Technical White Paper
Zetyra: A Validated Suite of Statistical Calculators for Efficient Clinical Trial Design
Comprehensive technical documentation for biostatisticians evaluating clinical trial design software.
Key Findings
Contents
1Executive Summary
FDA Draft Bayesian Guidance (January 12, 2026)
FDA released draft guidance extending Bayesian methodology to drugs and biologics (PDUFA VII commitment). This document is not yet final and is not for implementation.
“Bayesian methodologies help address two of the biggest problems of drug development: high costs and long timelines.”
— FDA Commissioner Marty Makary
This white paper demonstrates exactly this value proposition through validated calculators and quantified case studies.
The Challenge
Phase III clinical trials in oncology and cardiology average $50–100 million and require 4–6 years from first patient to database lock (DiMasi et al. 2016; Moore et al. 2018). Conservative statistical designs — failing to leverage baseline covariates, fixed-sample approaches without interim monitoring, and frequentist paradigms for Phase II decisions — often inflate sample sizes by 15–35% relative to efficient alternatives.
Established methods can substantially reduce trial costs and duration, but existing software packages (East, PASS, ADDPLAN, nQuery) are priced at $5,000–$15,000 annually and typically distribute validation documentation on a proprietary basis.
The Solution
Zetyra is a web-based platform offering 18 statistical calculators across four tiers:
- Methodological scope: Integrates CUPED, group sequential, Bayesian, survival, adaptive randomization, and master protocol (basket / umbrella / platform) methods across Free, Evidence Pro, Bayesian Toolkit, and Enterprise tiers
- Validation and transparency: Public validation suite (896 automated tests across 42 scripts) with quantified accuracy metrics, available for independent verification under MIT license
- Accuracy: Core gsDesign benchmark max deviation 0.0046 z-score; full benchmark set (including survival replications) max deviation 0.034 z-score — both within the pre-specified ±0.05 acceptance criterion
- Deployment and pricing: Web-based with no local installation; tiered pricing from free through enterprise, starting at $99/month vs. $5K–$15K annual perpetual licenses for comparable tools
Table 1
Key Results from Validation
| Tier / Group | Tests | Benchmark |
|---|---|---|
| Free Tier (Sample Size + Chi-Square) | 241 | Cohen (1988), Donner & Klar (2000), scipy.stats |
| Group Sequential Design | 103 | gsDesign (R), PACIFIC, MONALEESA-7 replications |
| CUPED | 55 | Analytical VRF, MC simulation |
| Bayesian (PPoS + Toolkit + Sequential) | 248 | Conjugate priors, Zhou & Ji (2024) |
| SSR (Blinded + Unblinded + Single-Arm) | 81 | Mehta-Pocock (2011), rpact, NCT03377023 |
| Adaptive Randomization | 37 | DBCD, Thompson Sampling, Pocock-Simon |
| Master Protocols (Basket + Umbrella + Platform) | 93 | I-SPY 2, STAMPEDE, REMAP-CAP |
| Total | 896 tests, 100% pass | 42 scripts, multiple benchmarks |
Illustrative Efficiency Gains (Scenario-Dependent)
The following reductions are achievable under specific assumptions and are not guaranteed outcomes. Realized gains depend on design parameters, endpoint characteristics, and trial context:
2Introduction
2.1 The Clinical Trial Efficiency Problem
Clinical development represents one of the most capital-intensive endeavors in modern medicine. DiMasi et al. (2016) estimated the capitalized cost to bring a single drug from discovery through FDA approval at $2.6 billion, with Phase II and Phase III trials accounting for approximately 60% of total development costs. Moore et al. (2018) analyzed 138 pivotal trials supporting FDA approvals in 2015–2016, finding median Phase III cost of $19 million (range $12M–$33M for trials with 50–300 patients).
Conservative design practices systematically inflate these already-substantial costs. Three common inefficiencies dominate:
Failure to leverage baseline covariates
Standard power calculations ignore correlations (ρ = 0.4–0.7 typical for many endpoints; Walters et al. 2019). For continuous outcomes, failing to adjust for baseline covariates inflates sample sizes by a factor of 1/(1−ρ²), yielding 15–35% overestimation when ρ ranges from 0.4 to 0.6 (Frison & Pocock 1992; Teerenstra et al. 2012).
