biotender-max/bio-clinical-biostatistics-bayesian-trials
Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.
npx skills add https://github.com/BioTender-max/awesome-bio-agent-skills --skill bio-clinical-biostatistics-bayesian-trialsReference examples tested with: R RBesT 1.7+ (Roche), OncoBayes2 0.8+ (Novartis), BOIN 2.7+, dfcrm 0.2-2+, escalation 0.1+, trialr 0.1.6+, bayesDP, psborrow2 (FDA-supported), rstan / cmdstanr, brms. Legacy: JAGS, WinBUGS.
Before using code patterns, verify installed versions match. If versions differ:
packageVersion('<pkg>') then ?function_nameIf code throws an error, introspect the installed package and adapt the example to match the actual API rather than retrying.
"Design a Bayesian clinical trial" -> Specify a prior, likelihood, and decision rule with frequentist operating characteristics demonstrated via simulation; for dose-finding use FDA-endorsed BOIN; for borrowing use robust MAP priors; for adaptive platforms use posterior probability of efficacy stopping with simulation-calibrated thresholds.
FDA 2010 CDRH Bayesian Devices Guidance (Feb 5 2010): the only Bayesian-specific FDA guidance until January 2026. Why devices were ahead: CDRH's PMA pathway permits one pivotal trial and accepts borrowing from prior/OUS data more readily than CDER. Example: Edwards SAPIEN (PARTNER B, PMA P100041, Nov 2011) approved using Bayesian propensity-matched comparison to registry of standard-of-care patients.
FDA January 2026 CDER Bayesian Methodology Draft (FDA-2025-D-3217; comment period closed March 13 2026): first-ever drug-side Bayesian guidance. Explicit that Bayesian primary inference in pivotals is acceptable provided:
Project Optimus (FDA OCE, launched 2021; final dose-optimisation guidance Aug 2024): rewrites Phase I/II oncology by requiring randomised dose comparison before registration. Has made multi-arm randomised dose-finding (BOIN-12, gBOIN-ET) much more important than classic MTD-finding.
FDA BOIN Fit-for-Purpose qualification (December 2021): first formal FDA endorsement of a specific dose-finding design under the Drug Development Tools program.
ICH E20 (Step 2b/3 draft June 2025; NOT final) treats Bayesian as a legitimate analytic framework but requires demonstration of acceptable frequentist operating characteristics (Type-I, power) over a pre-specified parameter space.
| Method | Use case | Software | Strength | Fails when |
|--------|----------|----------|----------|------------|
| BOIN | Phase I MTD | R BOIN (Yuan) | FDA Fit-for-Purpose 2021; pre-tabulated decisions; no bedside Bayesian software | Statistically less efficient than CRM under correct skeleton |
| mTPI-2 / Keyboard | Phase I MTD | R escalation; R Keyboard | Default replacement for mTPI; fixes Ockham bias | Tabulated; transparency |
| CRM | Phase I MTD | R dfcrm, trialr | Most efficient under correct skeleton | Skeleton mis-specification biases MTD |
| EWOC | Phase I MTD | R ewoc, dfcrm | Explicit overdose-control constraint (P(dose>MTD) <= 0.25) | More conservative than CRM in small trials |
| BOIN-12 / gBOIN-ET | Phase 1b dose-optimisation (Project Optimus) | R BOIN extensions | Multi-arm randomised dose comparison | Requires explicit efficacy + toxicity scoring |
| MAP prior | Borrowing from historical control arms | R RBesT::gMAP | Industry-standard borrowing | Sample-size of MAP prior must be calibrated (Schmidli 2014) |
| Robust MAP | Borrowing with prior-data conflict protection | R RBesT::robustify | Adds vague component (weight 0.1-0.3) to detach if conflict | Mixture weight choice affects borrowing |
| EXNEX | Basket trial across rare-disease strata | R bhmbasket; OncoBayes2 | Avoids HM catastrophic borrowing; mixture 0.5/0.5 default (Neuenschwander 2016) | Default weights may over-borrow |
| Dixon-Simon shrinkage | Subgroup analysis | Custom Stan/brms | Honest about no qualitative interaction prior | Prior on tau drives results |
