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 Published Major Guidance (January 12, 2026)
FDA released draft guidance extending Bayesian methodology to drugs and biologics.
“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. 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.
Three proven methodologies can substantially reduce trial costs and duration, but existing software packages are expensive ($5,000-$15,000 annually), complex to deploy, and lack transparent validation.
The Solution
Zetyra is a web-based platform offering three validated statistical calculators that enable efficient clinical trial design:
- Comprehensive methodology: Integrates CUPED, group sequential, and Bayesian methods in single platform
- Affordable: Monthly subscription vs. $5K-$15K perpetual licenses
- Transparent validation: Public validation suite (51 automated tests) vs. proprietary validation approaches
- Accessible: Web-based interface vs. IT department installation requirements
- Accurate: Maximum deviation 0.0046 z-score vs. pre-specified acceptance criterion of ±0.05
Table 1
Key Validation Results
| Calculator | Tests | Max Deviation | Reference |
|---|---|---|---|
| Group Sequential Design | 30 passed | 0.0046 z-score | gsDesign R package |
| CUPED | 12 passed | Exact match | Analytical VRF formula |
| Bayesian | 9 passed | Exact match | Conjugate prior solutions |
Business Impact (Representative Examples)
A Phase II oncology trial (240 patients standard design) can potentially be reduced to:
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.
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) between baseline measurements and treatment outcomes. 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.
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).
Frequentist paradigm for Phase II decisions
Traditional hypothesis tests provide binary answers (p<0.05 or not) without quantifying the probability of Phase III success. Bayesian predictive probability frameworks enable more nuanced decisions with quantitative risk assessment.
2.2 Existing Software Limitations
Table 2
Software Limitations and Impact
| Limitation | Impact on Adoption |
|---|---|
| High cost: $5,000-$15,000/year | Small biotechs (Series A/B) priced out |
| IT barriers: Desktop installation, version control | Requires IT department involvement, delays adoption |
| Limited scope: Separate tools for each methodology | Users must purchase multiple products, learn different interfaces |
| Opaque validation: No published accuracy benchmarks | "Trust us" model inappropriate for regulatory submissions |
| Poor documentation: Sparse regulatory guidance citations | Additional work required for FDA/EMA submissions |
2.3 Zetyra Platform Overview
Zetyra addresses these inefficiencies through three integrated, validated statistical calculators:
CUPED
Calculates sample size reduction from baseline covariate adjustment. Variance reduction factor (1-ρ²), adjusted sample size, expected power gain.
Group Sequential Design
Calculates stopping boundaries for interim analyses. O'Brien-Fleming, Pocock, and alpha-spending function boundaries with sample sizes at each look.
Bayesian Predictive Power
Calculates probability of trial success given interim data. Beta-binomial (binary) and normal-normal (continuous) models with futility/graduation thresholds.
3CUPED: Covariate-Adjusted Power Analysis
3.1 Theoretical Foundation
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.
The key insight is that if a baseline measurement X is correlated with the outcome Y, incorporating X into the analysis reduces unexplained variance and increases statistical power. This is mathematically equivalent to ANCOVA.
3.2 Mathematical Framework
Variance Reduction Factor
VRF = 1 - ρ²where ρ is the Pearson correlation between baseline covariate X and outcome Y.
Sample Size Adjustment
nCUPED = nstandard × (1 - ρ²)Sample size decreases proportionally to variance reduction.
Variance Reduction by Correlation
Table 3
VRF and Sample Size Reduction by Correlation
| Correlation (ρ) | VRF | Variance Reduction | Sample Size Reduction |
|---|---|---|---|
| 0.0 | 1.00 | 0% | 0% |
| 0.3 | 0.91 | 9% | 9% |
| 0.5 | 0.75 | 25% | 25% |
| 0.6 | 0.64 | 36% | 36% |
| 0.7 | 0.51 | 49% | 49% |
| 0.9 | 0.19 | 81% | 81% |
3.3 Regulatory Considerations
FDA Guidance (May 2023)
“FDA encourages sponsors to consider covariate adjustment as a way to improve the precision of treatment effect estimates and increase statistical power.”
The FDA released updated guidance explicitly encouraging covariate adjustment as "low-hanging fruit" to improve trial efficiency. Covariate adjustment should be pre-specified in the statistical analysis plan before database lock and unblinding.