Fixed-sample designs despite interim data
Most trials continue to planned completion despite accumulating interim evidence of efficacy or futility. Group sequential designs with pre-specified stopping boundaries can reduce expected sample size under the alternative hypothesis by 15–30% (O'Brien-Fleming) to 30–40% (Pocock), with commensurate reductions in expected trial duration (Jennison & Turnbull 2000).
Frequentist paradigm for Phase II go/no-go decisions
Traditional hypothesis tests provide binary answers (p < 0.05 or not) without quantifying the probability of Phase III success given Phase II data. Bayesian predictive probability frameworks enable more nuanced decisions; well-calibrated priors can reduce false-go rates relative to p-value thresholds, though the magnitude depends heavily on prior specification (Berry et al. 2010; Spiegelhalter & Freedman 1986).
2.2 Existing Software Limitations
Table 2
Limitations of existing clinical trial design software
| Limitation | Impact on Adoption |
|---|---|
| High cost: $5K–$15K/year | Small biotechs (Series A/B) priced out |
| IT barriers: Desktop install, version control | Requires IT department involvement |
| Limited scope: Separate tools per method | Users must purchase multiple products |
| Opaque validation: No published benchmarks | Public, independently reproducible test suites not typically provided |
| Poor documentation: Sparse regulatory citations | Additional work for FDA/EMA submissions |
2.3 Statistical Framework: Calibrated Bayesian Approach
Zetyra follows a calibrated Bayesian philosophy: frequentist operating characteristics (Type I error control, power) are preserved where required by regulatory convention, while Bayesian methods are used for decision support, design optimization, and inference in settings where prior information is scientifically justified.
Confirmatory trials (Phase III)
GSD boundaries maintain strict frequentist α control via alpha-spending functions. Bayesian PPoS serves as a supplementary internal decision metric.
Exploratory trials (Phase II)
Bayesian designs (single-arm SSR, basket BHM/EXNEX) use posterior probability thresholds as primary decision rules, with simulation-verified frequentist operating characteristics reported for regulatory transparency.
Adaptive designs
SSR and RAR methods are evaluated under both Bayesian (predictive probability, posterior allocation) and frequentist (conditional power, Type I error) criteria.
Sponsors using Bayesian calculators are expected to demonstrate prior sensitivity, prior-data conflict assessment, threshold calibration, and pre-specified documentation per Section 14 of the PDF and the FDA January 2026 draft.
3Validation Framework
Zetyra calculators undergo comprehensive external validation through three complementary approaches: (1) software benchmarking against established reference implementations, (2) analytical formula verification using closed-form solutions, and (3) published clinical trial replication.
Open Source Validation
All validation code, test data, and results are publicly available at github.com/evidenceinthewild/zetyra-validation under MIT license. GitHub Actions runs all 896 tests on every code change.
View Validation Repository3.1 Acceptance Criteria
| Calculator | Metric | Tolerance |
|---|---|---|
| GSD | Z-score boundary deviation | ±0.05 |
| CUPED | Variance reduction factor | Exact match |
| Bayesian | Predictive probability | ±0.001 |
3.2 Published Trial Replications
HPTN 083 (HIV Prevention, 2021)
4-look O'Brien-Fleming design replicated within 0.0046 z-score deviation at each look.
PACIFIC (NSCLC, 2017)
Survival-trial replication. Boundaries verified against gsDesign R package.
MONALEESA-7 (Breast Cancer)
Group sequential boundary replication for endocrine-therapy combination.
NCT03377023 (Single-Arm SSR)
Phase II ORR interim and final decisions replicated end-to-end via conjugate posterior + predictive-probability futility monitoring.
I-SPY 2 (Basket)
Adaptive breast cancer trial; basket BHM analysis replicated.
STAMPEDE / REMAP-CAP (Platform)
MAMS boundaries and staggered arm-entry behavior verified.
4Sample Size & Chi-Square (Free Tier)
Foundational calculators provide sample size, power, and categorical analysis for standard trial designs. Available in the Free Tier without login or subscription, they serve as the starting point for trial feasibility assessment.
