Calibrate according to posterior probability threshold and predictive probability threshold with interim futility monitoring

This function is meant to be used in the context of a clinical trial with a binary endpoint. For every combination of the provided posterior thresholds and predictive thresholds, the function simulates many trials and then calculates the average number of times a trial was positive. In the null case, this is the type I error for the given thresholds. In the alternative case, this is the power for the given thresholds.

Usage

calibrate_thresholds(
  p_null,
  p_alt,
  n,
  N,
  pp_threshold,
  ppp_threshold,
  direction = "greater",
  delta = NULL,
  monitoring = "futility",
  prior = c(0.5, 0.5),
  S = 5000,
  nsim = 1000
)

Arguments

p_null: vector of length two containing the probability of event in the standard of care and experimental arm c(p0, p1) for the two-sample case for the null scenario; integer of event probability for one-sample case
p_alt: vector of length two containing the probability of event in the standard of care and experimental arm c(p0, p1) for the two-sample case for the alternative scenario; integer of event probability for one-sample case
n: matrix containing the total number of patients accrued so far at each interim look in the standard of care (column 1) and experimental (column 2) arms for two-sample case; vector of sample size accrued so far at each interim look for one-sample case. The last value should be equal to the total sample size at the end of the trial. If only a single look will be done at the end of the trial, this can be a vector specifying the total sample size c(N0, N1) for the two-sample case or an integer specifying the total sample size N for the one-sample case
N: the total planned sample size at the end of the trial, c(N0, N1) for two-sample case; integer of total planned sample size at end of trial N for one-sample case
pp_threshold: the posterior probability threshold of interest
ppp_threshold: the posterior predictive probability threshold of interest for futility monitoring
direction: "greater" (default) if interest is in p(p1 > p0) and "less" if interest is in p(p1 < p0) for two-sample case. For one-sample case, "greater" if interest is in p(p > p0) and "less" if interest is in p(p < p0).
delta: clinically meaningful difference between groups. Typically 0 for the two-sample case. NULL for the one-sample case (default).
monitoring: the type of interim monitoring to be performed. One of "futility" or "efficacy". Default is "futility".
prior: hyperparameters of prior beta distribution. Beta(0.5, 0.5) is default
S: number of samples drawn from the posterior. Default is 5000
nsim: Number of simulated trial datasets.

Value

A list containing a

a tibble 'res_summary' containing the posterior probability threshold (pp_threshold), the predictive probability threshold (ppp_threshold), the mean sample size under the null (mean_n0_null and mean_n1_null for two-sample case; mean_n1_null for one-sample case), the proportion of positive trials under the null (prop_pos_null), the proportion of trials stopped early under the null (prop_stopped_null), the mean sample size under the alternative (mean_n0_alt and mean_n1_alt for two-sample case; mean_n1_alt for one-sample case), the proportion of positive trials under the alternative (prop_pos_alt), the proportion of trials stopped early under the alternative (prop_stopped_alt)
'call_list' containing the original function call
'calibrate_thresholds_inputs' a list containing the inputs to the original function call

The proportion of positive trials will be a measure of the type I error for a null setting, and a measure of the power in the alternative setting.

Examples


# One-sample case
set.seed(123)

calibrate_thresholds(
  p_null = 0.1, 
  p_alt = 0.4,
  n = seq(5, 15, 5), 
  N = 15,
  pp_threshold = c(0.85, 0.9),
  ppp_threshold = c(0.1, 0.2),
  S = 10, 
  nsim = 10
  )
#> Warning: package 'purrr' was built under R version 4.3.3
#> # A tibble: 4 × 8
#>   pp_threshold ppp_threshold mean_n1_null prop_pos_null prop_stopped_null
#>          <dbl>         <dbl>        <dbl>         <dbl>             <dbl>
#> 1         0.85           0.1         13.5           0.1               0.2
#> 2         0.85           0.2         10.5           0.1               0.6
#> 3         0.9            0.1         12.5           0                 0.3
#> 4         0.9            0.2         11             0.1               0.5
#> # ℹ 3 more variables: mean_n1_alt <dbl>, prop_pos_alt <dbl>,
#> #   prop_stopped_alt <dbl>

# Two-sample case
set.seed(456)

calibrate_thresholds(
  p_null = c(0.1, 0.1), 
  p_alt = c(0.1, 0.5),
  n = cbind(seq(5, 15, 5), seq(5, 15, 5)), 
  N = c(15, 15),
  pp_threshold = c(0.8, 0.85),
  ppp_threshold = c(0.2, 0.3),
  delta = 0,
  S = 10, 
  nsim = 10
  )
#> # A tibble: 4 × 10
#>   pp_threshold ppp_threshold mean_n0_null mean_n1_null prop_pos_null
#>          <dbl>         <dbl>        <dbl>        <dbl>         <dbl>
#> 1         0.8            0.2          9            9               0
#> 2         0.8            0.3          7.5          7.5             0
#> 3         0.85           0.2          8.5          8.5             0
#> 4         0.85           0.3          8            8               0
#> # ℹ 5 more variables: prop_stopped_null <dbl>, mean_n0_alt <dbl>,
#> #   mean_n1_alt <dbl>, prop_pos_alt <dbl>, prop_stopped_alt <dbl>