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Restricted mean survival time designs

Source: vignettes/rmst.Rmd
rmst.Rmd

Effect and hypothesis

method = "rmst" compares the area under the treatment and control Kaplan-Meier curves through one prespecified restriction time, rmst_tau. The estimated effect is treatment minus control RMST, measured in the same time units as follow-up. For an adverse event, positive values mean additional event-free time on treatment. This unadjusted, two-arm Wald analysis does not assume proportional hazards.

The default restriction time is end_of_study. A shorter rmst_tau may be chosen in advance, but it must be positive and cannot exceed end_of_study. The same value is used for every arm, look, imputation, and simulated trial. The planned follow-up and imputation horizon remain end_of_study.

For superiority use h0 = 0 and alternative = "greater". For non-inferiority allowing a loss of one time unit use h0 = -1 with the same alternative. A two-sided difference test uses alternative = "two.sided". Null values must lie in [-rmst_tau, rmst_tau].

A trial with a delayed treatment effect

Suppose time is measured in months and treatment begins reducing the event hazard after month three. The RMST endpoint summarizes event-free time through month nine, while follow-up continues through month twelve.

set.seed(1410)
trial <- survival_adapt(
  hazard_control = c(0.10, 0.10),
  hazard_treatment = c(0.10, 0.04),
  cutpoints = 3,
  N_total = 160,
  lambda = 8,
  interim_look = c(80, 120),
  end_of_study = 12,
  method = "rmst",
  rmst_tau = 9,
  alternative = "greater",
  h0 = 0,
  prob_ha = 0.975,
  N_impute = 100,
  return_trace = TRUE
)
trial$summary[, c("est_final", "post_prob_ha", "N_enrolled", "trial_success")]
#>   est_final post_prob_ha N_enrolled trial_success
#> 1 0.9182006    0.9601273        160         FALSE
trial$trace[, c("planned_N", "ppp_stop_now", "decision")]
#>   planned_N ppp_stop_now decision
#> 1        80         0.50 continue
#> 2       120         0.02 continue

est_final is the estimated additional event-free time in months through month nine. post_prob_ha is one minus the Wald-test P-value, not a posterior probability. Final success requires it to be strictly greater than prob_ha. An immediate-success decision instead ends the trial without a later final analysis, leaving these final-analysis summaries unavailable.

Prediction and loss to follow-up

The selected RMST analysis is applied to every predictively completed trial at both the current and maximum sample sizes. evaluate_interim() accepts the same method and rmst_tau for an observed interim data cut. Predictive imputation uses the piecewise-exponential model and the Gamma hazard priors. N_impute controls its Monte Carlo resolution; N_mcmc and binary_imputation do not change the RMST test.

The observed interim data vignette demonstrates an RMST look with event, pending, and early-censored records.

With imputed_final = FALSE, participants lost to follow-up contribute their observed right-censored data to Kaplan-Meier estimation. Each arm must have follow-up through the fixed restriction time, or its survival curve must already have reached zero. A positive survival tail ending earlier causes an explicit non-estimability error; the package does not shorten the horizon or extrapolate the tail. Independent censoring is required for this inference.

With imputed_final = TRUE, missing event times are generated from the final-stage hazard posterior using prior_surv_final. The RMST differences and within-imputation Greenwood variances are pooled using Rubin’s scalar rules with a t reference distribution. At least two imputations are needed. The test requires positive total variance, including after pooling; an individual arm or imputation may contribute zero variance. Final pooling is distinct from the interim calculation, which tests each completed trial separately and averages the success indicators.

Evaluate the design

Use sim_trials() with the same arguments and inspect both results and failures. The following small run demonstrates the interface; substantially more trials are needed to assess operating characteristics precisely.

sims <- sim_trials(
  hazard_control = 0.10,
  hazard_treatment = 0.10,
  N_total = 160,
  lambda = 8,
  interim_look = 80,
  end_of_study = 12,
  method = "rmst",
  rmst_tau = 9,
  alternative = "greater",
  prob_ha = 0.975,
  N_impute = 50,
  N_trials = 20,
  backend = "sequential",
  seed = 1411
)
summarise_sims(sims)
#> # A tibble: 1 × 44
#>   scenario backend     seed n_requested n_analyzed n_failed n_used failure_rate
#>   <chr>    <chr>      <dbl>       <int>      <int>    <int>  <int>        <dbl>
#> 1 1        sequential  1411          20         20        0     20            0
#> # ℹ 36 more variables: failure_rate_mcse <dbl>, failure_rate_mc_lower <dbl>,
#> #   failure_rate_mc_upper <dbl>, power <dbl>, power_mcse <dbl>,
#> #   power_mc_lower <dbl>, power_mc_upper <dbl>, stop_immediate_success <dbl>,
#> #   stop_immediate_success_mcse <dbl>, stop_immediate_success_mc_lower <dbl>,
#> #   stop_immediate_success_mc_upper <dbl>, stop_success <dbl>,
#> #   stop_success_mcse <dbl>, stop_success_mc_lower <dbl>,
#> #   stop_success_mc_upper <dbl>, stop_any_success <dbl>, …
sims$failures
#> [1] trial       error_class message    
#> <0 rows> (or 0-length row.names)

A nominal final-test threshold alone does not establish adaptive type I error control. Prespecify and calibrate the complete stopping rule, including any immediate-success boundary. Assess equal-survival nulls, equal-RMST nulls with crossing curves, nonzero margins, delayed benefits, dropout, and discrepancies between the generating and predictive hazard models. RMST avoids the proportional-hazards assumption for the completed-data test; it does not remove assumptions from prediction or final imputation.

The calibration vignette shows how to screen thresholds, assess Monte Carlo uncertainty, and validate a selected design with independent simulations, including how to adapt the workflow to RMST.

For maintainer validation, benchmarks/rmst-calibration.R runs fixed and adaptive scenarios with failure counts and Monte Carlo intervals, and benchmarks/rmst.R compares completed-data and predictive runtimes. The technical methods vignette gives the variance and pooling formulas.

References

Uno H, Claggett B, Tian L, et al. Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. Journal of Clinical Oncology. 2014;32:2380-2385. https://doi.org/10.1200/JCO.2014.55.2208.

The numerical reference tests use survRM2::rmst2(). Runtime calculations use the existing survival dependency; when every truncated event time is known, the equivalent empirical mean and Greenwood variance avoid rebuilding a survival fit for each predictive completion.