calibrate_thresholds {ppseq}

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

Description

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

1. 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)

2. 'call_list' containing the original function call

3. '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
  )

# 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
  )