{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Figures for 'A review of Bayesian perspectives on sample size derivation for confirmatory trials'\n", "\n", "The following notebook contains all code required to reproduce the figures in the manuscript." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "suppressPackageStartupMessages(library(tidyverse))\n", "\n", "source(\"../R/priors.R\")\n", "source(\"../R/functions.R\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison of required sample sizes for various prior choices (Figure 2)\n", "\n", "We start by defining a baisc parameters for the situation we look at, like maximal type one error rate etc." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# maximal sample size cut-off\n", "nmax <- 1000\n", "# one sided maximal type one error rate\n", "alpha <- 0.025\n", "# minimal power/expected power/probability of success is 1 - beta\n", "beta <- 0.2\n", "# upper boundary of the null hypothesis for the location parameter\n", "# H0: theta <= theta_null\n", "theta_null <- 0.0\n", "# minimal clinically important difference (MCID)\n", "theta_mcid <- 0.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define the range of prior (hyper)parameters to look at. We consider truncated normal priors (maximal entropy given mean/variance on compact interval)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "prior_lo <- -0.3\n", "prior_hi <- 0.7\n", "# range of prior means for location parameter\n", "prior_mean_range <- seq(prior_lo, prior_hi, by = .01)\n", "# range of prior standard deviations for location parameter\n", "prior_sd_range <- seq(.01, 1, by = .01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then evaluate the respective required sample sizes for the different approaches depending on the prior mean and standard deviation.\n", "See `R/priors.R` and `R/functions.R` for details." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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QktCWEZD2CJ8UWAGYB/+FEkixxp65xoMwC2zIF2bYAZ9zmXm1sBDYBPZPFZzABM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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# adjust plot output size\n", "options(repr.plot.width = 8, repr.plot.height = 3.15)\n", "\n", "# create 2d grid of prior mean/sd combinations\n", "expand_grid(\n", " mu = prior_mean_range,\n", " tau = prior_sd_range\n", ") %>%\n", "# compute the required sample sizes\n", "mutate(\n", " prior = map2(mu, tau, ~Normal(.x, .y, lo = prior_lo, hi = prior_hi)),\n", " `quantile 0.5` = map_dbl(prior, ~get_n_quantile(theta_null, ., .5, pwr = 1 - beta, alpha = alpha, upper_n = nmax)),\n", " `quantile 0.9` = map_dbl(prior, ~get_n_quantile(theta_null, ., .9, pwr = 1 - beta, alpha = alpha, upper_n = nmax)),\n", " EP = map_dbl(prior, ~get_n_ep(theta_null, ., pwr = 1 - beta, alpha = alpha, upper_n = nmax)),\n", " PoS = map_dbl(prior, ~get_n_pos(theta_null, ., pwr = 1 - beta, alpha = alpha, upper_n = nmax))\n", ") %>%\n", "pivot_longer(\n", " c(contains('quantile'), EP, PoS),\n", " values_to = 'required sample size',\n", " names_to = 'criterion'\n", ") %>%\n", "filter(\n", " `required sample size` <= nmax, # make sure maximal sample size is respected\n", " !is.na(`required sample size`) # throw out instances where the maximal sample size boundary was hit\n", ") %>%\n", "# plot\n", "ggplot() +\n", " aes(mu, tau, fill = `required sample size`, z = `required sample size`) +\n", " geom_raster() + # geom_raster leads to some pdf viewers interpolating, do not want that!\n", " scale_fill_gradient(limits = c(0, 1000), low = '#FFFFFF', high = '#000000') +\n", " guides(\n", " fill = guide_colorbar(\"required sample size\",\n", " barwidth = grid::unit(15, \"lines\"),\n", " barheight = grid::unit(.5, \"lines\")\n", " )\n", " ) +\n", " coord_cartesian(expand = FALSE) +\n", " xlab('prior mean') +\n", " ylab('prior standard deviation') +\n", " facet_wrap(~criterion, nrow = 1) +\n", " theme_bw() +\n", " theme(\n", " panel.grid = element_blank(),\n", " panel.spacing = unit(1.25, 'lines'),\n", " legend.position = 'top'\n", " )" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# save plot as pdf\n", "ggsave(\"../latex/figures/fig2-required-sample-size-comparison.pdf\", width = 8, height = 3.15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Probability of success as the basis for sample size derivation (Figure 3)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# function to compute all parts of PoS'\n", "PoS_all <- function(prior, n, c, null = 0, mrv = null) {\n", " part1 <- integrate(\n", " function(Delta) pdf(prior, Delta) * power(Delta, n, c), prior$lower, null\n", " )$value\n", " part2 <- integrate(\n", " function(Delta) pdf(prior, Delta) * power(Delta, n, c), null, mrv\n", " )$value\n", " part3 <- integrate(\n", " function(Delta) pdf(prior, Delta) * power(Delta, n, c), mrv, prior$upper\n", " )$value\n", " return(tibble(a = part1, b = part2, c = part3))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now plot the relative composition of PoS' for varying prior mean and standard deviation." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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bVraWFhf7O0ncwLULorVRp3AHBwkFMn1UgkEolEBgBarcbVT36pzWcSqcRohlGQ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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# adjust plot output size\n", "options(repr.plot.width = 7.5, repr.plot.height = 2.75)\n", "\n", "expand_grid(\n", " prior_mean = seq(-0.1, .2, .025),\n", " prior_sd = seq(.025, .15, .025)\n", ") %>%\n", "mutate(\n", " tmp = pmap(\n", " list(prior_mean, prior_sd),\n", " ~PoS_all(\n", " Normal(..1, ..2, -.3, .7),\n", " 150,\n", " qnorm(1 - .05),\n", " mrv = theta_mcid)\n", " )\n", ") %>%\n", "unnest(tmp) %>%\n", "mutate(\n", " id = row_number(),\n", " total = a + b + c,\n", " A = a/total,\n", " B = b/total,\n", " C = c/total\n", ") %>% {\n", "ggplot(.) +\n", " scatterpie::geom_scatterpie(\n", " aes(x = prior_mean, y = prior_sd, group = id, r = .01),\n", " data = ., cols = c(\"A\", \"B\", \"C\"), color = NA\n", " ) +\n", " geom_text(\n", " aes(x = prior_mean, y = prior_sd, label = sprintf(\"%.2f\", total)),\n", " size = 2\n", " ) +\n", " theme_bw() +\n", " coord_equal() +\n", " scale_x_continuous(\"prior mean\", breaks = seq(-.2, .3, .05)) +\n", " scale_y_continuous(\"prior standard deviation\", breaks = seq(0.05, .25, .05)) +\n", " scale_fill_manual(\"\",\n", " values = c(\n", " A = scales::muted(\"red\", l = 75, c = 60),\n", " B = scales::muted(\"blue\", l = 75, c = 60),\n", " C = scales::muted(\"green\", l = 75, c = 60)\n", " )\n", " ) +\n", " theme(\n", " legend.position = \"right\",\n", " panel.grid = element_blank()\n", " )}" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "ggsave(\"../latex/figures/fig3-pos-prime-composition.pdf\", width = 7.5, height = 2.75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution of random power under a constraint on expected power (Figure 4)\n", "\n", "We now look at three particular situations with the following prior means and standard deviations:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
label | n |
---|---|
<chr> | <dbl> |
mean=-0.25, sd=0.40, n=172 | 172 |
mean=0.30, sd=0.12, n=109 | 109 |
mean=0.50, sd=0.05, n=33 | 33 |