---
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 laste mean of events per time-unit it has been seen that when the sample size is to great
it can improve the finite sample properties to employ a transformation such as $\sqrt$ or cube-root, and
thus consider 
\begin{align*}
 E( (\frac{N(D \wedge t)}{D \wedge t})^.33 ) 
\end{align*}

```{r}
data(hfaction_cpx12)

dtable(hfaction_cpx12,~status)
dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfaction_cpx12,time=2,death.code=2)
summary(dd)

dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfaction_cpx12,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.

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


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