vignettes/while-alive.Rmd
while-alive.Rmd
We consider two while-alive estimands for recurrent events data and the mean of the subject specific events per time-unit 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
data(hfactioncpx12)
dtable(hfactioncpx12,~status)
#>
#> status
#> 0 1 2
#> 617 1391 124
dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,death.code=2)
summary(dd)
#> While-Alive summaries:
#>
#> RMST, E(min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 1.859 0.02108 1.817 1.900 0
#> treatment1 1.924 0.01502 1.894 1.953 0
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... -0.06517 0.02588 -0.1159 -0.01444 0.0118
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> mean events, E(N(min(D,t))):
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 1.572 0.09573 1.384 1.759 1.375e-60
#> treatment1 1.453 0.10315 1.251 1.656 4.376e-45
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... 0.1185 0.1407 -0.1574 0.3943 0.4
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> _______________________________________________________
#> Ratio of means E(N(min(D,t)))/E(min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 0.8457 0.05264 0.7425 0.9488 4.411e-58
#> treatment1 0.7555 0.05433 0.6490 0.8619 5.963e-44
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... 0.09022 0.07565 -0.05805 0.2385 0.233
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> _______________________________________________________
#> Mean of Events per time-unit E(N(min(D,t))/min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treat0 1.0725 0.1222 0.8331 1.3119 1.645e-18
#> treat1 0.7552 0.0643 0.6291 0.8812 7.508e-32
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treat0] - [treat1] 0.3173 0.1381 0.04675 0.5879 0.02153
#>
#> Null Hypothesis:
#> [treat0] - [treat1] = 0
dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,
death.code=2,trans=.333)
summary(dd,type="log")
#> While-Alive summaries, log-scale:
#>
#> RMST, E(min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 0.6199 0.011340 0.5977 0.6421 0
#> treatment1 0.6543 0.007807 0.6390 0.6696 0
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... -0.03446 0.01377 -0.06145 -0.007478 0.01231
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> mean events, E(N(min(D,t))):
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 0.4523 0.06090 0.3329 0.5716 1.119e-13
#> treatment1 0.3739 0.07097 0.2348 0.5130 1.376e-07
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... 0.07835 0.09352 -0.1049 0.2616 0.4022
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> _______________________________________________________
#> Ratio of means E(N(min(D,t)))/E(min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treatment0 -0.1676 0.06224 -0.2896 -0.04563 7.081e-03
#> treatment1 -0.2804 0.07192 -0.4214 -0.13947 9.651e-05
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treatment0] - [treat.... 0.1128 0.09511 -0.07361 0.2992 0.2356
#>
#> Null Hypothesis:
#> [treatment0] - [treatment1] = 0
#> _______________________________________________________
#> Mean of Events per time-unit E(N(min(D,t))/min(D,t))
#> Estimate Std.Err 2.5% 97.5% P-value
#> treat0 -0.3833 0.04939 -0.4801 -0.2865 8.487e-15
#> treat1 -0.5380 0.05666 -0.6491 -0.4270 2.191e-21
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> [treat0] - [treat1] 0.1548 0.07517 0.007459 0.3021 0.03948
#>
#> Null Hypothesis:
#> [treat0] - [treat1] = 0
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
,
for example,
where
are the marks related to
and are
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)
sessionInfo()
#> R version 4.5.1 (2025-06-13)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.3 LTS
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#> Matrix products: default
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#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
#> [4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
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#>
#> time zone: UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
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#> other attached packages:
#> [1] mets_1.3.7
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#> loaded via a namespace (and not attached):
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#> [37] tools_4.5.1 globals_0.18.0 survival_3.8-3
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