---
title: "Average treatment effect (ATE) for Restricted mean survival and years lost of Competing risks"
author: Klaus Holst & Thomas Scheike
date: "`r Sys.Date()`"
output:
  rmarkdown::html_vignette:
    fig_caption: yes
    fig_width: 7.15
    fig_height: 5.5        
vignette: >
  %\VignetteIndexEntry{Average treatment effect (ATE) for Restricted mean survival and years lost of Competing risks}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(mets)
```


RMST 
====

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.


```{r}
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)
```

Average treatment effect 
=========================

Computes average treatment effect for restricted mean survival and years lost in competing risks situation

```{r}

 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
============


```{r}
sessionInfo()
```


