In kkholst/mets: Analysis of Multivariate Event Times

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}

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)

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)
summary(ddm)