| Berry-Berry 3-level hierarchical | AE multiplicity (AE within PT within SOC) | R c212; JMP Clinical | Tames safety multiplicity | Spike-and-slab tuning matters |
| Posterior probability stopping | Adaptive sequential | Custom; FACTS commercial | Bayesian likelihood-principle compatible | Threshold calibration via simulation |
| Predictive probability of success | End-of-Phase-2 go/no-go | Custom Stan | Decision-theoretic; integrates over posterior | Requires Phase 3 design specified |
| Spiegelhalter skeptical/enthusiastic prior | Sensitivity for regulatory pivotals | Custom | Frames regulator-vs-sponsor evidence | Prior elicitation effort |
| Power prior | Pediatric extrapolation borrowing from adults | R bayesDP, psborrow2 | Partial borrowing with discount gamma | gamma choice (Jan 2026 FDA draft: 0.3-0.6) |
Postdoc reading list:
| Scenario | Recommended approach | Why |
|----------|---------------------|-----|
| Phase 1 oncology, single-agent MTD | BOIN with target DLT 30%; cohort size 3 | FDA Fit-for-Purpose 2021; tabulated escalation |
| Phase 1 oncology, combination (2 agents) | BLRM with EXNEX in OncoBayes2 | Multi-dimensional dose; industry standard at Novartis/Roche |
| Phase 1b/2 dose-optimisation (Project Optimus) | BOIN-12 or gBOIN-ET; randomised 2-dose comparison | Aug 2024 FDA dose-optimisation guidance |
| Phase 3 with historical control arms available | Robust MAP via RBesT; gMAP() + robustify() | Industry standard borrowing with prior-data conflict protection |
| Basket trial across rare-disease strata | EXNEX (0.5 EX / 0.5 NEX mixture) via OncoBayes2 | Avoids HM catastrophic borrowing |
| Pediatric extrapolation from adult data | Power prior with discount gamma 0.3-0.6 | working convention; the FDA Bayesian Jan 2026 draft does not prescribe a specific gamma range -- check the draft for the current language before quoting |
| Phase 3 trial with single arm + RWE comparator | Propensity-score-integrated power prior via psborrow2 | FDA-supported package for external controls |
| Adaptive trial wanting posterior-probability stopping | Custom Stan model + simulation-calibrated threshold | Bayesian likelihood-principle compatible; no penalty for repeated looks |
| End-of-Phase-2 go/no-go | Predictive probability of success in Phase 3 | Integrates posterior over Phase 3 design |
| Hypothesis-generating safety AE analysis (>100 PTs) | Berry-Berry 3-level hierarchical (AE within PT within SOC) | Tames multiplicity; spike-and-slab on log OR |
| Subgroup analysis post-signal | Bayesian shrinkage (Dixon-Simon, RBesT) | Hemmings-Koch 2019: shrinkage for replication planning, NOT signal generation |
| Regulatory pivotal sensitivity | Spiegelhalter skeptical-prior framework | Frames "evidence for regulators" vs "evidence for sponsor" |
library(BOIN)
# Generate escalation table for protocol
boundary_table <- get.boundary(
target = 0.30, # target DLT rate
ncohort = 10, # 10 cohorts -> max 30 patients with size 3
cohortsize = 3,
n.earlystop = 12, # stop early at lowest dose if 12 patients show futility
p.saf = 0.6 * 0.30, # "safe" escalation boundary
p.tox = 1.4 * 0.30 # "toxic" de-escalation boundary
)
print(boundary_table)
# Pre-printed at investigator desk; no bedside Bayesian software
# Operating characteristics simulation
oc_boin <- get.oc(
target = 0.30,
p.true = c(0.05, 0.10, 0.20, 0.30, 0.40, 0.55), # true DLT per dose
ncohort = 10,
cohortsize = 3,
ntrial = 1000
)
print(oc_boin)
# Reports: MTD selection accuracy, overdose risk, average sample size
BOIN's transparency-over-modelling philosophy: unlike CRM, BOIN does NOT use information from intermediate dose levels in a model-based way. The Jin-Yuan vs Neuenschwander/Mozgunov debate (Stat Med, Pharm Stat, since ~2018): BLRM/CRM are statistically more efficient under correct model; BOIN is operationally simpler and more transparent.
