{ "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": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\n", "
A tibble: 3 × 2
labeln
<chr><dbl>
mean=-0.25, sd=0.40, n=172172
mean=0.30, sd=0.12, n=109 109
mean=0.50, sd=0.05, n=33 33
\n" ], "text/latex": [ "A tibble: 3 × 2\n", "\\begin{tabular}{ll}\n", " label & n\\\\\n", " & \\\\\n", "\\hline\n", "\t mean=-0.25, sd=0.40, n=172 & 172\\\\\n", "\t mean=0.30, sd=0.12, n=109 & 109\\\\\n", "\t mean=0.50, sd=0.05, n=33 & 33\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A tibble: 3 × 2\n", "\n", "| label <chr> | n <dbl> |\n", "|---|---|\n", "| mean=-0.25, sd=0.40, n=172 | 172 |\n", "| mean=0.30, sd=0.12, n=109 | 109 |\n", "| mean=0.50, sd=0.05, n=33 | 33 |\n", "\n" ], "text/plain": [ " label n \n", "1 mean=-0.25, sd=0.40, n=172 172\n", "2 mean=0.30, sd=0.12, n=109 109\n", "3 mean=0.50, sd=0.05, n=33 33" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# prior configurations to look at\n", "tbl_poi <- tibble(\n", " mu = c(-.25, .3, .5),\n", " tau = c(.4, .125, .05)\n", " ) %>%\n", " mutate(\n", " prior = map2(mu, tau, ~Normal(..1, ..2, prior_lo, prior_hi)),\n", " n = map_dbl(prior, ~get_n_ep(theta_null, ., theta_mcid, 1 - beta, alpha)),\n", " label = sprintf(\"mean=%.2f, sd=%.2f, n=%i\", mu, tau, round(n))\n", " )\n", "\n", "tbl_poi %>% \n", " select(label, n)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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jB5o/3GufEo7xZS+KXz2R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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 = 6)\n", "\n", "plt_priors <- tbl_poi %>%\n", " mutate(\n", " tmp = map(prior, ~tibble(\n", " theta = seq(prior_lo - 0.1, prior_hi + 0.1, .01),\n", " `unconditional prior` = pdf(., theta) %>%\n", " {ifelse(theta == theta[which.min(abs(prior_lo - theta))] | (theta == theta[which.min(abs(prior_hi - theta))]), NA_real_, .)},\n", " `conditional prior` = pdf(condition(., lo = theta_mcid), theta) %>%\n", " {ifelse(theta == theta[which.min(abs(theta_mcid - theta))] | (theta == theta[which.min(abs(prior_hi - theta))]), NA_real_, .)}\n", " )\n", " )\n", " ) %>%\n", " unnest(tmp) %>%\n", " pivot_longer(c(`conditional prior`, `unconditional prior`)) %>%\n", " ggplot(aes(theta, value, linetype = label)) +\n", " geom_line() +\n", " facet_wrap(~name) +\n", " scale_linetype_discrete(\"prior\") +\n", " scale_x_continuous(expression(theta)) +\n", " scale_y_continuous(\"PDF\") +\n", " theme_bw() +\n", " theme(\n", " legend.position = \"top\",\n", " panel.grid.minor = element_blank(),\n", " strip.text = element_text(size = 6)\n", " )\n", "\n", "plt_power_curves <- full_join(\n", " tbl_poi,\n", " expand_grid(\n", " theta = seq(prior_lo, prior_hi, by = 0.01),\n", " n = tbl_poi$n\n", " ),\n", " by = \"n\"\n", " ) %>%\n", " mutate(\n", " power = map2_dbl(theta, n, ~power(..1, ..2, qnorm(1 - alpha)))\n", " ) %>%\n", " ggplot() +\n", " aes(theta, power, linetype = label) +\n", " geom_line() +\n", " scale_color_discrete(\"\") +\n", " scale_x_continuous(expression(theta), breaks = c(0, 0.5)) +\n", " scale_y_continuous(\"probability to reject\", breaks = seq(0, 1, .2)) +\n", " scale_linetype(\"\") +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " legend.position = \"top\"\n", " )\n", "\n", "set.seed(42)\n", "tbl_samples <- tbl_poi %>%\n", " mutate(\n", " unconditional = map(prior, ~get_sample(., 1e5)),\n", " conditional = map(prior, ~get_sample(condition(., lo = theta_mcid), 1e5))\n", " ) %>%\n", " unnest(c(conditional, unconditional)) %>%\n", " pivot_longer(c(conditional, unconditional), names_to = \"type\", values_to = \"rtheta\") %>%\n", " mutate(\n", " power = map2_dbl(rtheta, n, ~power(..1, ..2, qnorm(1 - alpha)))\n", " )\n", "\n", "tbl_probs <- tbl_samples %>%\n", " group_by(label, type) %>%\n", " summarise(\n", " tmp = mean(power >= 1 - beta),\n", " power = 1 - beta,\n", " .groups = \"drop\"\n", " )\n", "\n", "plt_power_distribution <- tbl_samples %>%\n", " mutate(\n", " type = ifelse(type == \"conditional\",\n", " \"random power\",\n", " \"random probability to reject\"\n", " )\n", " ) %>%\n", " ggplot(aes(power)) +\n", " geom_histogram(aes(y = stat(ndensity)), bins = 25, fill = \"darkgray\") +\n", " geom_vline(aes(xintercept = 0.8), color = \"black\") +\n", " geom_text(\n", " aes(\n", " label = sprintf(\"%.2f\", tmp),\n", " ),\n", " y = .9,\n", " x = 0.91,\n", " size = 3,\n", " color = \"black\",\n", " data = tbl_probs %>%\n", " mutate(\n", " type = ifelse(type == \"conditional\",\n", " \"random power\",\n", " \"random probability to reject\"\n", " )\n", " )\n", " ) +\n", " scale_y_continuous(\"\", breaks = c(), limits = c(0, 1.1)) +\n", " scale_x_continuous(\"probability to reject\", breaks = seq(0, 1, .2)) +\n", " coord_cartesian(expand = FALSE) +\n", " facet_grid(type ~ label, scales = \"free_y\") +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " panel.spacing = unit(1.25, \"lines\"),\n", " strip.text = element_text(size = 6)\n", " )\n", "\n", "legend <- cowplot::get_legend(plt_power_curves)\n", "\n", "cowplot::plot_grid(\n", " legend,\n", " cowplot::plot_grid(\n", " plt_priors + theme(legend.position = \"none\"),\n", " plt_power_curves + theme(legend.position = \"none\"),\n", " rel_widths = c(2, 1.2),\n", " nrow = 1\n", " ),\n", " plt_power_distribution,\n", " rel_heights = c(.1, 1, 1.75),\n", " ncol = 1\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "ggsave(\"../latex/figures/fig4-power-distribution-ep-approach.pdf\", width = 7.5, height = 6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution of random power under quantile approach (Figure 5)\n", "\n", "We now restrict the analysis to a single prior configuration and explore the sensitivity of the prior-quantile approach towards the choice of $\\gamma$ and $\\beta$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "prior <- Normal(0.3, 0.2, prior_lo, prior_hi)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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1tuT0j419qZ3qnAovcpd/S0R5iuFder3Uhai3u17W1tuWAICffynU0266S6gUWU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\nUwEJiSH0zgl3zpu30/0XZkBCkJAES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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 = 6)\n", "\n", "# plot conditional and unconditional priors\n", "plt_priors <- tibble(\n", " mu = .3,\n", " tau = .2,\n", " prior = list(Normal(.3, .2, lo = prior_lo, hi = prior_hi)),\n", " label = sprintf(\"mean=%.2f, sd=%.2f\", mu, tau)\n", " ) %>%\n", " mutate(\n", " tmp = map(prior, ~tibble(\n", " theta = seq(prior_lo - 0.1, prior_hi + 0.1, .005),\n", " `unconditional prior` = pdf(., theta) %>%\n", " {ifelse(theta == theta[which.min(abs(prior_lo - theta))] | (theta == theta[which.min(abs(prior_hi - theta))]), NA_real_, .)},\n", " `conditional prior` = pdf(condition(., lo = theta_mcid), theta) %>%\n", " {ifelse(theta == theta[which.min(abs(theta_mcid - theta))] | (theta == theta[which.min(abs(prior_hi - theta))]), NA_real_, .)