trt)=0']]$est[1]
res.5y[i,1]<-sum.wbl[['as.factor(trt)=0']]$est[2]
res.10y[i,1]<-sum.wbl[['as.factor(trt)=0']]$est[3]
res.2y[i,2]<-sum.wbl[['as.factor(trt)=1']]$est[1]
res.5y[i,2]<-sum.wbl[['as.factor(trt)=1']]$est[2]
res.10y[i,2]<-sum.wbl[['as.factor(trt)=1']]$est[3]
#end.time<-Sys.time()
#print(end.time-start.time)
################## 8. Pseudo-observations method
#start.time<-Sys.time()
i<-match("PO",methods) #Index number of this method
#Find median survival - need to use the whole curve
#pseudo.obs<-pseudosurv(dat$time, dat$fail) #,tmax=cutoffs)
#Too computationally intensive to compute pseudo-obs at each failure
#Instead use 1-month increments
cutoffs<-seq(from=1/12,to=15,by=1/12)
cutoffs.obs<-cutoffs[cutoffs>min(dat$time[dat$fail==1]) & cutoffs<max(dat$time[dat$fail==1])]
pseudo.obs<-pseudosurv(dat$time, dat$fail,tmax=cutoffs.obs)
#get the pseudo-observations
pseudo.obs.mat<-as.matrix(pseudo.obs$pseudo)
#Weight them by the propensity score weights
pseudo.obs.mat.wt<-diag(dat$ps.IPTW)%*%pseudo.obs.mat
#Survival at each time is the average of the weighted pseudo observations
S_t_0<-colSums(pseudo.obs.mat.wt[dat$trt==0,])/dim(dat)[1]
S_t_1<-colSums(pseudo.obs.mat.wt[dat$trt==1,])/dim(dat)[1]
#Find the first time where the survival curve is <0.5
res.median[i,1]<-min(pseudo.obs$time[S_t_0<0.5])
res.median[i,2]<-min(pseudo.obs$time[S_t_1<0.5])
#Pseudo mean - built in function
pseudo.RMS = pseudomean(dat$time, dat$fail,tmax=last.obs.time)
res.RMS[i,1]<-sum(pseudo.RMS[dat$trt==0]*dat$ps.IPTW[dat$trt==0])/dim(dat)[1]
res.RMS[i,2]<-sum(pseudo.RMS[dat$trt==1]*dat$ps.IPTW[dat$trt==1])/dim(dat)[1]
#Survival at specific timepoints
#cutoffs <- c(1:14)
#pseudo.obs<-pseudosurv(dat$time, dat$fail,tmax=cutoffs)
pseudo.obs.df<-data.frame(pseudo.obs$pseudo)
#Directly estimate the probability of surviving to time t
#This is just the mean of the pseudo observations
#Applying propensity score weights
res.2y[i,1]<-sum(pseudo.obs.df$time.2[dat$trt==0]*dat$ps.IPTW[dat$trt==0])/dim(dat)[1]
res.2y[i,2]<-sum(pseudo.obs.df$time.2[dat$trt==1]*dat$ps.IPTW[dat$trt==1])/dim(dat)[1]
res.5y[i,1]<-sum(pseudo.obs.df$time.5[dat$trt==0]*dat$ps.IPTW[dat$trt==0])/dim(dat)[1]
res.5y[i,2]<-sum(pseudo.obs.df$time.5[dat$trt==1]*dat$ps.IPTW[dat$trt==1])/dim(dat)[1]
res.10y[i,1]<-sum(pseudo.obs.df$time.10[dat$trt==0]*dat$ps.IPTW[dat$trt==0])/dim(dat)[1]
res.10y[i,2]<-sum(pseudo.obs.df$time.10[dat$trt==1]*dat$ps.IPTW[dat$trt==1])/dim(dat)[1]
#end.time<-Sys.time()
#print(end.time-start.time)
#Format the results to output
diff.median<-res.median[,2]-res.median[,1]
diff.RMS<-res.RMS[,2]-res.RMS[,1]
diff.2y<-res.2y[,2]-res.2y[,1]
diff.5y<-res.5y[,2]-res.5y[,1]
diff.10y<-res.10y[,2]-res.10y[,1]
res.median<-cbind(res.median,diff.median)
res.RMS<-cbind(res.RMS,diff.RMS)
res.2y<-cbind(res.2y,diff.2y)
res.5y<-cbind(res.5y,diff.5y)
res.10y<-cbind(res.10y,diff.10y)
rownames(res.median)<-rownames(res.RMS)<-rownames(res.2y)<-rownames(res.5y)<-rownames(res.10y)<-methods
colnames(res.median)<-colnames(res.RMS)<-colnames(res.2y)<-colnames(res.5y)<-colnames(res.10y)<-c("Untreated","Treated","Difference")
return(list(res.median,res.RMS,res.2y,res.5y,res.10y))
}
#Helper functions
median.ggam <- function(mu, sigma, Q) {qgengamma(0.5, mu = mu, sigma = sigma,
Q=Q)}
median.weibull <- function(shape, scale) { qweibull(0.5, shape = shape, scale = scale)}