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Fast window mean survival time and between-group difference

Source: R/wmst_fast.R
wmst_fast.Rd

Estimates the window mean survival time (WMST) for a single group, or the difference in WMST between a treatment group and a control group, together with standard errors, confidence intervals and a Wald test for the difference. The WMST is the area under the Kaplan-Meier curve between the window limits tau1 and tau2. With tau1 = 0 it is the restricted mean survival time at tau2, and the result then matches survRM2::rmst2. The single scan over the sorted data is performed in C++ for use inside simulation loops.

Usage

wmst_fast(
  time,
  event,
  group = NULL,
  control = NULL,
  tau1 = 0,
  tau2 = NULL,
  side = 2,
  conf.level = 0.95,
  presorted = FALSE,
  data = NULL
)

Arguments

time

Numeric vector of event or censoring times. Alternatively, a formula Surv(time, event) ~ group or Surv(time, event) ~ 1, with the variables in data; see formula_interface.

event

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

group

Optional grouping vector with exactly two distinct levels for a two-group comparison. If omitted, a single-group WMST is returned.

control

The level of group that denotes the control group. Required when group is supplied. With the formula interface it defaults to the first level of the group variable.

tau1

Lower limit of the window. Defaults to 0.

tau2

Upper limit of the window. If omitted, the largest time common to both groups is used (the minimum over groups of the maximum observed time), or the maximum observed time for a single group. A supplied value larger than that gives a warning, because the Kaplan-Meier curve is not estimated beyond it. The window must be finite: when that default is infinite (for example when each group has a subject without a finite event or dropout time in simulated data), tau2 must be supplied.

side

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

conf.level

Confidence level for the intervals.

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. The order is checked, and an error is given when it does not hold.

data

A data frame in which the variables of a formula given as time are evaluated. Used only with the formula interface; see formula_interface.

Value

A named numeric vector of class "wmst_fast". For a single group the elements are the WMST, its standard error and confidence limits. For two groups the elements are the control and treatment WMST values, their difference, the standard errors, the confidence limits and the Wald statistics for the difference. The object also has the class "fastsurv", whose as.data.frame(), coef(), and confint() methods are described in as.data.frame.fastsurv.

Details

The variance of the WMST estimate uses the counting process (Greenwood) form in which each event time at or before tau2 contributes the squared remaining window area. Event times at or before tau1 contribute the full window area, since the hazard before tau1 scales the survival curve throughout the window.

The difference is computed as treatment minus control, so a positive difference indicates a longer mean survival time within the window under treatment.

References

Paukner, M., & Chappell, R. (2021). Window mean survival time. Statistics in Medicine, 40(25), 5521-5533.

Examples

set.seed(1)
n <- 200
g <- rep(0:1, each = n / 2)
tt <- c(rexp(n / 2, 0.1), rexp(n / 2, 0.07))
cc <- rexp(n, rate = 0.02)
time <- pmin(tt, cc)
event <- as.integer(tt <= cc)
wmst_fast(time, event, group = g, control = 0, tau1 = 2, tau2 = 12)
#> Window mean survival time (two-group)
#> 
#>   window = [2, 12],  control = 0
#>   alternative = two.sided
#> 
#>             wmst std.err lower 95% upper 95%
#> control   5.8371   0.402    5.0491    6.6251
#> treatment 6.6057   0.402    5.8177    7.3936
#> 
#>                                     Est. lower 95% upper 95%     z Pr(>|z|)
#> difference (treatment - control)  0.7686   -0.3458    1.8829 1.352    0.176

# Formula interface
d <- data.frame(time, event, g)
wmst_fast(Surv(time, event) ~ g, data = d, tau1 = 2, tau2 = 12)
#> Window mean survival time (two-group)
#> 
#>   window = [2, 12],  control = 0
#>   alternative = two.sided
#> 
#>             wmst std.err lower 95% upper 95%
#> control   5.8371   0.402    5.0491    6.6251
#> treatment 6.6057   0.402    5.8177    7.3936
#> 
#>                                     Est. lower 95% upper 95%     z Pr(>|z|)
#> difference (treatment - control)  0.7686   -0.3458    1.8829 1.352    0.176