knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) library(mets)
Regression for rmst outcome $E(T \wedge t | X) = exp(X^T \beta)$ based on IPCW adjustment for censoring, thus solving the estimating equation \begin{align} & X^T [ (T \wedge t) \frac{I(C > T \wedge t)}{G_C(T \wedge t,X)} - exp(X^T \beta) ] = 0 . \end{align} This is done with the resmeanIPCW function. For fully saturated model with full censoring model this is equal to the integrals of the Kaplan-Meier estimators as illustrated below.
We can also compute the integral of the Kaplan-Meier or Cox based survival estimator to get the RMST (with the resmean.phreg function) [ \int_0^t S(s|X) ds ].
For competing risks the years lost can be computed via cumulative incidence functions (cif.yearslost)
or as IPCW estimator since
[ E( I(\epsilon=1) ( t - T \wedge t ) | X) = \int_0^t F_1(s) ds. ]
For fully saturated model with full censoring model these estimators are equivalent as illustrated below.
set.seed(100) data(bmt); bmt$time <- bmt$time+runif(nrow(bmt))*0.001 # E( min(T;t) | X ) = exp( a+b X) with IPCW estimation out <- resmeanIPCW(Event(time,cause!=0)~tcell+platelet+age,bmt, time=50,cens.model=~strata(platelet),model="exp") summary(out) ### same as Kaplan-Meier for full censoring model bmt$int <- with(bmt,strata(tcell,platelet)) out <- resmeanIPCW(Event(time,cause!=0)~-1+int,bmt,time=30, cens.model=~strata(platelet,tcell),model="lin") estimate(out) out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet),data=bmt) rm1 <- resmean.phreg(out1,times=30) summary(rm1) ## competing risks years-lost for cause 1 out <- resmeanIPCW(Event(time,cause)~-1+int,bmt,time=30,cause=1, cens.model=~strata(platelet,tcell),model="lin") estimate(out) ## same as integrated cumulative incidence rmc1 <- cif.yearslost(Event(time,cause)~strata(tcell,platelet),data=bmt,times=30,cause=1) summary(rmc1) ## plotting the years lost for different horizon's and the two causes par(mfrow=c(1,3)) plot(rm1,years.lost=TRUE,se=1) ## cause refers to column of cumhaz for the different causes plot(rmc1,cause=1,se=1) plot(rmc1,cause=2,se=1)
Computes average treatment effect for restricted mean survival and years lost in competing risks situation
dfactor(bmt) <- tcell~tcell bmt$event <- (bmt$cause!=0)*1 out <- resmeanATE(Event(time,event)~tcell+platelet,data=bmt,time=40,treat.model=tcell~platelet) summary(out) out1 <- resmeanATE(Event(time,cause)~tcell+platelet,data=bmt,cause=1,outcome="rmst-cause", time=40,treat.model=tcell~platelet) summary(out1) out2 <- resmeanATE(Event(time,cause)~tcell+platelet,data=bmt,cause=2,outcome="rmst-cause", time=40,treat.model=tcell~platelet) summary(out2)
sessionInfo()
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