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Compare Milestone Survival Probabilities Between Two Groups

Source: R/milestone_fast.R
milestone_fast.Rd

Compares the Kaplan-Meier survival probabilities of two groups at a prespecified milestone timepoint. The point estimate of interest is the difference in milestone survival, treatment minus control. Three inference methods are provided. The "wald" method uses the unpooled Greenwood variance directly. The "loglog" and "mover" methods build the confidence interval for the difference with the method of variance estimates recovery (MOVER), recovering the variance from the one-sample complementary log-log and log transformed confidence intervals respectively. See Tang (2021) for the MOVER difference interval and Tang (2022) for the use of milestone survival in trial design.

Usage

milestone_fast(
  time,
  event,
  group,
  control,
  side = 2,
  conf.level = 0.95,
  tau,
  method = c("wald", "loglog", "mover"),
  presorted = FALSE
)

Arguments

time

A numeric vector of follow-up times.

event

An integer vector of event indicators, 1 for an event and 0 for a censored observation.

group

A vector with exactly two distinct values identifying the group.

control

The value of group that denotes the control group. The other value is the treatment group and the difference is reported as treatment minus control.

side

1 for a one-sided test in the direction of treatment benefit (treatment milestone survival larger than control) or 2 for a two-sided test (default 2). The confidence interval is always reported as a two-sided interval at conf.level.

conf.level

The confidence level for the reported intervals.

tau

The milestone timepoint at which the survival probabilities are compared. A single positive number.

method

The inference method for the difference in milestone survival, one of "wald", "loglog", or "mover".

presorted

Logical. If TRUE the input is assumed to be sorted by time in ascending order and the internal sort is skipped. This is intended for repeated calls inside simulation loops.

Value

An object of class "milestone_fast", a list with the per-group milestone survival estimates and standard errors, the difference estimate with its confidence interval, the test statistic, and the p-value.

References

Tang, Y. (2021). Some new confidence intervals for Kaplan-Meier based estimators from one and two sample survival data. Statistics in Medicine, 40(23), 4961-4976.

Tang, Y. (2022). Complex survival trial design by the product integration method. Statistics in Medicine, 41(4), 798-814.

Examples

set.seed(1)
time <- c(rexp(50, 0.1), rexp(50, 0.07))
event <- rep(1, 100)
group <- rep(c(0, 1), each = 50)
milestone_fast(time, event, group, control = 0, tau = 10, method = "loglog")
#> Milestone survival (two-group)
#> 
#>   tau = 10,  control = 0
#>   method = loglog,  alternative = two.sided
#> 
#>           survival std.err lower 95% upper 95%
#> control       0.42  0.0698    0.2829    0.5510
#> treatment     0.56  0.0702    0.4124    0.6842
#> 
#>                                      Est. lower 95% upper 95%      z Pr(>|z|)
#> difference (treatment - control)  0.14000  -0.05738   0.32500 -1.395    0.163