---
title: "While Alive estimands for Recurrent Events"
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{While Alive estimands for Recurrent Events}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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


While Alive estimands for Recurrent Events
==========================================

We consider two while-alive estimands for recurrent events data
\begin{align*}
 \frac{E(N(D \wedge t))}{E(D \wedge t)}
\end{align*}
and the mean of the subject specific events per time-unit 
\begin{align*}
 E( \frac{N(D \wedge t)}{D \wedge t} ) 
\end{align*}
for two treatment-groups in the case of an RCT. 
For the mean of events per time-unit it has been seen that when the sample size is small 
one can improve the finite sample properties by employing a transformation such as square or cube-root, and
thus consider 
\begin{align*}
 E( (\frac{N(D \wedge t)}{D \wedge t})^.33 ) 
\end{align*}

```{r while-alive}
data(hfactioncpx12)

dtable(hfactioncpx12,~status)
dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,death.code=2)
summary(dd)

dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,
		   death.code=2,trans=.333)
summary(dd,type="log")

```

We see that the ratio of means are not very different, but that the subject specific 
mean of events per time-unit shows that those on the active treatment has fewer events per time-unit on average. 


Composite outcomes involving death and marks 
============================================

The number of events can be generalized in various ways by using other outcomes than $N(D \wedge t)$, for example,  
\begin{align*}
 \tilde N(D \wedge t) = \int_0^t I(D \geq s) M(s) dN(s)  +  \sum_j  M_j I(D \leq t,\epsilon=j) ) 
\end{align*}
where $M(s)$ are the marks related to $N(s)$ and are $M_j$ marks associated with the different 
causes of the terminal event. This provides an extension of the weighted composite outcomes  measure of Mao & Lin (2022).

The marks (or here weights) can be stochastic if we are couting hosptial expenses, for example, and is 
vector on the data-frame. The marks for the event times (defined through the causes) will then be used. 

Here weighting death with weight 2 and otherwise couting the recurrent of events as before (with weight 1)

```{r wa-composite}
hfactioncpx12$marks <- runif(nrow(hfactioncpx12))

##ddmg <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,
##cause=1:2,death.code=2,marks=hfactioncpx12$marks)
##summary(ddmg)

ddm <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,
cause=1:2,death.code=2,marks=hfactioncpx12$status)

```

SessionInfo
============


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