library(dfcrm)
prior_skeleton <- getprior(halfwidth = 0.05, target = 0.30, nu = 3, nlevel = 6)
# Lee-Cheung 2009 indifference-interval calibration
crm_sim <- crmsim(
PI = c(0.05, 0.10, 0.20, 0.30, 0.40, 0.55),
prior = prior_skeleton,
target = 0.30,
n = 30,
x0 = 1, # starting dose
nsim = 1000,
method = 'bayes',
model = 'logistic'
)
print(crm_sim)
Skeleton mis-specification is the canonical CRM failure mode. Lee-Cheung 2009 indifference-interval method gives a systematic calibration approach.
# Babb-Rogatko-Zacks 1998: explicit P(dose > MTD) <= alpha (default 0.25)
# Implementation in dfcrm::ewoc; or `ewoc` package
Schmidli et al 2014 *Biometrics* 70:1023: Meta-Analytic-Predictive prior. Fit random-effects meta-analysis of historical control arms; derive predictive distribution for new control arm; use as informative prior. Effective sample size from history typically 20-80% of new control arm.
library(RBesT)
# Historical control data (4 prior studies)
historical_data <- data.frame(
study = c('s1', 's2', 's3', 's4'),
n = c(40, 35, 50, 45),
r = c(8, 6, 12, 9) # responders
)
# Fit MAP via gMAP (Stan-based random-effects meta-analysis)
map_prior <- gMAP(
cbind(r, n - r) ~ 1 | study,
data = historical_data,
family = binomial,
tau.dist = 'HalfNormal',
tau.prior = 0.5, # between-study SD prior
beta.prior = cbind(0, 2) # weakly informative on logit response
)
print(map_prior)
# Approximate posterior with mixture for downstream computation
map_mix <- automixfit(map_prior, Nc = 2)
print(map_mix)
# Effective sample size
ess(map_mix)
# Robust MAP: add vague mixture component (weight 0.1-0.3) to guard against prior-data conflict
robust_map <- robustify(map_mix, weight = 0.2, mean = 0.5, n = 1)
print(robust_map)
ess(robust_map)
Robust MAP rationale: if the new data disagree with historical (prior-data conflict), the mixture down-weights the informative component automatically. Schoenfeld 2017 critique: Schmidli 2014's choice of mixture weight requires sensitivity analysis.
Neuenschwander, Wandel, Roychoudhury, Bailey 2016 *Pharm Stat* 15:123: Mixture of exchangeable (shared mean+variance) + non-exchangeable (per-basket independent), typically weighted 0.5/0.5. Avoids HM catastrophic borrowing when one basket truly different.
library(OncoBayes2) # Novartis-developed; canonical EXNEX implementation
# Or simplified via bhmbasket
library(bhmbasket)
# Conceptual: each basket has its own posterior, with shrinkage governed by exchangeability mixture
# Default weights 0.5 EX / 0.5 NEX
# Sensitivity over weights (0.1, 0.3, 0.5, 0.7, 0.9) is essential
Neoadjuvant breast cancer; 10 biomarker-defined subtypes × multiple arms; Bayesian RAR; graduation criterion = posterior predictive probability of success in 300-patient Phase 3 ≥ 0.85. Berry Consultants designed engine.
# Conceptual implementation requires custom Stan or FACTS (Berry Consultants commercial)
# Pseudocode:
# 1. Fit hierarchical model to platform data: response ~ arm + biomarker_subtype + arm:subtype
# 2. Posterior draws of treatment effect by subtype
# 3. For each draw, simulate Phase 3 trial: n=300, treatment vs control, observed effect
# 4. Compute proportion of draws meeting Phase 3 success criterion
# 5. If proportion >= 0.85, arm graduates
Severe pneumonia, repurposed for COVID-19; Bayesian factorial multi-domain design. Generated corticosteroid signal independently of RECOVERY.
