Fast non-parametric median survival time and between-group difference

Estimates the Kaplan-Meier median survival time for a single group, or the difference in median survival time between a treatment group and a control group, together with standard errors, confidence intervals and a Wald test for the difference. The estimator is designed for repeated evaluation inside simulation loops, with the single scan over the sorted data performed in C++.

Usage

medsurv_fast(
  time,
  event,
  group = NULL,
  control = NULL,
  side = 2,
  conf.level = 0.95,
  conf.type = "log",
  method = c("km", "nph"),
  bw = NULL,
  presorted = FALSE
)

Arguments

time: Numeric vector of event or censoring times.
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 median is returned.
control: The level of group that denotes the control group. Required when group is 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.
conf.type: Confidence interval type for each group median, either "plain" or "log". The interval for the difference is always on the plain scale.
method: Variance method, either "km" (Greenwood increment with a kernel hazard) or "nph" (local constant hazard with a sum 1 / (Y - k)^2 increment, matching nph::nphparams).
bw: Optional kernel bandwidth for the hazard at the median, used only when method = "km". Either a single value applied to both groups or one value per group. If omitted, a Silverman type default is used.
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 "medsurv_fast". For a single group the elements are the median, its standard error and confidence limits. For two groups the elements are the control and treatment medians, their difference, the standard errors, the confidence limits and the Wald statistics for the difference.

Details

The median in each group is the first event time at which the Kaplan-Meier estimate drops to 0.5 or below, matching the convention used by survfit. The point estimate is the same for both variance methods.

Two variance methods are available through the method argument. With method = "km" the variance of the estimated median follows the counting process delta method, var(median) = greenwood_sum / hazard^2, where the instantaneous hazard at the median is obtained by a Ramlau-Hansen kernel smoother with an Epanechnikov kernel and bandwidth bw. With method = "nph" the variance reproduces the computation used by nph::nphparams with param_type = "Q" and haz_method = "local": a local constant hazard at the median and a sum 1 / (Y - k)^2 variance increment. The two methods give the same median but generally different standard errors, since the variance of a quantile depends on the local hazard estimate. When the Kaplan-Meier and Nelson-Aalen medians coincide, which is the usual case, method = "nph" reproduces the nph::nphparams standard error and p-value to numerical precision.

The difference is computed as treatment minus control, so a positive difference indicates a longer median survival time under treatment.

References

Fleming, T. R., & Harrington, D. P. (1991). Counting Processes and Survival Analysis. New York: John Wiley & Sons.

Examples

set.seed(1)
n <- 200
g <- rep(0:1, each = n / 2)
tt <- rexp(n, rate = ifelse(g == 0, 0.1, 0.07))
cc <- rexp(n, rate = 0.02)
time <- pmin(tt, cc)
event <- as.integer(tt <= cc)
medsurv_fast(time, event, group = g, control = 0)
#> Median survival time (two-group)
#> 
#>   control = 0
#>   method = km,  alternative = two.sided
#> 
#>            median std.err lower 95% upper 95%
#> control    8.1851  0.9708    6.4873   10.3273
#> treatment 10.7251  1.4586    8.2156   14.0012
#> 
#>                                     Est. lower 95% upper 95%    z Pr(>|z|)
#> difference (treatment - control)  2.5400   -0.8942    5.9742 1.45    0.147
medsurv_fast(time, event, group = g, control = 0, method = "nph")
#> Median survival time (two-group)
#> 
#>   control = 0
#>   method = nph,  alternative = two.sided
#> 
#>            median std.err lower 95% upper 95%
#> control    8.1851  0.9813    6.4710   10.3533
#> treatment 10.7251  1.6181    7.9796   14.4152
#> 
#>                                    Est. lower 95% upper 95%     z Pr(>|z|)
#> difference (treatment - control)  2.540    -1.169     6.249 1.342     0.18