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Analyze Power for a Multiplicative Stratified RMST Model (Analytic)

MS.power.analytical.Rd

Performs power analysis for a multiplicative, stratified RMST model using an analytic method based on the work of Wang et al. (2019).

Usage

MS.power.analytical(
  pilot_data,
  time_var,
  status_var,
  arm_var,
  strata_var,
  sample_sizes,
  linear_terms = NULL,
  L,
  alpha = 0.05
)

Arguments

pilot_data

A data.frame with pilot study data.

time_var

A character string for the time-to-event variable.

status_var

A character string for the event status variable (1=event, 0=censored).

arm_var

A character string for the treatment arm variable (1=treatment, 0=control).

strata_var

A character string for the stratification variable.

sample_sizes

A numeric vector of sample sizes per stratum to calculate power for.

linear_terms

An optional character vector of other covariate names.

L

The numeric value for the RMST truncation time.

alpha

The significance level (Type I error rate).

Value

A list containing:

results_data

A data.frame with sample sizes and corresponding powers.

results_plot

A ggplot object visualizing the power curve.

Details

This function is based on the method for evaluating center (stratum) effects using a multiplicative model for RMST: \(\mu_{ij} = \mu_{0j} \exp\{\beta'Z_i\}\). The method uses IPCW with a stratified Cox model for the censoring distribution.

The formal estimation of \(\beta\) requires an iterative solver for a complex estimating equation (Equation 8 in the paper). As this is computationally intensive, this implementation uses a practical approximation by fitting a weighted log-linear model (lm(log(Y_rmst) ~ ...)), which is conceptually similar and provides robust estimates for the effect size and its variance.

The power calculation relies on the asymptotic variance of the log-RMST ratio estimator, \(\hat{\beta}\). The variance is derived from the robust variance-covariance matrix of the lm fit, which serves as a proxy for the formal sandwich estimator \(A^{-1}B(A^{-1})'\) described in Theorem 1 of the paper.

Examples

set.seed(123)
pilot_df_strat <- data.frame(
 time = rexp(120, 0.15),
 status = rbinom(120, 1, 0.6),
 arm = rep(0:1, each = 60),
 region = factor(rep(c("A", "B", "C"), each = 40))
)
pilot_df_strat$time[pilot_df_strat$arm == 1] <- pilot_df_strat$time[pilot_df_strat$arm == 1] * 1.5

power_results <- MS.power.analytical(
 pilot_data = pilot_df_strat,
 time_var = "time", status_var = "status", arm_var = "arm", strata_var = "region",
 sample_sizes = c(50, 75, 100),
 L = 10, alpha = 0.05
)
#> --- Estimating parameters from pilot data (log-linear approximation)... ---
#> Approximation Model: log(Y_rmst) ~ arm + region
#> --- Calculating power for specified sample sizes... ---
print(power_results$results_data)
#>   N_per_Stratum     Power
#> 1            50 0.4415527
#> 2            75 0.6027274
#> 3           100 0.7270471