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Fast weighted Kaplan-Meier (Pepe-Fleming) two-sample test

Source: R/wkm_fast.R
wkm_fast.Rd

Computes the weighted Kaplan-Meier (WKM) statistic of Pepe and Fleming for comparing two survival curves. The statistic is the weighted integral of the difference between the Kaplan-Meier estimates of the treatment and control groups over the observed range, standardized to a Wald z statistic. Unlike weighted log-rank tests, this test targets the integrated difference in survival and is sensitive to differences even when the hazard functions cross. The single scan over the sorted data is performed in C++ for use inside simulation loops.

Usage

wkm_fast(
  time,
  event,
  group,
  control = NULL,
  side = 2,
  conf.level = 0.95,
  weight = c("PF", "sqrtPF", "constant"),
  presorted = FALSE
)

Arguments

time

Numeric vector of event or censoring times.

event

Integer vector, 1 for an event and 0 for censoring.

group

Grouping vector with exactly two distinct levels.

control

The level of group that denotes the control group.

side

Either 2 for a two-sided test or 1 for a one-sided test of treatment superiority (weighted difference greater than 0).

conf.level

Confidence level for the interval of the weighted difference.

weight

Weight function, one of "PF" (Pepe-Fleming combined censoring weight), "sqrtPF" (its square root) or "constant" (weight 1).

presorted

Logical; set to TRUE when time, event and group are already sorted in ascending order of time, to skip the internal sort. Defaults to FALSE.

Value

A named numeric vector of class "wkm_fast" with the weighted integrated difference, its standard error and confidence limits, and the Wald statistics for the test.

Details

The default weight is the Pepe-Fleming combined censoring weight w(t) = n G1(t) G2(t) / (n1 G1(t) + n2 G2(t)), where G1 and G2 are the Kaplan-Meier estimates of the censoring survival functions of the two groups. This weight gives less weight to regions with heavy censoring and stabilizes the variance in the tail. The choice weight = "sqrtPF" uses its square root, and weight = "constant" uses a weight of 1, in which case the numerator reduces to the difference in restricted mean survival time over the observed range. With weight = "PF" the result reproduces nphsim::wkm.Stat for data without tied times.

The weighted difference is computed as treatment minus control, so a positive value and a positive z indicate longer survival under treatment.

References

Pepe, M. S., & Fleming, T. R. (1989). Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. Biometrics, 45(2), 497-507.

Pepe, M. S., & Fleming, T. R. (1991). Weighted Kaplan-Meier statistics: large sample and optimality considerations. Journal of the Royal Statistical Society. Series B (Methodological), 53(2), 341-352.

Examples

set.seed(1)
n <- 300
g <- rep(0:1, each = n / 2)
tt <- c(rexp(n / 2, log(2) / 12), rexp(n / 2, log(2) / 16))
cc <- rexp(n, rate = 0.02)
time <- pmin(tt, cc)
event <- as.integer(tt <= cc)
wkm_fast(time, event, group = g, control = 0)
#> Weighted Kaplan-Meier test (Pepe-Fleming, two-group)
#> 
#>   control = 0
#>   weight = PF,  alternative = two.sided
#> 
#>                                             Est. lower 95% upper 95%     z
#> weighted difference (treatment - control) 2.8030    0.4869    5.1192 2.372
#>                                           Pr(>|z|)  
#> weighted difference (treatment - control)   0.0177 *
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1