Bio Clinical Biostatistics Adaptive Designs

Version Compatibility

Reference examples tested with: R rpact 4.2+ (Wassmer/Brannath), gsDesign 3.6+ and gsDesign2 1.1+ (Anderson/Merck), adaptr, simtrial. Commercial: East/EastHorizon (Cytel), ADDPLAN (ICON), FACTS (Berry Consultants).

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name
• Python adaptive packages are limited; R is the regulatory de facto standard

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

Adaptive Clinical Trial Designs

"Design an adaptive trial" -> Pre-specify a design with one or more interim adaptations (early stopping, sample-size re-estimation, treatment selection, population enrichment, randomisation ratio changes) that strongly controls Type-I error at the trial-wide level via combination tests or the Conditional Rejection Probability principle.

Regulatory Status -- The 2024-2026 Landscape

FDA 2019 Final Adaptive Designs Guidance (Federal Register 2019-25986, Dec 2 2019) finalised the 2010 and 2018 drafts. Recognises 5 design types: group-sequential, blinded SSR, unblinded SSR, adaptive enrichment, adaptive randomisation.

FDA 2022 Final Master Protocols Guidance (March 2022, NOT 2018 — common citation error): basket (one drug, many diseases), umbrella (multiple drugs, one disease), platform (perpetual, drugs enter/exit).

ICH E20 Adaptive Clinical Trials: Step 2b draft June 25 2025; Step 3 public consultation (EU deadline Nov 30 2025; FDA Federal Register Sept 30 2025); Step 4 final expected in 2026. As of May 2026, ICH E20 is NOT final. The EFPIA/PhRMA position paper preceded the formal ICH work; Berry Consultants public comment letter is one of the more important submissions.

FDA CDER Bayesian Methodology Draft (Jan 2026) (FDA-2025-D-3217): first-ever drug-side Bayesian guidance; permits Bayesian primary inference in pivotals with simulation-based Type-I error calibration.

Project Optimus (FDA OCE, 2021-2024): rewrites Phase I/II oncology by requiring randomised dose comparison before registration, replacing MTD-and-go. Made BOIN, mTPI-2, and multi-arm dose-finding the default.

Algorithmic Taxonomy

Postdoc reading list:

• Bauer P, Köhne K 1994 Biometrics 50:1029 (combination test; original adaptive)
• Cui L, Hung HMJ, Wang SJ 1999 Biometrics 55:853 (CHW weighted test for unblinded SSR)
• Müller HH, Schäfer H 2001 Biometrics 57:886 (CRP principle — theoretical bedrock)
• Mehta CR, Pocock SJ 2011 Stat Med 30:3267 (promising zone)
• Jennison C, Turnbull BW 2015 Stat Med 34(29):3793-3810 (Mehta-Pocock critique)
• Friede T, Kieser M 2006 Biom J 48:537 (blinded SSR)
• Lan KKG, DeMets DL 1983 Biometrika 70:659 (alpha spending function)
• O'Brien PC, Fleming TR 1979 Biometrics 35:549 (OBF boundary)
• Pocock SJ 1977 Biometrika 64:191 (Pocock boundary)
• Hey SP, Kimmelman J 2015 Clin Trials 12:102 (RAR ethics critique)
• Berry DA 2015 commentary Clin Trials 12:107 (counter)
• Robertson DS, Lee KM, López-Kolkovska BC, Villar SS 2023 Stat Sci 38:185 (canonical modern RAR review)
• Wassmer G, Brannath W 2016 Group Sequential and Confirmatory Adaptive Designs in Clinical Trials (Springer)
• Jennison C, Turnbull BW 2000 Group Sequential Methods with Applications to Clinical Trials (CRC)

Decision Tree by Scenario

Group-Sequential Designs

O'Brien-Fleming -- the regulatory default

library(gsDesign)

# OBF boundaries; 3 interim looks at 33%, 67%, 100% information
design <- gsDesign(
    k = 4,                  # total analyses including final
    test.type = 1,          # 1-sided efficacy
    alpha = 0.025,
    beta = 0.10,            # power = 0.90
    sfu = sfLDOF,           # Lan-DeMets approximation of OBF
    timing = c(0.25, 0.50, 0.75, 1.0)
)
print(design)
plot(design)

OBF is very conservative at early looks (nominal alpha approximately 0.0001 at 25% info) and near-nominal at final analysis (~0.024 of 0.025). Preferred by FDA because the final-analysis penalty is small.

