# Speed comparison

# 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 shipped in the package sources.

The reported figures are median times from microbenchmark replicates on a single desktop machine. 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, the reference implementation used by Dormuth et al. (2024). 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.

Function | Replaces | Approximate speed gain
--- | --- | ---
`survfit_fast()` | `survfit()` + `summary()` at one time point | ~40x
`survdiff_fast()` | `survdiff()` | ~40x
`coxph_fast()` | `coxph()` (point estimate + Wald CI) | ~30x
`rmst_fast()` | `survRM2::rmst2()` | ~40x
`survdiff_fast(weight = "fh")` | `nph::logrank.test()` | ~350x
`wmst_fast()` | `survWMST::wmst()` | ~560x
`milestone_fast()` | `survfit()` + `summary()` at a milestone | ~20x
`medsurv_fast()` | `nph::nphparams()` | ~30x
`maxcombo_fast()` | `nph::logrank.maxtest()` | ~320x
`rmw_fast()` | `nphRCT::wlrt()` (two components) | ~80x
`ahsw_fast()` | `survAH::ah2()` | ~410x
`ahr_fast()` | `AHR::ahrKM()` | ~130x

# 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.