4.1 Sample Size Calculator
- • Outcome types: Continuous (mean difference), binary (proportion difference), survival (hazard ratio)
- • Hypothesis frameworks: Superiority, non-inferiority (margin ΔNI), equivalence (TOST)
- • Design extensions: Cluster-randomized (DE = 1 + (m−1) × ICC with ICC uncertainty bands and small-cluster t-correction), longitudinal / repeated-measures with AR(1) or compound-symmetric correlation
- • Three solve-for modes: Sample Size, Power, Effect Size
- • Dropout adjustment: Inflate by 1/(1−d)² (continuous/binary) or 1/(1−d) (survival)
4.2 Chi-Square Calculator
- • R×C contingency tables with Pearson χ², Yates correction (2×2), expected-cell matrix, φ coefficient, Cramér's V
- • Fisher's exact test for small samples or expected counts < 5
- • McNemar's test for paired binary outcomes
- • Sample size planning via the arcsine transformation
5CUPED: Covariate-Adjusted Power Analysis
CUPED (Controlled-experiment Using Pre-Experiment Data) is a variance reduction technique that leverages baseline covariates to improve statistical power. Originally developed by Microsoft Research (Deng et al. 2013) for online A/B testing, CUPED has proven applications in clinical trial design where baseline measurements correlate with treatment outcomes.
5.1 Mathematical Foundation
YCUPED = Y − θ(X − E[X])
where θ* = Cov(X, Y) / Var(X) (the OLS regression coefficient)
VRF = 1 − ρ²
where ρ is the Pearson correlation between baseline and outcome
nCUPED = nstandard × (1 − ρ²)
5.2 Variance Reduction by Correlation
| Correlation (ρ) | VRF | Sample-Size Reduction |
|---|---|---|
| 0.0 | 1.00 | 0% |
| 0.5 (moderate) | 0.75 | 25% |
| 0.7 (strong) | 0.51 | 49% |
| 0.9 (very strong) | 0.19 | 81% |
5.3 Regulatory Context
- • FDA (May 2023): “Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products” — explicitly encourages covariate adjustment as “low-hanging fruit” for trial efficiency
- • EMA (February 2015): EMA/CHMP/295050/2013, parallel guidance on adjustment for baseline covariates
- • ICH E9(R1) (November 2019): Estimands framework clarifies role of ANCOVA-adjusted analysis
6Group Sequential Design
Group Sequential Designs allow pre-planned interim analyses during clinical trials while maintaining overall Type I error control via alpha-spending functions (Lan & DeMets 1983). This enables early termination for efficacy (if the treatment effect is compelling) or futility (if success appears unlikely), substantially reducing expected trial duration and sample size compared with fixed-sample designs.
6.1 Spending Functions
- • O'Brien-Fleming: Conservative early boundaries that preserve final-analysis significance level
- • Pocock: Constant boundaries across interim analyses
- • Hwang-Shih-DeCani (HSD): Tunable spending via γ parameter
- • Kim-DeMets: Power-family spending function
6.2 Validation: HPTN 083 Replication
| Analysis | Info % | gsDesign Z | Zetyra Z | Deviation |
|---|---|---|---|---|
| Look 1 | 25% | 4.049 | 4.0444 | 0.0046 |
| Look 2 | 50% | 2.863 | 2.8598 | 0.0032 |
| Look 3 | 75% | 2.337 | 2.3351 | 0.0019 |
| Final | 100% | 2.024 | 2.0222 | 0.0018 |
6.3 Regulatory Context
- • FDA Adaptive Designs Guidance (November 2019): Establishes regulatory expectations for pre-specification, DMC charter, and Type I error control
- • ICH E9 / E9(R1): Statistical Principles for Clinical Trials and the Estimands Addendum
7Bayesian Predictive Power
Bayesian Predictive Power (also called weight-averaged conditional power or predictive probability of success, PPoS) integrates conditional power over the posterior distribution of the treatment effect, given accumulating interim data. Conjugate families enable closed-form computation: Beta-Binomial for binary endpoints, Normal-Normal for continuous endpoints, Gamma-Poisson for count endpoints.