Pocock -- constant nominal

Constant nominal alpha at each look. Easy early stopping but large final-analysis penalty (~0.018 of 0.025 with k=4). Rarely used in confirmatory.

Lan-DeMets spending function -- the modern flexibility

# Lan-DeMets OBF-like spending function (sfLDOF)
# Allows analysis timing to differ from pre-specified
design_flex <- gsDesign(
    k = 3,
    sfu = sfLDOF,      # OBF-like spending
    alpha = 0.025,
    beta = 0.10
)

# Actual analyses can occur at different information fractions
# Spending function returns alpha to spend at each look based on actual timing

The flexibility: sponsor can perform analyses at different information fractions than originally planned. FDA's de facto preferred framework.

Sample-size for group-sequential

# Time-to-event group-sequential
library(gsDesign)
n_gs <- gsSurv(
    k = 3,
    test.type = 2,    # 2-sided
    alpha = 0.025,
    beta = 0.10,
    sfu = sfLDOF,
    lambdaC = 0.04,   # control hazard per month
    hr = 0.70,        # treatment HR
    eta = 0.005,      # dropout hazard
    T = 24,           # total study duration
    minfup = 12       # minimum follow-up
)
print(n_gs)

Sample-Size Re-Estimation

Blinded SSR (Friede-Kieser 2006)

Re-estimate nuisance parameter (variance σ² for continuous, control event rate p_0 for binary, overall event rate for survival) from blinded interim data. No Type-I error inflation when test statistic ignores the SSR.

library(rpact)
# Blinded SSR for continuous outcome
design_blinded_ssr <- getDesignGroupSequential(
    kMax = 2,
    alpha = 0.025,
    beta = 0.20,
    sided = 1,
    informationRates = c(0.5, 1)
)

# At interim, re-estimate variance and recompute n
# (manual implementation; rpact has built-in support via getDesignInverseNormal for unblinded)

EMA Reflection Paper 2007 and FDA 2019 explicitly endorse blinded SSR. Uncontroversial.

Unblinded SSR (Cui-Hung-Wang 1999)

Interim effect estimate triggers sample-size change. Type-I inflation if naive: Cui-Hung-Wang showed 8% Type-I vs 2.5% target.

The Cui-Hung-Wang weighted test uses pre-specified weights from the original design:

Z_weighted = w_1 * Z_1 + w_2 * Z_2_residual

where w_1, w_2 are the pre-specified weights (based on original n_1, n_2) and Z_2_residual is the test statistic on the data after the interim. Pre-specified weights preserve alpha even if the actual n at stage 2 differs.

library(rpact)
design_unblinded_ssr <- getDesignInverseNormal(
    kMax = 2,
    alpha = 0.025,
    beta = 0.20,
    sided = 1,
    informationRates = c(0.5, 1),
    typeOfDesign = 'WT',  # Wang-Tsiatis power family
    deltaWT = 0.25
)

# Use inverse normal combination for adaptive SSR
analysis_result <- getAnalysisResults(
    design_unblinded_ssr,
    dataInput = getDataMeans(...)
)

Mehta-Pocock Promising Zone (2011)

At interim, compute conditional power (CP) given observed effect:

• Unfavourable zone (CP < ~30%): stop or continue without modification
• Promising zone (CP in 30-80%): increase n to recover power; NO Type-I penalty if increase rule pre-specified and uses original test statistic with original weights
• Favourable zone (CP > 80%): continue without change

# rpact implementation
# Sample size recalculation in promising zone
n_increased <- getSampleSizeMeans(
    design_unblinded_ssr,
    alternative = 5,        # detect mean diff of 5
    stDev = 12,
    groups = 2
)

The mathematical sleight: promising zone is constructed so unconditional Type-I error inflation is negligible (~0.001) even WITHOUT CHW weighting. Jennison-Turnbull 2015 critique: stealth alpha inflation in unpublished simulation assumptions; inefficient relative to CHW-weighted GSD. Mehta defends on operational grounds.

Edwards et al 2020 Trials 21:1000 is the systematic review.

Combination Tests and CRP Principle

Bauer-Köhne 1994 Biometrics 50:1029: combine stagewise p-values via Fisher's product test. Permits design modifications post-interim while controlling Type-I error.

Müller-Schäfer 2001 Biometrics 57:886: Conditional Rejection Probability (CRP) principle — preserve the null conditional rejection probability at every adaptation, and unconditional Type-I is preserved. The theoretical bedrock of all post-2001 confirmatory adaptive designs.

