In kkmann/badr: Optimal Binary Adaptive (Single-Arm) Designs in R

knitr::opts_chunk$set(
    collapse = TRUE,
    comment  = "#>"
)

Optimal binary two stage designs

library(dplyr)
library(tidyr)
library(ggplot2)
library(badr)

# make sure Julia is installed and found by JuliaCall package
load_julia_package()

Define a prior on the response probability

A mixture prior between an informative component and a uniform distribution is a good choice since it is more robust than just an informarive prior. The prior can be defined in terms of its mean and standard deviation.

informative    <- Beta_mu_sd(mu = 0.35, sd = 0.1)
noninformative <- Beta(1, 1)
mixture        <- 0.9*informative + 0.1*noninformative

tbl_prior_densities <- tibble(
      p           = seq(0, 1, by = .01),
      informative = density(informative, p),
      uniform     = density(noninformative, p),
      mixture     = density(mixture, p)
  ) %>% 
  pivot_longer(
      -p, 
      names_to = "name", 
      values_to = "PDF"
  ) 

ggplot(tbl_prior_densities) +
    aes(p, PDF, color = name) + 
    geom_line()

prior <- mixture <= 0.7

tbl_prior_densities <- bind_rows(
    tbl_prior_densities,
    tibble(
        p    = seq(0, 1, by = .01),
        name = "pragmatic",
        PDF  = density(prior, p) %>% ifelse(between(p, 0.69, 0.7), NA, .)
    )
)

ggplot(tbl_prior_densities) +
    aes(p, PDF, color = name) + 
    geom_line()

design <- Problem(
    minimise(SampleSize(prior)),
    Power(prior %|% 0.2) <= 0.05,
    Power(prior >= 0.3)  >= 0.8,
    label = "expected power design"
) %>% 
optimise_design()