bio-clinical-biostatistics-bayesian-trials

Version Compatibility

Reference 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:

• R: packageVersion('<pkg>') then ?function_name
• Confirmatory regulatory work: validate against pinned package versions in submission

If code throws an error, introspect the installed package and adapt the example to match the actual API rather than retrying.

Bayesian Clinical Trials

"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.

Regulatory Status -- The 2024-2026 Bayesian Pivot

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) was approved on a single randomized pivotal trial (TAVR vs standard therapy in inoperable patients); the later SAPIEN 3 intermediate-risk PMA used a propensity-score comparison of a single-arm cohort against PARTNER IIA surgical controls -- illustrating CDRH's acceptance of non-randomized/borrowed comparisons.

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:

• Prospective specification
• Simulation-based operating characteristics (including frequentist Type-I error under null scenarios — agency still wants calibration)
• Justified priors
• Code/data sufficient for FDA replication

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.

Algorithmic Taxonomy

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:

• FDA 2010 Guidance for Industry: Use of Bayesian Statistics in Medical Device Clinical Trials (Feb 5 2010)
• FDA 2026 Draft Use of Bayesian Methodology in Clinical Trials (FDA-2025-D-3217, Jan 2026)
• Berry SM, Carlin BP, Lee JJ, Müller P 2010 Bayesian Adaptive Methods for Clinical Trials (CRC)
• Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B 2014 Biometrics 70:1023 (MAP + robust MAP)
• Weber S, Li Y, Seaman J, Kakizume T, Schmidli H 2021 J Stat Softw 100:19 (RBesT)
• Neuenschwander B, Wandel S, Roychoudhury S, Bailey S 2016 Pharm Stat 15:123 (EXNEX)
• Liu S, Yuan Y 2015 J R Stat Soc C 64:507 (BOIN)
• O'Quigley J, Pepe M, Fisher L 1990 Biometrics 46:33 (CRM)
• Babb J, Rogatko A, Zacks S 1998 Stat Med 17:1103 (EWOC)
• Ji Y, Liu P, Li Y, Bekele BN 2010 Clin Trials 7:653 (mTPI)
• Guo W, Wang SJ, Yang S, Lynn H, Ji Y 2017 Contemp Clin Trials 58:23 (mTPI-2 / Keyboard)
• Berry SM, Broglio KR, Groshen S, Berry DA 2013 Clin Trials 10:720 (basket trial hierarchical)
• Berry SM, Berry DA 2004 Biometrics 60:418 (three-level AE hierarchical)
• Spiegelhalter DJ, Freedman LS, Parmar MKB 1994 JRSS-A 157:357 (skeptical/enthusiastic prior framework)
• Rugo HS et al 2016 NEJM 375:23 (I-SPY 2 veliparib-carboplatin)
• Angus DC et al 2020 JAMA (REMAP-CAP COVID rationale)

Decision Tree by Scenario

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"

Phase I Dose-Finding -- BOIN, CRM, mTPI-2

BOIN (FDA-preferred operational)

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.

CRM with calibrated skeleton

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.

EWOC (overdose control)

# Babb-Rogatko-Zacks 1998: explicit P(dose > MTD) <= alpha (default 0.25)
# Implementation in dfcrm::ewoc; or `ewoc` package

MAP Priors and RBesT

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. The mixture weight on the informative component is a tuning choice and should be varied in a pre-specified sensitivity analysis.

EXNEX for Basket Trials

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

Bayesian Platform Trials

I-SPY 2 (Rugo et al 2016 NEJM 375:23)

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

REMAP-CAP (Angus 2020 JAMA)

Severe pneumonia, repurposed for COVID-19; Bayesian factorial multi-domain design. Generated corticosteroid signal independently of RECOVERY.

Drop-the-loser vs promising-the-winner

• Adaptive arm-dropping (futility): posterior P(beating control) drops below threshold -> close. Mathematically straightforward.
• "Promising-the-winner": selection bias. Bias-adjusted estimators (Robertson 2023; conditional MLE) standard in I-SPY 2 reports.

Hierarchical Models for Safety Multiplicity (Berry-Berry 2004)

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

Power Priors for Borrowing

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

External Control Arms and Real-World Evidence (RWE)

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.

