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

Source:`R/calibrate_thresholds.R`

`calibrate_thresholds.Rd`

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>
```