7.1 Phase II Go/No-Go Decision Framework
| PPoS | Interpretation | Recommendation |
|---|---|---|
| < 0.10 | Futility | Stop, no-go |
| 0.10–0.30 | Low probability | Likely no-go |
| 0.30–0.70 | Moderate probability | Continue enrollment |
| > 0.70 | High probability | Continue with confidence |
FDA Draft Bayesian Guidance (January 12, 2026)
The FDA released draft guidance on the use of Bayesian methodology in clinical trials of drug and biological products (satisfying PDUFA VII commitment). This complements the long-standing 2010 FDA Bayesian medical-device guidance.
The draft guidance is not yet final and is not for implementation. Sponsors should evaluate Bayesian designs against frequentist operating characteristics via simulation.
8Survival Power Analysis
Event-driven designs for time-to-event endpoints using the Schoenfeld (1981) and Freedman (1982) formulas for the log-rank test. Supports superiority, non-inferiority, three solve-for modes (events, sample size, hazard ratio), and integrates with the Group Sequential Design calculator for interim monitoring of survival endpoints.
d = 4(zα + zβ)² / (log HR)²
required number of events (Schoenfeld 1981)
N = d / P(event)
total patients given event probability under the planned accrual and follow-up window
9Adaptive Designs: SSR & RAR
Blinded SSR (Kieser-Friede)
Re-estimate nuisance parameters (variance, event rate, response rate) from blinded interim data without inflating Type I error. Supports continuous, binary, and survival endpoints.
Unblinded SSR (Mehta-Pocock)
Promising-zone sample-size re-estimation using interim efficacy data. Inverse-normal combination test preserves familywise α (Cui-Hung-Wang 1999).
Single-Arm SSR (Phase II ORR)
Bayesian PPoS or CP promising-zone rules with decoupled γefficacy / γfinal thresholds. NCT03377023 replication; in-product calibration helper for γfinal (Qian 2026).
Response-Adaptive Randomization
DBCD (Hu & Zhang 2004), Thompson Sampling, Rosenberger optimal allocation, plus Pocock-Simon covariate-adaptive minimization. Burn-in safeguards mitigate operational bias risks.
Qian 2026 (under peer review): Conditional-power promising-zone re-estimation in single-arm binary trials can inflate Type I error uniformly above α across the entire grid of CPlower values. The Bayesian PP rule with appropriately calibrated γfinal preserves T1E. The Single-Arm SSR calculator now includes an in-product calibration helper for both modes.
10Master Protocols
Master protocols allow simultaneous evaluation of multiple treatments, indications, or biomarkers within a single overarching framework. The FDA Master Protocol Guidance (March 2022) provides regulatory clarity for these designs.
Basket Trial
Single treatment across multiple indications. Independent, BHM (Berry et al. 2013), or EXNEX (Neuenschwander et al. 2016) information-borrowing analyses. I-SPY 2 replication.
Umbrella Trial
Biomarker-stratified sub-studies in a single disease. Shared control allocation with Bonferroni/Holm multiplicity control. Operating characteristics by biomarker prevalence.
Platform Trial
MAMS (multi-arm multi-stage) with staggered arm entry, three control-pooling modes (concurrent/full/hybrid), and alpha-spending boundaries. STAMPEDE and REMAP-CAP replications.
11Bayesian Toolkit (Add-on)
The Bayesian Toolkit ($149/month add-on; $49/month .edu) provides six modules for advanced Bayesian trial design. All modules use closed-form conjugate families for sub-second computation and deterministic reproducibility.
- • Prior Elicitation: Expert elicitation, moment matching, visual calibration, Morita-Thall-Müller effective sample size
- • Bayesian Borrowing: Power priors (Ibrahim & Chen 2000), commensurate priors, MAP priors (Schmidli et al. 2014)
- • Single-Arm Design: Historical-control borrowing for rare disease and pediatric indications
- • Two-Arm Design: Augmenting concurrent control with historical information
- • Sequential Monitoring: Zhou-Ji posterior-probability boundaries with optional dual-threshold (statistical + clinical) stopping rules
- • Bayesian PPoS: Extended calculations with mixed priors and hierarchical models
See the companion Bayesian Toolkit Technical White Paper for full mathematical treatment of each module, including prior-data conflict diagnostics and ESS-based sensitivity analyses.
Read the Bayesian Toolkit White Paper12Case Studies
Illustrative scenarios constructed from published trial parameters (HPTN 083, HeartMate II, industry benchmarks) and literature-supported assumptions. Trial-cost savings are the primary defensible economic benefit; revenue-timing gains are highly assumption-dependent.