Berry SM, Berry DA 2004 *Biometrics* 60:418: three-level hierarchical model for AE multiplicity (AE within MedDRA PT within SOC); spike-and-slab on the log OR. Tames the FDA-feared multiplicity in safety summaries.
library(c212) # Berry-Berry implementation
# Conceptual: each AE has log OR drawn from spike-and-slab prior
# Spike at 0 (no effect); slab as N(mu_SOC, sigma_SOC)
# SOC-level parameters from N(mu_overall, sigma_overall)
# Borrowing within SOC; shrinkage toward 0 if no evidence
# JMP Clinical also implements this for industry use
library(bayesDP)
library(psborrow2) # FDA-supported package
# Power prior: combines current data L(theta | D_current) with historical L(theta | D_hist)^gamma
# gamma in [0, 1]; gamma = 0 = no borrowing; gamma = 1 = full pooling
# Typical pediatric extrapolation: gamma = 0.3 to 0.6 per FDA Bayesian Jan 2026 draft
The 2024-2026 regulatory shift: FDA has materially expanded acceptance of external/historical/synthetic control arms in rare disease, paediatric, and accelerated-approval settings. Key documents: FDA 2018 RWE Framework (and 2024 enhancements), FDA 2023 Considerations for Use of RWE/RWD for Regulatory Decisions, EMA Reflection Paper on Use of RWE in Regulatory Decision-Making (effective 2024). Bayesian methods are the natural fit because historical data become prior information rather than concurrent control.
| Method | Borrowing mechanism | Discount control | When to use |
|--------|---------------------|------------------|-------------|
| Power prior (Ibrahim-Chen 2000) | Likelihood of historical data raised to power gamma | gamma in [0, 1] fixed or modelled | When historical data is single source; gamma ~ Beta in adaptive power prior |
| Robust MAP (Schmidli 2014) | Meta-analytic-predictive prior + vague mixture | Mixture weight (typ 0.1-0.3) | Multiple historical control arms; standard for borrowing |
| Commensurate prior (Hobbs 2011) | Conditional model on agreement parameter | Tau estimated from data | When agreement between historical and current is data-determined |
| Propensity-integrated power prior | Power prior weighted by PS overlap | gamma * (PS-trimmed overlap) | RWE comparator with covariate imbalance |
| Doubly robust ATT via causal inference | IPW + outcome regression | n/a | RWE comparator; identifies marginal ATT |
The psborrow2 package (Genentech / Bayer / FDA-Janssen collaboration; CRAN 2024+) is the canonical R implementation for propensity-score-integrated Bayesian Dynamic Borrowing. The skeleton below illustrates the workflow conceptually; verify exact function names and arguments against the current psborrow2 vignette before use (the package API has evolved through 2024-2026).
library(psborrow2)
# Define external and internal data
ext_data <- data.frame(usubjid = ..., trt = 0, outcome = ..., covariates = ...)
int_data <- data.frame(usubjid = ..., trt = 0 | 1, outcome = ..., covariates = ...)
# Create borrowing design
borrowing_design <- borrowing_full(
method_name = "BDB", # Bayesian Dynamic Borrowing
ext_flag_col = "ext",
tau_prior = prior_gamma(0.001, 0.001) # weakly informative on borrowing
)
# Outcome model (Cox for TTE; logistic for binary)
outcome_model <- outcome_surv_exponential(
time_var = "time",
cens_var = "cens",
baseline_prior = prior_normal(0, 100),
trt_prior = prior_normal(0, 100)
)
# Run Bayesian analysis with covariate adjustment + borrowing
result <- create_analysis_obj(
data_matrix = borrow_obj,
outcome = outcome_model,
borrowing = borrowing_design,
covariates = c("age", "ecog", "baseline_severity")
)
mcmc_result <- mcmc_sample(result, n_chains = 4, n_iter = 4000)
Spiegelhalter, Freedman, Blackburn 1986 *Stat Med* 5:421: the trip-wire / skeptical-prior framework. Pre-specify a skeptical prior centred at the null and an enthusiastic prior centred at the alternative; stopping requires the skeptic to be convinced (posterior under skeptical prior exceeds threshold).
Frames "evidence for regulators" vs "evidence for sponsor" in Bayesian language; still cited in modern Bayesian-trial protocols.