Müller-Schäfer 2004 Stat Med 23:2497 extended to ANY design change at ANY time.

# rpact natively supports combination tests
design_comb <- getDesignFisher(
    kMax = 3,
    alpha = 0.025,
    sided = 1
)

# Or inverse normal combination
design_inv_norm <- getDesignInverseNormal(
    kMax = 3,
    alpha = 0.025,
    informationRates = c(0.33, 0.67, 1.0)
)

Adaptive Enrichment

Drop sub-populations failing futility; re-power on responders. Closed-test stage-wise to control familywise error across full and enriched populations.

# rpact: enrichment design via getDesignEnrichmentSubgroup
# Standard implementation requires explicit definition of full population (F)
# and enriched population (S)

Postdoc concern: selection bias on the enriched population — the observed treatment effect on the enriched subgroup is biased upward by selection. Bias-correction via simulation or hierarchical Bayesian.

Response-Adaptive Randomisation -- The Ethics Fight

Hey & Kimmelman 2015 Clin Trials 12:102 "Are outcome-adaptive allocation trials ethical?" Argued RAR's purported ethical advantage (equipoise, sub-optimal exposure minimisation) fails in two-arm and early-phase settings because:

1. Drift bias inflates Type-I error / biases estimates (time trends confounded with allocation)
2. Consent dynamics confused — patients believe allocation is "personalised" when stochastic
3. Marginal patient-welfare benefit is statistical and small while operational risks real

Counter-arguments:

• Berry DA 2015 commentary Clin Trials 12:107: RAR enables learn-and-confirm, multi-arm platforms (I-SPY 2 model) where the patient-welfare argument IS the point and equal allocation would be unethical given accumulating evidence.
• Saville & Berry 2016 Clin Trials 13:358: RAR's operating characteristics are competitive in multi-arm platforms. Drift bias and Type-I inflation are controlled by adjusting for temporal trends (time-trend covariates) alongside stratification and proper analysis weights -- the "Bayesian time machine" approach developed in later work.
• Buyse 2015 Clin Trials 12:119: Hey-Kimmelman correct for 2-arm but wrong for multi-arm.

Consensus position (2020s; ICH E20): RAR appropriate when (a) multi-arm (>=3 arms), (b) rare disease / limited pool, (c) strong PoC of differential biomarker response, (d) robust drift-bias adjustment and pre-specified analysis weights. Inappropriate for confirmatory 2-arm trials.

Robertson, Lee, López-Kolkovska, Villar 2023 Stat Sci 38:185 ("Response-adaptive randomization: from myths to practical considerations") is the canonical modern review settling the debate.

Bayesian Platform Trials

I-SPY 2 (Barker-Sigman 2009 Clin Pharmacol Ther; Park-Liu 2016 NEJM 375:11): neoadjuvant breast cancer; 10 biomarker-defined subtypes × multiple arms; Bayesian RAR; graduation criterion = posterior predictive probability of success in 300-patient Phase 3 ≥ 85%. Berry Consultants designed the engine. Multiple drugs graduated (neratinib, veliparib, pembrolizumab).

GBM AGILE (Alexander 2018; published readouts beginning 2024): glioblastoma; response-adaptive Bayesian; first global registrational platform in neuro-oncology. Regorafenib readout 2025 JCO JCO-25-01137.

REMAP-CAP (Angus 2020 JAMA): severe pneumonia, repurposed for COVID-19 in 2020; Bayesian factorial multi-domain design — multiple intervention domains tested simultaneously and combinatorially. Generated corticosteroid signal in COVID independently of RECOVERY.

Drop-the-loser vs promising-the-winner

• Adaptive arm-dropping (futility): Bayesian posterior probability of beating control drops below threshold -> arm closes. Mathematically straightforward; FDA-acceptable.
• "Promising-the-winner" (graduate to Phase 3): introduces selection bias. Bias-adjusted estimators (Robertson 2023; conditional MLE) now standard in I-SPY 2 reports.

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

Why FDA prefers BOIN operationally: qualified as Fit-for-Purpose under FDA's Drug Development Tools program (FDA Determination Letter, December 10, 2021). Investigator uses pre-printed escalation table — no real-time Bayesian software at the bedside.

R packages: BOIN, dfcrm (Cheung — author of CRM textbook), trialr (Brock — includes EffTox), escalation (Brock — unified framework).