Table 3
Case Study Enrollment Cost & Timeline Savings
| Case Study | Enrollment Cost Savings | Time Savings |
|---|---|---|
| Oncology Phase II (CUPED) | $3.6M (30% fewer patients) | 3.6 months |
| CV Phase III (GSD) | $18.1M (24%) | 12 months |
| Rare Disease (Bayesian) | Avoided $10M futile enrollment | 18 months |
| Full Program (Integrated) | $14.1M (14%) | 16 months (24%) |
| Survival Power + GSD | $4.5M (9%) | 9 months (17%) |
| Adaptive SSR (CV) | +$6.4M to enable success | Trial succeeded vs fixed-design failure |
| Basket (Tissue-Agnostic) | $2.5M (33% fewer patients) | 6 months |
| Platform (Anti-Infectives) | $14.8M (35% shared control) | 6 months |
See PDF Section 21 for the full case-study walkthroughs, including trial design parameters, interim analyses, and ROI sensitivity analyses.
13Conclusions
Zetyra provides a validated, integrated platform of 18 statistical calculators covering frequentist, Bayesian, and adaptive trial design methods, validated through 896 automated tests with 100% pass rate. The eight case studies demonstrate that adoption of established efficient design methods — covariate adjustment, group sequential monitoring, adaptive sample size re-estimation, and master protocol designs — can reduce enrollment costs by 9–35% and shorten timelines by 3–18 months, depending on trial characteristics and design assumptions.
As regulatory agencies formalize guidance for these methods (FDA May 2023 covariate adjustment, January 2026 Bayesian draft, 2022 Master Protocol), the methodologies documented here are increasingly well-supported for regulatory submissions. Sponsors should evaluate each method's fit within their specific trial context and quality management system. A companion Bayesian Toolkit White Paper provides extended methodology for Bayesian practitioners.
13.1 Competitive Positioning
| Capability | Zetyra | East | PASS | nQuery |
|---|---|---|---|---|
| CUPED Calculator | ✓ | — | — | — |
| Group Sequential | ✓ | ✓ | ✓ | — |
| Bayesian PPoS + Toolkit | ✓ | — | — | — |
| SSR (Blinded + Unblinded + Single-Arm) | ✓ | ✓ | — | — |
| Adaptive Randomization | ✓ | — | — | — |
| Master Protocols (Basket/Umbrella/Platform) | ✓ | — | — | — |
| Public Validation Suite | ✓ | — | — | — |
| Web-Based | ✓ | — | — | — |
| Annual Cost (single seat) | $1,188 | $15,000 | $7,995 | $5,995 |
The future of clinical trial design is transparent, validated, accessible, and efficient.
As regulatory agencies increasingly encourage efficient designs, methodologies like covariate adjustment, group sequential monitoring, Bayesian predictive power, and master protocols are transitioning from competitive advantage to industry standard.
14Limitations & Future Directions
These limitations reflect both current platform scope and broader methodological constraints. We distinguish between platform-specific limitations (features not yet implemented) and statistical limitations (inherent tradeoffs in the underlying methods).
14.1 Methodological & Feature Enhancements
- • Conjugate prior reliance: The Bayesian Toolkit uses Beta-Binomial, Normal-Normal, and Gamma-Poisson conjugate families for closed-form computation. Users requiring non-conjugate posteriors (multi-source random-effects borrowing, joint longitudinal-survival models) should use dedicated MCMC software (Stan, JAGS, BUGS).
- • Single endpoint focus: Multiplicity adjustments for co-primary, key-secondary, or multi-dose endpoints are not currently integrated. Bretz et al. (2009) graphical approaches are recommended for sponsors with hierarchical testing strategies.
- • Dose-escalation modules: CRM, BOIN, and mTPI-2 designs are planned to address the FDA Jan 2026 draft's explicit endorsement of Bayesian methods for early-phase dose selection.
- • Covariate-adjusted survival analysis: CUPED VRF currently applies to continuous outcomes. ANCOVA-adjusted log-rank tests (Lu 2008), AIPW, and stratified Cox extensions are planned.
