Purpose

FastSurvival is designed for repeated evaluation inside large simulation loops. This vignette shows how to benchmark each estimation and testing function against an established reference and reports representative results. The benchmark code is shown but not executed when the vignette is built, because timing many microbenchmark replicates would exceed the build-time limits. To reproduce the numbers, run the code blocks interactively. The same code is collected in the tools/benchmark_speed.R script of the package’s GitHub repository.

The reported figures are median times of 1,000 microbenchmark replicates, measured on 2026-09-29 with R 4.6.0 on Windows 11 (x86_64) for the data set of 500 subjects below, all of whom have an event. The FastSurvival functions are timed on presorted input, so the single sort of the data is excluded from their times, whereas the reference functions sort internally; in a simulation loop the sort is paid once per data set. coxph_fast() computes a closed-form approximation of the Cox estimate (the Pike-Halley Estimator) rather than the iterative maximum partial likelihood estimate, so its row compares two estimators of the same quantity. Absolute timings depend on hardware, sample size, and event rate, so the ratios matter more than the raw values.

library(FastSurvival)
library(survival)
library(microbenchmark)

Setup

The key to the speed gain is that the analysis functions accept pre-sorted vectors. Inside a simulation loop the data are sorted once and reused, so the sort cost is paid a single time rather than on every call. We build a single two-group dataset of 500 subjects with simdata_fast() and prepare the sorted vectors, the binary arm indicator, and the restriction horizon used by the time-restricted methods.

dataset <- simdata_fast(
  nsim     = 1,
  n        = 500,
  a.time   = c(0, 12.5),
  a.rate   = 40,
  e.median = list(5.811, 4.3),
  seed     = 1
)

# Sort once and reuse, the intended pattern for the pre-sorted fast path.
ord <- order(dataset$tte)
t_s <- dataset$tte[ord]
e_s <- dataset$event[ord]
g_s <- dataset$group[ord]

# Control is group 1, treatment is group 2.
arm <- as.integer(dataset$group == 2)

# Restriction horizon within both arms' follow-up.
tau <- floor(min(tapply(t_s, g_s, max)))

# Factor arm for the nphRCT reference used in the rmw_fast benchmark.
df_rmw <- data.frame(
  tte   = dataset$tte,
  event = dataset$event,
  arm   = factor(ifelse(dataset$group == 1, "control", "treatment"),
                 levels = c("control", "treatment"))
)

survfit_fast vs survfit + summary

microbenchmark(
  fast = survfit_fast(t_s, e_s, t_eval = tau, presorted = TRUE),
  ref  = summary(survfit(Surv(tte, event) ~ 1, data = dataset), times = tau),
  times = 1000
)

survdiff_fast vs survdiff

microbenchmark(
  fast = survdiff_fast(t_s, e_s, g_s, control = 1, side = 1, presorted = TRUE),
  ref  = survdiff(Surv(tte, event) ~ group, data = dataset),
  times = 1000
)

coxph_fast vs coxph

microbenchmark(
  fast = coxph_fast(t_s, e_s, g_s, control = 1, side = 1, presorted = TRUE),
  ref  = coxph(Surv(tte, event) ~ I(group == 2), data = dataset),
  times = 1000
)

rmst_fast vs survRM2::rmst2

microbenchmark(
  fast = rmst_fast(t_s, e_s, g_s, control = 1, tau = tau, side = 1,
                   presorted = TRUE),
  ref  = survRM2::rmst2(time = dataset$tte, status = dataset$event,
                        arm = arm, tau = tau),
  times = 1000
)

survdiff_fast(weight = “fh”) vs nph::logrank.test

microbenchmark(
  fast = survdiff_fast(t_s, e_s, g_s, control = 1, side = 1,
                       weight = "fh", rho = 0, gamma = 1, presorted = TRUE),
  ref  = nph::logrank.test(dataset$tte, dataset$event, dataset$group,
                           rho = 0, gamma = 1),
  times = 1000
)

wmst_fast vs survWMST::wmst

The window mean survival time is benchmarked against wmst() from the survWMST package. survWMST is distributed on GitHub (pauknemj/survWMST), not CRAN, so this benchmark is shown as a static block rather than a live chunk, and the vignette carries no undeclared dependency. Install survWMST with remotes::install_github("pauknemj/survWMST") and run the block to reproduce it.

