Find Sample Size for a Stratified Additive RMST Model (Analytic)

Calculates the required sample size for a target power using the analytic method for a stratified, additive RMST model.

Usage

additive.ss.analytical(
  pilot_data,
  time_var,
  status_var,
  arm_var,
  strata_var,
  target_power,
  linear_terms = NULL,
  L,
  alpha = 0.05,
  n_start = 50,
  n_step = 25,
  max_n_per_arm = 2000
)

Arguments

pilot_data

A data.frame containing 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.

target_power

A single numeric value for the desired power.

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).

n_start

The starting sample size per stratum for the search.

n_step

The increment in sample size at each step of the search.

max_n_per_arm

The maximum sample size per stratum to search up to.

Value

A list containing:

results_data

A data.frame with the target power and required sample size.

results_plot

A ggplot object visualizing the search path.

results_summary

A data.frame summarizing the estimated treatment effect.

Details

This function performs an iterative search for the sample size required to achieve a specified target_power. It uses the same underlying theory as additive.power.analytical, based on stratum-centering of covariates. It performs a one-time estimation of the additive treatment effect and its asymptotic variance from the pilot data, then uses these parameters in an analytic formula to efficiently find the required sample size.

Examples

set.seed(123)
pilot_df_strat <- data.frame(
 time = rexp(150, 0.1),
 status = rbinom(150, 1, 0.8),
 arm = rep(0:1, each = 75),
 region = factor(rep(c("A", "B", "C"), each = 50)),
 age = rnorm(150, 60, 10)
)
# Introduce an additive treatment effect
pilot_df_strat$time[pilot_df_strat$arm == 1] <-
  pilot_df_strat$time[pilot_df_strat$arm == 1] + 1.5

  # Find the required sample size per stratum for 80% power
  ss_results <- additive.ss.analytical(
    pilot_data = pilot_df_strat,
    time_var = "time", status_var = "status",
    arm_var = "arm", strata_var = "region",
    target_power = 0.50,
    L = 18, #
    n_start = 200,
    n_step = 50,
    max_n_per_arm = 1000
  )
#> --- Estimating parameters from pilot data for analytic search... ---
#> --- Searching for Sample Size (Method: Additive Analytic) ---
#>   N = 200/stratum, Calculated Power = 0.399
#>   N = 250/stratum, Calculated Power = 0.478
#>   N = 300/stratum, Calculated Power = 0.55
#> 
#> --- Calculation Summary ---
#> 
#> 
#> Table: Required Sample Size
#> 
#> | Target_Power| Required_N_per_Stratum|
#> |------------:|----------------------:|
#> |          0.5|                    300|
  print(ss_results$results_data)
#>   Target_Power Required_N_per_Stratum
#> 1          0.5                    300
  print(ss_results$results_plot)