14.2 Platform & Operational Considerations
- • 21 CFR Part 11 compliance: Free, Evidence Pro, and Bayesian Toolkit tiers do not currently claim Part 11 compliance. The Enterprise tier roadmap includes audit trails, electronic signatures, IQ/OQ documentation, and SOC 2 Type II certification. Until available, sponsors should treat Zetyra outputs as planning tools and perform independent verification using validated software for submission-critical calculations.
- • Missing data & imputation: Current calculators assume complete-case inputs. Substantial missingness (> 10%) can bias VRF estimates; tipping-point and pattern-mixture sensitivity analyses are recommended externally.
- • CTMS/EDC integration: Zetyra does not currently connect to live trial data. A planned integration layer will provide API connectors for Medidata Rave, Veeva Vault CDMS, Oracle Clinical One, and REDCap.
- • External data exchangeability: The Bayesian Borrowing module provides power priors and commensurate priors, but the burden of justifying exchangeability remains entirely with the sponsor.
14.3 Strategic & Educational Enhancements
- • Prior-data conflict resolution decision framework: Tail-area diagnostics with concrete sponsor recommendations across strong / moderate / acceptable agreement.
- • Prior sensitivity panel: Automated five-prior comparison (proposed, skeptical, enthusiastic, non-informative, robust mixture) for FDA submission packages.
- • Commercial Sensitivity Analyzer: CFO-ready ROI sensitivity tables across optimistic/base/conservative scenarios.
- • Submission template library: Pre-written SAP sections, annotated Bayesian analysis plans, and EMA Scientific Advice response templates.
15References
The following selected references span statistical methodology, regulatory guidance, software, and published clinical trials cited throughout this paper. The complete 85-entry bibliography is maintained in the public validation repository and the PDF whitepaper.
Statistical Methodology
7. Pocock SJ. Group sequential methods in the design and analysis of clinical trials. Biometrika 1977;64(2):191-199.
8. O'Brien PC, Fleming TR. A multiple testing procedure for clinical trials. Biometrics 1979;35(3):549-556.
9. Lan KKG, DeMets DL. Discrete sequential boundaries for clinical trials. Biometrika 1983;70(3):659-663.
10. Schoenfeld DA. Sample-size formula for the proportional-hazards regression model. Biometrics 1983;39(2):499-503.
15. Jennison C, Turnbull BW. Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC Press, 2000.
20. Deng A, Xu Y, Kohavi R, Walker T. Improving the sensitivity of online controlled experiments by utilizing pre-experiment data. WSDM 2013:123-132.
29. Spiegelhalter DJ, Freedman LS, Blackburn PR. Monitoring clinical trials: conditional or predictive power? Controlled Clinical Trials 1986;7(1):8-17.
31. Berry SM, Carlin BP, Lee JJ, Muller P. Bayesian Adaptive Methods for Clinical Trials. CRC Press, 2010.
33. Zhou T, Ji Y. On Bayesian sequential clinical trial designs. NEJ Stat Data Sci 2024;2(1).
38. Kieser M, Friede T. Simple procedures for blinded sample size adjustment that do not affect the type I error rate. Statistics in Medicine 2003;22(23):3571-3581.
39. Mehta CR, Pocock SJ. Adaptive increase in sample size when interim results are promising. Statistics in Medicine 2011;30(28):3267-3284.
50. Berry SM, Broglio KR, Groshen S, Berry DA. Bayesian hierarchical modeling of patient subpopulations. Clinical Trials 2013;10(5):720-734.
51. Neuenschwander B, et al. Robust exchangeability designs for early phase clinical trials with multiple strata. Pharmaceutical Statistics 2016;15(2):123-134.
Regulatory Guidance
57. U.S. Food and Drug Administration. Master Protocols: Efficient Clinical Trial Design Strategies to Expedite Development of Oncology Drugs and Biologics. March 2022.
58. U.S. Food and Drug Administration. Adaptive Designs for Clinical Trials of Drugs and Biologics. November 2019.
59. U.S. Food and Drug Administration. Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products. May 2023.
60. U.S. Food and Drug Administration. Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products: Draft Guidance for Industry. January 12, 2026.