microbenchmark(
  fast = wmst_fast(t_s, e_s, g_s, control = 1, tau1 = 0, tau2 = tau,
                   side = 1, presorted = TRUE),
  ref  = survWMST::wmst(time = dataset$tte, status = dataset$event,
                        arm = arm, tau0 = 0, tau1 = tau),
  times = 1000
)

milestone_fast vs survfit + summary

microbenchmark(
  fast = milestone_fast(t_s, e_s, g_s, control = 1, tau = tau, side = 1,
                        presorted = TRUE),
  ref  = summary(survfit(Surv(tte, event) ~ group, data = dataset),
                 times = tau),
  times = 1000
)

medsurv_fast vs nph::nphparams

microbenchmark(
  fast = medsurv_fast(t_s, e_s, g_s, control = 1, side = 1,
                      method = "nph", presorted = TRUE),
  ref  = nph::nphparams(time = dataset$tte, event = dataset$event,
                        group = as.integer(dataset$group == 2),
                        param_type = "Q", param_par = 0.5),
  times = 1000
)

maxcombo_fast vs nph::logrank.maxtest

microbenchmark(
  fast = maxcombo_fast(t_s, e_s, g_s, control = 1, side = 1,
                       rho = c(0, 0, 1), gamma = c(0, 1, 0), presorted = TRUE),
  ref  = nph::logrank.maxtest(dataset$tte, dataset$event,
                              as.integer(dataset$group == 2)),
  times = 1000
)

rmw_fast vs nphRCT::wlrt

rmw_fast() combines a standard and a modestly-weighted log-rank statistic, so the reference computes both weighted log-rank components with nphRCT.

microbenchmark(
  fast = rmw_fast(t_s, e_s, g_s, control = 1, side = 1, s_star = 0.5,
                  presorted = TRUE),
  ref  = {
    nphRCT::wlrt(Surv(tte, event) ~ arm, data = df_rmw,
                 method = "mw", s_star = 1)
    nphRCT::wlrt(Surv(tte, event) ~ arm, data = df_rmw,
                 method = "mw", s_star = 0.5)
  },
  times = 1000
)

wkm_fast vs nphsim::wkm.Stat

The weighted Kaplan-Meier (Pepe-Fleming) test is benchmarked against wkm.Stat() from the nphsim package. nphsim is distributed on GitHub (keaven/nphsim), not CRAN, so this benchmark is shown as a static block. Install nphsim with remotes::install_github("keaven/nphsim") and run the block to reproduce it.

microbenchmark(
  fast = wkm_fast(t_s, e_s, g_s, control = 1, side = 1, weight = "PF",
                  presorted = TRUE),
  ref  = nphsim::wkm.Stat(survival = dataset$tte, cnsr = 1 - dataset$event,
                          trt = ifelse(dataset$group == 1,
                                       "control", "experimental")),
  times = 1000
)

ahsw_fast vs survAH::ah2

microbenchmark(
  fast = ahsw_fast(t_s, e_s, g_s, control = 1, tau = tau, side = 1,
                   presorted = TRUE),
  ref  = survAH::ah2(time = dataset$tte, status = dataset$event,
                     arm = arm, tau = tau),
  times = 1000
)

ahr_fast vs AHR::ahrKM

The Kalbfleisch-Prentice average hazard ratio is benchmarked against ahrKM() from the AHR package, which Dormuth et al. (2024) used to compute the average hazard ratio. Because AHR has been archived on CRAN, this benchmark is shown as a static block rather than a live chunk. Install AHR with remotes::install_github("cran/AHR") and run the block to reproduce it.

microbenchmark(
  fast = ahr_fast(t_s, e_s, g_s, control = 1, tau = tau, side = 1,
                  presorted = TRUE),
  ref  = AHR::ahrKM(tau, Surv(tte, event) ~ group, dataset),
  times = 1000
)

Representative results

The table below summarizes representative median timings on the n = 500 two-group dataset generated above, with presorted = TRUE and one-sided tests where applicable. The exact values will differ on your machine, but the order of magnitude of the speedup is stable. The wkm_fast() row is missing because nphsim was not installed when the table was produced.

Why it is faster

Each function avoids the overhead that the standard implementations incur on every call. The standard functions parse a formula, build an S3 model object, and construct intermediate vectors before producing the result, which is appropriate for interactive use but wasteful when the same operation is repeated thousands of times. The FastSurvival functions take plain vectors, do the core computation in a single C++ pass over the data, and return a lightweight numeric vector. When the input is already sorted the sort cost is avoided entirely. In a simulation loop these savings accumulate across every iteration.

Whole simulation studies

The per-call gains carry over to complete simulation studies. The scripts in tools/paper/ of the package’s GitHub repository run the same designs with FastSurvival and with other simulation packages and record the operating characteristics and the elapsed time. For a two-arm group-sequential design with 600 subjects and two event-driven log-rank analyses, the time per simulated trial was about 200 times longer with simtrial and about 80 times longer with TrialSimulator than with FastSurvival, and for a crossover after a positive progression-free survival analysis in an illness-death model it was about 50 times longer with TrialSimulator. The power and the analysis times agreed within Monte Carlo error. With FastSurvival, generating 10,000 such trials and computing the log-rank and RMST statistics at the two looks each took about one second. The max-combo p-values, one multivariate normal integral per trial and look, take most of the computing time; when only the decisions at given nominal levels are needed, the mc.alpha argument of analysis_fast() restricts the integration to the p-values near those levels.

References

Dormuth, I., Pauly, M., Rauch, G., & Herrmann, C. (2024). Sample size calculation under nonproportional hazards using average hazard ratios. Biometrical Journal, 66(6), e202300271.