Methodology taxonomy

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

psborrow2 — the FDA-supported RWE framework

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)

Operational rules (FDA 2024-2025 RWE practice)

1. Pre-specify the RWE source and document acquisition (registry, EHR, claims, RWD vendor)
2. Demonstrate comparability via propensity-score overlap (standardised mean differences <0.25 for key prognostic factors)
3. Apply discount priors — full pooling (gamma=1) is regulatory-rejected; typical discount gamma 0.3-0.6
4. Sensitivity over borrowing strength — report results at multiple gamma or mixture weights
5. Tipping-point analysis on prior-data agreement — at what discount does the conclusion flip?
6. E-value or bound for unmeasured confounding (VanderWeele-Ding 2017) — required for FDA submissions; reports the minimum strength of unmeasured confounding that could overturn the result

When RWE is NOT acceptable

• Trial sponsor and RWE source have meaningful incentive misalignment (e.g., RWE from non-disinterested source)
• RWE captured before standard-of-care evolved (constancy violation, similar to NI biocreep)
• Outcome definitions differ between RWE and current trial (variable harmonisation impossible)
• Censoring patterns in RWE differ structurally from trial (administrative vs disease-driven)
• Highly variable baseline characteristics impossible to balance via propensity weighting

Recent decisive cases (2024-2026)

• Zynteglo (FDA 2022, ongoing post-market): beta-thalassemia gene therapy; single-arm trial vs natural history RWE comparator
• Skysona (FDA 2022): cerebral adrenoleukodystrophy; RWE natural-history comparator
• Multiple ultra-rare disease accelerated approvals 2024-2025: RWE/external control increasingly accepted in <100-patient trials

Spiegelhalter Skeptical/Enthusiastic Priors

Spiegelhalter, Freedman, Parmar 1994 JRSS-A 157:357: 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

Per-Method Failure Modes

CRM with mis-calibrated skeleton

• Trigger: Default or arbitrary skeleton without indifference-interval calibration.
• Mechanism: Skeleton dictates target dose; mis-calibration biases MTD.
• Symptom: MTD selection differs systematically from clinical expectation.
• Fix: Calibrate via Lee-Cheung 2009; or switch to BOIN.

MAP prior with prior-data conflict

• Trigger: Historical control rate differs substantially from observed current control.
• Mechanism: Informative MAP prior pulls toward historical; current data poorly fit.
• Symptom: Posterior dominated by prior; current data evidence under-weighted.
• Fix: Robust MAP with mixture weight 0.2-0.3; verify prior-data conflict via posterior predictive checks.

EXNEX with default 0.5/0.5 weights

• Trigger: Default mixture weights without sensitivity.
• Mechanism: 50% EX weight allows substantial borrowing even when basket differs.
• Symptom: Detected differential basket "softened" by borrowing.
• Fix: Sensitivity analysis over weights (0.1, 0.3, 0.5, 0.7, 0.9); report range.

Posterior probability stopping without simulation-calibrated threshold

• Trigger: Stopping rule P(theta > 0 | data) > 0.975 applied without Type-I simulation.
• Mechanism: Bayesian rule may not control frequentist Type-I in regulatory sense.
• Symptom: FDA review flags lack of Type-I demonstration.
• Fix: Simulate under null; calibrate threshold so frequentist Type-I = nominal.

I-SPY 2 graduation criterion without bias correction

• Trigger: Graduated arm's effect estimate reported uncorrected.
• Mechanism: Selection on PP > 0.85 inflates estimate.
• Symptom: Phase 3 confirmation finds smaller effect than platform suggested.
• Fix: Bias-correction via conditional MLE or hierarchical Bayesian; cite Robertson 2023.

Bayesian shrinkage for signal discovery (Dane vs Hemmings)

• Trigger: Hierarchical model fit during signal discovery rather than replication planning.
• Mechanism: Shrinkage pre-emptively damps heterogeneity being searched for.
• Symptom: Signal detected by causal forest gets shrunken to null in shrinkage analysis.
• Fix: Hemmings-Koch 2019 position — shrinkage for replication planning, not signal generation; cite Dane et al 2019 EFSPI white paper + critique.

Power prior with gamma = 1 (full pooling)

• Trigger: Full pooling of historical and current data.
• Mechanism: Ignores between-study heterogeneity; biases estimate.
• Symptom: Overconfident posterior; cross-validation reveals poor fit.
• Fix: Working-convention discount gamma 0.3-0.6 (the FDA Bayesian Jan 2026 draft does not prescribe a specific range); sensitivity over gamma.

WinBUGS reproducibility

• Trigger: Submission contains WinBUGS code without containerised environment.
• Mechanism: Older Windows-only software; reproducibility fragile.
• Symptom: Reviewer cannot replicate analysis.
• Fix: Migrate to Stan (rstan/cmdstanr); Docker/renv-pinned environment; include seeds + posterior diagnostics (R-hat <1.01, ESS >1000 per chain).

Quantitative Thresholds