62. U.S. Food and Drug Administration. Non-Inferiority Clinical Trials to Establish Effectiveness. November 2016.
63. ICH. E9 Statistical Principles for Clinical Trials. February 1998.
64. ICH. E9(R1) Addendum on Estimands and Sensitivity Analysis. November 2019.
66. European Medicines Agency. Guideline on Adjustment for Baseline Covariates. EMA/CHMP/295050/2013. February 2015.
Published Clinical Trials
67. Antonia SJ, et al. Overall survival with durvalumab after chemoradiotherapy in stage III NSCLC (PACIFIC). NEJM 2018;379(24):2342-2350.
68. Im SA, et al. Overall survival with ribociclib plus endocrine therapy in breast cancer (MONALEESA-7). NEJM 2019;381:307-316.
69. Barker AD, et al. I-SPY 2: An adaptive breast cancer trial design. Clinical Pharmacology & Therapeutics 2009;86(1):97-100.
71. Angus DC, et al. Effect of hydrocortisone on mortality and organ support in patients with severe COVID-19 (REMAP-CAP). JAMA 2020;324(13):1317-1329.
73. Landovitz RJ, et al. Cabotegravir for HIV prevention (HPTN 083). NEJM 2021;385(7):595-608.
Software and Validation
77. Anderson K. gsDesign: Group Sequential Design. R package v3.6.4, 2024.
78. Wassmer G, Pahlke F. rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. R package v4.0, 2024.
80. Qian L. Zetyra: A Validated Suite of Statistical Calculators for Efficient Clinical Trial Design. Technical White Paper. Evidence in the Wild, April 2026.
81. Qian L. Zetyra: A Validated, Regulatory-Aligned Calculator Suite for Adaptive and Bayesian Clinical Trial Design. Manuscript prepared for the Joint Statistical Meetings, August 2026.
82. Qian L. Conditional Power Promising Zone Sample Size Re-estimation Inflates Type I Error in Single-Arm Binary Trials: An Exact-Enumeration Study and Comparison with Bayesian Predictive Probability SSR. Under peer review, Statistics in Biopharmaceutical Research, 2026.
Full 85-reference bibliography available in the PDF version (Section 24), including foundational statistical works, computational methods, and additional regulatory documents.
16Appendices
Appendix A: API Documentation
Zetyra provides a RESTful API for programmatic access to all 18 calculators. Authentication via X-API-Key header; rate limits 100 req/min (Evidence Pro), 500 req/min (Evidence Collective).
Appendix B: Validation Test Results
All 896 tests across 42 scripts are publicly maintained under MIT license. Reproduce by cloning the repository and running the script suite against any deployment:
Appendix C: Regulatory Guidance Quick Reference
• CUPED / Covariate Adjustment: FDA (May 2023), EMA/CHMP/295050/2013 (February 2015), ICH E9(R1) (November 2019)
• Group Sequential Design: FDA Adaptive Designs Guidance (November 2019), ICH E9
• Bayesian Methods: FDA Bayesian Draft Guidance (January 12, 2026), FDA Medical Device Bayesian Guidance (February 2010)
• Adaptive Designs (SSR, RAR): FDA Adaptive Designs Guidance (November 2019)
• Master Protocols: FDA Master Protocol Guidance (March 2022)
• Non-Inferiority: FDA NI Guidance (November 2016), ICH E10 (July 2000)
• Estimands: ICH E9(R1) (November 2019)
Appendix D: Glossary
Full glossary in PDF Appendix C.
Appendix E: Platform Architecture
Frontend
Next.js + React + TypeScript, Tailwind CSS, Recharts, KaTeX
Backend
Python FastAPI, NumPy/SciPy, gsDesign via rpy2 for benchmark cross-checks
Infrastructure
Google Cloud Run, Supabase Postgres, 99.9% uptime SLA (Enterprise)
Security
OAuth 2.0, TLS 1.3, AES-256 at rest, SOC 2 Type II in progress
Suggested Citation
Qian, Lu. (2026). Zetyra: A Validated Suite of Statistical Calculators for Efficient Clinical Trial Design (Version 2.3, May 2026). Evidence in the Wild. Zenodo. https://doi.org/10.5281/zenodo.20218751
Validation repository: github.com/evidenceinthewild/zetyra-validation (MIT license).
DOI: 10.5281/zenodo.20218751Ready to design more efficient trials?
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