knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) library(mets)
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.
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)
sessionInfo()
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