inst/sbc/sbc_report.R

In OncoBayes2: Bayesian Logistic Regression for Oncology Dose-Escalation Trials

#' ---
#' title: Simulation based calibration for OncoBayes2
#' author: ""
#' date: "`r date()`"
#' output: html_vignette
#' params:
#'   include_plots: FALSE
#' vignette: >
#'   %\VignetteIndexEntry{Simulation based calibration for OncoBayes2}
#'   %\VignetteEngine{knitr::rmarkdown}
#'   %\VignetteEncoding{UTF-8}
#' ---
#'
#+ include=FALSE
here::i_am("inst/sbc/sbc_report.R")
library(here)
library(knitr)
library(tools)
library(assertthat)
library(dplyr)
library(tidyr)
library(broom)
library(ggplot2)
theme_set(theme_bw())
source(here("inst", "sbc", "sbc_tools.R"))

knitr::opts_chunk$set(
  fig.width = 1.62 * 4,
  fig.height = 4,
  cache = FALSE,
  echo = FALSE
)
#'
#' This report documents the results of a simulation based calibration
#' (SBC) run for `OncoBayes2`. TODO
#'
#' The calibration data presented here has been generated at and with
#' the `OncoBayes` git version as:
cat(readLines(here("inst", "sbc", "calibration.md5")), sep = "\n")
#'
#' The MD5 hash of the calibration data file presented here must match
#' the above listed MD5:
md5sum(here("inst", "sbc", "calibration.rds"))
#'
#' # Introduction
#'
#' Simulation based calibration (SBC) is a necessary condition which
#' must be met for any Bayesian analysis with proper priors. The
#' details are presented in Talts, et. al (see
#' https://arxiv.org/abs/1804.06788).
#'
#' Self-consistency of any Bayesian analysis with a proper prior:
#'
#' $$ p(\theta) = \iint \mbox{d}\tilde{y} \, \mbox{d}\tilde{\theta} \, p(\theta|\tilde{y}) \, p(\tilde{y}|\tilde{\theta}) \, p(\tilde{\theta}) $$
#' $$ \Leftrightarrow p(\theta) = \iint \mbox{d}\tilde{y} \, \mbox{d}\tilde{\theta} \, p(\theta,\tilde{y},\tilde{\theta}) $$
#'
#' SBC procedure:
#'
#' Repeat $s=1, ..., S$ times:
#'
#' 1. Sample from the prior $$\tilde{\theta} \sim p(\theta)$$
#'
#' 2. Sample fake data $$\tilde{y} \sim p(y|\tilde{\theta})$$
#'
#' 3. Obtain $L$ posterior samples $$\{\theta_1, ..., \theta_L\} \sim p(\tilde{\theta}|\tilde{y})$$
#'
#' 4. Calculate the *rank* $r_s$ of the prior draw $\tilde{\theta}$ wrt to
#' the posterior sample $\{\theta_1, ..., \theta_L\} \sim p(\tilde{\theta}|\tilde{y})$ which falls into the range $[0,L]$
#' out of the possible $L+1$ ranks. The rank is calculated as
#' $$r_s = \sum_{l=1}^L \mathbb{I}[ \theta_l < \tilde{\theta}]$$
#'
#' The $S$ ranks then form a uniform $0-1$ density and the count in
#' each bin has a binomial distribution with probability of
#' $$p(r \in \mbox{Any Bin}) =\frac{(L+1)}{S}.$$
#'
#' ## Model description TODO
#'
#' The fake data simulation function returns ... TODO. Please refer to
#' the `sbc_tools.R` and `make_reference_rankhist.R` R programs for the
#' implementation details.
#'
#' The reference runs are created with $L=1023$ posterior draws for
#' each replication and a total of $S=10^4$ replications are run per
#' case. For the evaluation here the results are reduced to
#' $B=L'+1=64$ bins to ensure a sufficiently large sample size per
#' bin.
#'

calibration <- readRDS(here("inst", "sbc", "calibration.rds"))

have_raw <- file.exists(here("inst", "sbc", "calibration_data.rds"))
if (have_raw) {
  calibration_raw <- readRDS(here("inst", "sbc", "calibration_data.rds"))
}

include_plots <- TRUE
if ("params" %in% ls()) {
  include_plots <- params$include_plots
}

# The summary function we use here scales down the $L+1=1024$ bins to
# smaller number of rank bins. This improves the number of counts
# expected per rank bin ($S/(L+1)$) and is thus more robust in terms
# of large number laws. We choose $L=1023$ samples from the posterior
# such that we have $1024 = 2^10$ bins for the ranks. Thus any power
# of $2$ can be used to scale down the number of bins.