}\n", " )\n", " )\n", " ) %>%\n", " unnest(tmp) %>%\n", " pivot_longer(c(`conditional prior`, `unconditional prior`)) %>%\n", " ggplot(aes(theta, value, linetype = label)) +\n", " geom_line(aes(linetype = name)) +\n", " scale_x_continuous(expression(theta)) +\n", " scale_y_continuous(\"PDF\") +\n", " scale_linetype_discrete(\"\") +\n", " theme_bw() +\n", " theme(\n", " legend.position = \"top\",\n", " panel.grid.minor = element_blank()\n", " )\n", "\n", "tbl_gamma <- expand_grid(\n", " gamma = c(.5, .9),\n", " target_power = c(0.7, 0.8)\n", " ) %>%\n", " mutate(\n", " n = map2_dbl(\n", " gamma,\n", " target_power,\n", " ~get_n_quantile(theta_null, prior, ..1, theta_mcid, ..2, alpha)),\n", " label = sprintf(\"gamma = %.2f\\n1 - beta = %.2f\\nn = %i\", gamma, target_power, round(n))\n", " )\n", "\n", "\n", "plt_power_curves <- full_join(\n", " tbl_gamma,\n", " expand_grid(\n", " theta = seq(prior_lo, prior_hi, by = 0.01),\n", " n = tbl_gamma$n\n", " ),\n", " by = \"n\"\n", " ) %>%\n", " mutate(\n", " power = map2_dbl(theta, n, ~power(..1, ..2, qnorm(1 - alpha)))\n", " ) %>%\n", " ggplot() +\n", " aes(theta, power, linetype = label) +\n", " geom_line() +\n", " scale_linetype_discrete(\"\", guide = guide_legend(nrow = 1)) +\n", " scale_x_continuous(expression(theta), breaks =c(0, 0.5)) +\n", " scale_y_continuous(\"probability to reject\", breaks = seq(0, 1, .2)) +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " legend.position = \"top\",\n", " legend.text = element_text(size = 5),\n", " legend.key.size = unit(0.9,\"line\")\n", " )\n", "\n", "\n", "set.seed(42)\n", "tbl_samples <- tbl_gamma %>%\n", " mutate(\n", " `random probability to reject` = map(gamma, ~get_sample(prior, 1e5)),\n", " `random power` = map(gamma, ~get_sample(condition(prior, lo = theta_mcid), 1e5))\n", " ) %>%\n", " unnest(c(`random probability to reject`, `random power`)) %>%\n", " pivot_longer(\n", " c(`random probability to reject`, `random power`),\n", " names_to = \"type\",\n", " values_to = \"rtheta\"\n", " ) %>%\n", " mutate(\n", " power = map2_dbl(rtheta, n, ~power(..1, ..2, qnorm(1 - alpha)))\n", " )\n", "\n", "tbl_probs <- tbl_samples %>%\n", " group_by(label, type) %>%\n", " summarise(\n", " tmp = mean(power >= 1 - beta),\n", " power = 1 - beta,\n", " .groups = \"drop\"\n", " )\n", "\n", "plt_power_distribution <- tbl_samples %>%\n", " ggplot(aes(power)) +\n", " geom_histogram(aes(y = stat(ndensity)), bins = 25, fill = \"darkgray\") +\n", " geom_vline(aes(xintercept = 0.8), color = \"black\") +\n", " geom_text(\n", " aes(\n", " label = sprintf(\"%.2f\", tmp),\n", " ),\n", " y = .9,\n", " x = 0.91,\n", " size = 3,\n", " color = \"black\",\n", " data = tbl_probs\n", " ) +\n", " scale_y_continuous(\"\", breaks = c(), limits = c(0, 1.1)) +\n", " scale_x_continuous(\"probability to reject\", breaks = seq(0, 1, .2)) +\n", " coord_cartesian(expand = FALSE) +\n", " facet_grid(type ~ label, scales = \"free_y\") +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " panel.spacing = unit(1.25, \"lines\"),\n", " strip.text = element_text(size = 6)\n", " )\n", "\n", "legend_priors <- cowplot::get_legend(plt_priors)\n", "legend_pwr <- cowplot::get_legend(plt_power_curves)\n", "\n", "cowplot::plot_grid(\n", " cowplot::plot_grid(\n", " plt_priors , plt_power_curves,\n", " rel_widths = c(1, 1)\n", " ),\n", " plt_power_distribution,\n", " rel_heights = c(1, 1.5),\n", " ncol = 1\n", ")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "ggsave(\"../latex/figures/fig5-power-distribution-quantile-approach.pdf\", width = 7.5, height = 6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A clinical trial example / utility matching (Figures 6 + 7)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "prior <- Normal(0.2, 