# Skeptical prior: N(0, sd_sk) — centred at null
# Enthusiastic prior: N(delta_alt, sd_en) — centred at clinically meaningful effect
# Decision: stop for efficacy if P(theta > 0 | skeptical posterior) > 0.975
# stop for futility if P(theta < delta_alt | enthusiastic posterior) > 0.80
rstan/cmdstanr); Docker/renv-pinned environment; include seeds + posterior diagnostics (R-hat <1.01, ESS >1000 per chain).| Threshold | Source | Rationale |
|-----------|--------|-----------|
| FDA BOIN Fit-for-Purpose qualification (Dec 2021) | FDA Drug Development Tools program | First formal FDA dose-finding endorsement |
| Target DLT rate 30% (Phase 1 oncology) | Standard convention | Modal target across oncology Phase 1 |
| MAP prior effective sample size 20-80% of new control | Schmidli 2014 | Borrowing strength typical range |
| Robust MAP mixture weight 0.1-0.3 | Schmidli 2014 | Guards against prior-data conflict |
| EXNEX default 0.5 EX / 0.5 NEX | Neuenschwander 2016 | Standard starting weight; sensitivity required |
| I-SPY 2 graduation PP >= 0.85 | Barker 2009 | Bayesian platform standard |
| Power prior gamma 0.3-0.6 for pediatric extrapolation | working convention; the FDA Bayesian Jan 2026 draft does not prescribe a specific range | Partial borrowing default |
| Stan R-hat <1.01, ESS >1000 per chain | Vehtari 2021 *Bayesian Analysis* | Posterior convergence criteria |
| EWOC overdose constraint P(dose > MTD) <= 0.25 | Babb-Rogatko-Zacks 1998 | Safety floor |
| Error / symptom | Cause | Solution |
|-----------------|-------|----------|
| CRM with arbitrary skeleton | No calibration | Lee-Cheung 2009 indifference-interval; or BOIN |
| MAP without prior-data conflict check | Posterior dominated by prior | Robust MAP; PP-check; sensitivity over mixture weight |
| EXNEX with single weight scheme | No sensitivity | Weights 0.1, 0.3, 0.5, 0.7, 0.9; report range |
| Posterior probability stopping without Type-I sim | Regulatory rejection | Simulate under null; calibrate threshold |
| I-SPY 2 graduated arm reported uncorrected | Selection bias | Conditional MLE; cite Robertson 2023 |
| Bayesian shrinkage for signal discovery | Hemmings-Koch critique | Shrinkage for replication only |
| Power prior gamma = 1 | Full pooling | Discount 0.3-0.6 per FDA 2026 draft |
| WinBUGS without containerisation | Reproducibility | Stan + Docker/renv-pinned |
| BOIN vs CRM comparison without simulation OCs | Apples-to-oranges | Compare OCs over same true DLT rates |
| FDA cited for Bayesian drugs guidance pre-2026 | Confusion | FDA 2010 is DEVICES; FDA 2026 (draft) is drugs |
| Pushback | Response |
|----------|----------|
| "Type-I error control?" | Simulation under null demonstrates frequentist Type-I = nominal at threshold chosen; documented in SAP appendix |
| "Prior justification?" | MAP from historical control arms via gMAP; robust mixture weight 0.2 for prior-data conflict; sensitivity over prior provided |
| "Why BOIN over CRM?" | BOIN Fit-for-Purpose qualified Dec 2021; pre-tabulated escalation; no bedside Bayesian software; OCs comparable to CRM in simulation |
| "EXNEX weight sensitivity?" | Reported over weights 0.1, 0.3, 0.5, 0.7, 0.9; results stable; primary at 0.5/0.5 per Neuenschwander 2016 |
| "Power prior gamma?" | Discount 0.5 per FDA Bayesian Jan 2026 draft; sensitivity over 0.3-0.7 provided |
| "Posterior probability threshold?" | Calibrated via simulation to frequentist Type-I 0.025 one-sided; cite Berry 2010 |
| "Stan reproducibility?" | Docker container + renv-pinned R + Stan version; seeds provided; R-hat <1.01, ESS >2000 per parameter |
| "Bias correction on platform graduation?" | Conditional MLE applied to estimate Phase 3 effect; cite Robertson 2023 |
| "Why not frequentist instead?" | Bayesian framework permits borrowing (rare disease, pediatric); working convention; the FDA Bayesian Jan 2026 draft does not prescribe a specific gamma range -- check the draft for the current language before quoting primary inference with simulation calibration |
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