plot_binned <- function(cal_df) {
  pl <- NULL

  if (!include_plots) {
    return(pl)
  }

  if (!all(cal_df$count == 0)) {
    S <- calibration$S
    B <- calibration$B

    c95 <- qbinom(c(0.025, 0.5, 0.975), S, 1 / B)

    dd <- cal_df %>%
      arrange(param, bin) %>%
      group_by(param) %>%
      mutate(ecdf = cumsum(count) / S, ecdf_ref = (bin + 1) / B) %>%
      filter(!all(ecdf == 0))

    nparam <- length(unique(dd$param))
    if (unique(dd$partype) %in% c("mu_eta", "tau_eta")) {
      nc <- nparam
    } else {
      nc <- 2
    }

    nr <- max(1, ceiling(nparam / nc))

    pl <- list()
    pl[["hist"]] <- ggplot(dd, aes(bin, count)) +
      facet_wrap(~param, nrow = nr, ncol = nc) +
      geom_col() +
      geom_hline(yintercept = c95[c(1, 3)], linetype = I(2)) +
      geom_hline(yintercept = c95[c(2)], linetype = I(3))
    pl[["ecdf_diff"]] <- ggplot(dd, aes(bin, ecdf - ecdf_ref)) +
      facet_wrap(~param, nrow = nr, ncol = nc) +
      geom_step() +
      geom_hline(yintercept = 0, linetype = I(3))
    pl
  }

  return(pl)
}


B <- calibration$B
S <- calibration$S

bins_all <- calibration$data %>%
  tidyr::gather(key = "param", value = "count", -data_scenario, -bin) %>%
  mutate(
    partype = sapply(strsplit(param, "[[]"), "[", 1),
    group = interaction(data_scenario, partype)
  )


cal_split <- split(bins_all, bins_all$group)

pl_split <- lapply(cal_split, function(cal_df) plot_binned(cal_df))


#' # SBC results
#'
#' ## Sampler Diagnostics Overview
#'
kable(calibration$sampler_diagnostics, digits = 3)


#'
#+ include=include_plots&have_raw, eval=include_plots&have_raw, fig.width=8,fig.height=6
calibration_raw %>%
  select(starts_with("min_"), "max_Rhat", starts_with("lp_"), "data_scenario") %>%
  pivot_longer(!data_scenario, names_to = "metric") %>%
  ggplot(aes(value)) +
  facet_grid(data_scenario ~ metric, scales = "free_x") +
  geom_histogram(bins = 60) +
  xlab(NULL) +
  scale_x_log10() +
  theme(axis.text.x = element_text(angle = 60, vjust = 1, hjust = 1)) +
  ggtitle("Sampler diagnostics")

#'
#' Large Rhat is defined as exceeding $1.1$.
#'
#' ## Sampler Adaptation & Performance Overview
#'
#'
#+ include=include_plots&have_raw, eval=include_plots&have_raw
sampler_performance <- calibration_raw %>%
  select("time.running", starts_with("lp_"), "stepsize", "accept_stat", "data_scenario") %>%
  mutate(lp_ess_bulk_speed = lp_ess_bulk / time.running, lp_ess_tail_speed = lp_ess_tail / time.running) %>%
  select("data_scenario", "stepsize", "accept_stat", ends_with("_speed"))

sampler_performance %>%
  group_by(data_scenario) %>%
  summarize(across(where(is.numeric), list(mean = mean, sd = sd)), N = n()) %>%
  relocate(data_scenario, N) %>%
  kable(digits = 3)

#'
#' ESS speed is in units of ESS per second.
#'

#+ include=include_plots&have_raw, eval=include_plots&have_raw, fig.width=8,fig.height=6
sampler_performance %>%
  pivot_longer(!data_scenario, names_to = "metric") %>%
  mutate(metric = factor(metric, c("accept_stat", "stepsize", "lp_ess_bulk_speed", "lp_ess_tail_speed"))) %>%
  ggplot(aes(value)) +
  facet_grid(data_scenario ~ metric, scales = "free_x") +
  geom_histogram(bins = 60) +
  xlab(NULL) +
  scale_x_log10() +
  theme(axis.text.x = element_text(angle = 60, vjust = 1, hjust = 1)) +
  ggtitle("Sampler adaptation & performance")

#'
#'
chisq <- bins_all %>%
  arrange(data_scenario, partype, param, bin) %>%
  group_by(data_scenario, partype, param) %>%
  mutate(allna = all(count == 0)) %>%
  filter(!allna) %>%
  do(tidy(chisq.test(.$count))[, c(1, 3, 2)]) %>%
  rename(df = parameter) %>%
  ungroup()

#'
#' ## $\chi^2$ Statistic: Single-agent logistic regression, stratified
#'

kable(chisq %>% filter(data_scenario == "log2bayes_EX") %>% select(-data_scenario, -partype), digits = 3)

#'
#' ## $\chi^2$ Statistic: Single-agent logistic regression, EXchangeable/NonEXchangeable
#'

kable(chisq %>% filter(data_scenario == "log2bayes_EXNEX") %>% select(-data_scenario, -partype), digits = 3)

#'
#' ## $\chi^2$ Statistic: Double combination, fully exchangeable, stratified
#'


kable(chisq %>% filter(data_scenario == "combo2_EX") %>% select(-data_scenario, -partype), digits = 3)

#'
#' ## $\chi^2$ Statistic: Double combination, EXchangeable/NonEXchangeable
#'

kable(chisq %>% filter(data_scenario == "combo2_EXNEX") %>% select(-data_scenario, -partype), digits = 3)

#'
#' ## $\chi^2$ Statistic: Triple combination, EXchangeable/NonEXchangeable
#'

kable(chisq %>% filter(data_scenario == "combo3_EXNEX") %>% select(-data_scenario, -partype), digits = 3)

#+ results="asis", include=include_plots, eval=include_plots
spin_child("sbc_report_plots.R")

#'
#' ## Session Info
#'
sessionInfo()