0.2, -0.3, 0.7)\n", "# minimal clinically important difference (MCID)\n", "theta_mcid <- 0.05" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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jbJWCkeyXUc/pEtv/r7ougINrU5k9qUSUljEpswcfFMbDzpdPXJ5YzVlnPp8u5K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\nZz755JM5c+bU+7NtaD1OTk5O3759ly9frlAoNm3atHLlys8++6zujWpKP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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# adjust plot output size\n", "options(repr.plot.width = 10, repr.plot.height = 4)\n", "\n", "# plot the conditional/unconditional priors\n", "plt_prior <- tibble(\n", " theta = seq(-0.5, 1.0, .01),\n", " `unconditional prior` = pdf(prior, theta) %>%\n", " {ifelse(theta == .7 | theta == prior$lower, NA_real_, .)},\n", " `conditional prior` = pdf(condition(prior, lo = theta_mcid), theta) %>%\n", " {ifelse(theta == .7 | (theta == theta[which.min(abs(theta_mcid - theta))]), NA_real_, .)}\n", " ) %>%\n", " pivot_longer(-theta, names_to = \"type\", values_to = \"PDF\") %>%\n", " ggplot() +\n", " aes(theta, PDF, linetype = type) +\n", " geom_line() +\n", " scale_linetype_discrete(\"\") +\n", " scale_x_continuous(expression(theta)) +\n", " theme_bw() +\n", " theme(\n", " legend.position = \"top\"\n", " )\n", "\n", "# compute required sample sizes\n", "tbl_samplesizes <- tibble(\n", " \"MCID\" = get_n(theta_null, theta_mcid),\n", " \"EP\" = get_n_ep(theta_null, prior, mrv = theta_mcid, pwr = 1 - beta, alpha = alpha),\n", " \"quantile, 0.9\" = get_n_quantile(theta_null, prior, .9, mrv = theta_mcid, pwr = 1 - beta, alpha = alpha),\n", " \"quantile, 0.5\" = get_n_quantile(theta_null, prior, .5, mrv = theta_mcid, pwr = 1 - beta, alpha = alpha)\n", " ) %>%\n", " pivot_longer(everything(), names_to = \"type\", values_to = \"n\")\n", "\n", "# plot power curves\n", "plt_powr_curves <- full_join(\n", " tbl_samplesizes,\n", " expand_grid(\n", " theta = seq(-0.2, 0.7, by = 0.01),\n", " n = tbl_samplesizes$n\n", " ),\n", " by = \"n\"\n", " ) %>%\n", " mutate(\n", " power = map2_dbl(theta, n, ~power(..1, ..2, qnorm(1 - alpha))),\n", " name = sprintf(\"%s (n = %i)\", type, n)\n", " ) %>%\n", " ggplot() +\n", " aes(theta, power, color = name) +\n", " geom_line() +\n", " scale_color_discrete(\"\") +\n", " scale_x_continuous(expression(theta), breaks = seq(-1, 1, .1)) +\n", " scale_y_continuous(\"probability to reject\", breaks = seq(0, 1, .1), expand = c(0, 0)) +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " legend.position = \"top\"\n", " )\n", "\n", "n <- 1e5\n", "rtheta <- numeric(n)\n", "cprior <- condition(prior, lo = theta_mcid)\n", "i <- 1\n", "while (i < n) {\n", " sample <- rnorm(1, mean = cprior$mu, sd = cprior$tau)\n", " if (between(sample, cprior$lower, cprior$upper)) {\n", " rtheta[i] <- sample\n", " i <- i + 1\n", " }\n", "}\n", "\n", "plt_power_cdf <- full_join(\n", " tbl_samplesizes,\n", " expand_grid(\n", " rtheta = rtheta,\n", " n = tbl_samplesizes$n\n", " ),\n", " by = \"n\"\n", " ) %>%\n", " mutate(\n", " rpower = map2_dbl(rtheta, n, ~power(..1, ..2, qnorm(1 - alpha))),\n", " name = sprintf(\"%s (n = %i)\", type, n)\n", " ) %>%\n", " select(name, rpower) %>%\n", " group_by(name) %>%\n", " nest() %>%\n", " transmute(\n", " ecdf = map(data, ~tibble(\n", " power = seq(0, 1, .01),\n", " CDF = ecdf(.$rpower)(power)\n", " ))\n", " ) %>%\n", " unnest(ecdf) %>%\n", " ggplot(aes(power, CDF, color = name)) +\n", " geom_line() +\n", " scale_color_discrete(\"\") +\n", " scale_x_continuous(\"random power\", breaks = seq(0, 1, .1)) +\n", " scale_y_continuous(breaks = seq(0, 1, .1)) +\n", " coord_cartesian(expand = FALSE) +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank(),\n", " legend.position = \"top\"\n", " )\n", "\n", "legend <- cowplot::get_legend(plt_powr_curves)\n", "\n", "cowplot::plot_grid(plt_prior,\n", " cowplot::plot_grid(\n", " legend,\n", " cowplot::plot_grid(\n", " plt_powr_curves + theme(legend.position = \"none\"),\n", " plt_power_cdf + theme(legend.position = \"none\"),\n", " nrow = 1\n", " ),\n", " rel_heights = c(1, 8),\n", " ncol = 1\n", " ),\n", " rel_widths = c(1, 2),\n", " nrow = 1\n", ")" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "ggsave(\"../latex/figures/fig6-clinical-trial-example.pdf\", width = 10, height = 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we plot implied utilities (Figure 7)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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K4sgMUcwKIDWGTWgfUP8b7OpYxHayjN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\nOYBFF9RgFX8YK0SH1OecXt1+zpt7CF6wjnGMA7DYA1h0QQxWwbv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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "utility <- function(n, lambda) {\n", " lambda * PoS(prior, n, qnorm(1 - alpha), theta_mcid) - n\n", "}\n", "\n", "get_implied_lambda <- function(expected_power) uniroot(\n", " function(lambda) {\n", " EP(\n", " prior,\n", " round(optimize(function(n) utility(n, lambda), c(10, 1e4), maximum = TRUE)$maximum),\n", " c = qnorm(1 - alpha),\n", " mrv = theta_mcid\n", " ) - expected_power\n", " },\n", " c(1, 1e6)\n", ")\n", "\n", "tbl_implied_lambda <- tibble(\n", " power = seq(0.6, 0.95, by = 0.01)\n", " ) %>%\n", " mutate(\n", " n_ep = map_dbl(\n", " power,\n", " ~get_n_ep(theta_null, prior, mrv = theta_mcid, pwr = ., alpha = alpha)\n", " ),\n", " lambda_implied = map_dbl(power, ~get_implied_lambda(.)$root)\n", " )\n", "\n", "ggplot(tbl_implied_lambda) +\n", " aes(power, lambda_implied) +\n", " geom_point() +\n", " geom_line() +\n", " scale_x_continuous(\"expected power\", breaks = seq(0.6, 0.95, by = 0.05)) +\n", " scale_y_continuous(\"implied reward [average per-patient costs]\", breaks = seq(0, 20000, by = 2500)) +\n", " theme_bw() +\n", " theme(\n", " panel.grid.minor = element_blank()\n", " )" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "ggsave(\"../latex/figures/fig7-matched-reward.pdf\", width = 8, height = 3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's the implied reward for 80% expected power?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1732" ], "text/latex": [ "1732" ], "text/markdown": [ "1732" ], "text/plain": [ "[1] 1732" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "get_implied_lambda(0.8)$root %>% round" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get utility maximising sample size for $\\lambda = 3333$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "329" ], "text/latex": [ "329" ], "text/markdown": [ "329" ], "text/plain": [ "[1] 329" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "optimize(function(n) utility(n, 3333), c(10, 1e4), maximum = TRUE)$maximum %>%\n", " round" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and the corresponging expected power" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.864299528145842" ], "text/latex": [ "0.864299528145842" ], "text/markdown": [ "0.864299528145842" ], "text/plain": [ "[1] 0.8642995" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "EP(prior, 342, c = qnorm(1 - alpha), mrv = theta_mcid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 4 }