3.4 Benchmark Correlations (Walters et al., 2019)
Analysis of 464 correlations from 20 UK Health Technology Assessment trials:
4Group Sequential Design
4.1 Theoretical Foundation
Group Sequential Designs (GSD) allow pre-planned interim analyses during clinical trials while maintaining overall Type I error control. This adaptive approach enables early termination for efficacy (if treatment effect is compelling) or futility (if success appears unlikely), substantially reducing expected trial duration and sample size.
Type I Error Without Adjustment
Table 4
Type I Error Inflation Without Multiple Testing Adjustment
| Number of Looks (K) | Naive α = 0.05 per look | True Type I Error |
|---|---|---|
| 1 | 0.05 | 0.050 |
| 2 | 0.05 | 0.083 |
| 3 | 0.05 | 0.106 |
| 5 | 0.05 | 0.141 |
Group sequential methods achieve error control through carefully calibrated critical values at each analysis using alpha-spending functions.
4.2 Alpha-Spending Functions
O'Brien-Fleming
Conservative early boundaries that preserve final analysis power. Most commonly used in confirmatory trials.
Very high thresholds early (Z = 4.56 at 20% info), approaches 1.96 at end.
Pocock
Constant boundaries across analyses. More aggressive early stopping but requires larger sample size.
Equal alpha allocation, constant Z ≈ 2.41 for K=5.
Sample Size Inflation Factor
Table 5
Sample Size Inflation by Boundary Type
| Boundary Type | K=2 | K=3 | K=4 | K=5 |
|---|---|---|---|---|
| O'Brien-Fleming | 1.01 | 1.02 | 1.02 | 1.03 |
| Pocock | 1.10 | 1.14 | 1.16 | 1.17 |
4.3 Example: HPTN 083 Trial
The HPTN 083 HIV prevention trial (Landovitz et al., NEJM 2021) used a 4-look O'Brien-Fleming design:
| Analysis | Events | Z-boundary | HR Boundary |
|---|---|---|---|
| Look 1 (25%) | 44 | 4.333 | 0.39 |
| Look 2 (50%) | 88 | 2.963 | 0.66 |
| Look 3 (75%) | 132 | 2.359 | 0.82 |
| Look 4 (100%) | 176 | 1.993 | 0.91 |
Outcome: Trial stopped at Look 1 with observed HR = 0.29, crossing the efficacy boundary. FDA approved cabotegravir for PrEP in December 2021.
5Bayesian Predictive Power
5.1 Theoretical Foundation
Bayesian Predictive Probability of Success (PPoS) provides a framework for interim decision-making by computing the probability that a trial will succeed at its final analysis, given accumulated interim data and prior beliefs. Unlike frequentist conditional power (which conditions on a fixed parameter value), Bayesian predictive power integrates over the posterior distribution, properly accounting for parameter uncertainty.
Conditional Power vs. Predictive Power
Table 6
Comparison of Frequentist and Bayesian Approaches
| Aspect | Conditional (Frequentist) | Predictive (Bayesian) |
|---|---|---|
| Parameter Treatment | Fixed at specific value θ* | Distribution π(θ|data) |
| Uncertainty | Ignores parameter uncertainty | Fully accounts for uncertainty |
| Interpretation | "If true effect is θ*, probability of success" | "Given what we know now, probability of success" |
5.2 Conjugate Prior Families
Beta-Binomial (Binary)
For response rates, success/failure outcomes
Posterior: Beta(α₀ + x, β₀ + n - x)Normal-Normal (Continuous)
For mean changes, biomarkers
Posterior: Precision-weighted mean5.3 Decision Framework
Table 7
PPoS Decision Thresholds
| PPoS Range | Recommendation | Rationale |
|---|---|---|
| < 10% | Stop for futility | <10% chance of success; avoid wasting resources |
| 10-30% | Borderline; re-evaluate | Consider design modifications, biomarker refinement |
| 30-50% | Continue with caution | May proceed if unmet medical need high |
| > 50% | Proceed to Phase III | >50% success probability justifies investment |
| > 85% | Consider early graduation | Very promising; I-SPY 2 uses 85% threshold |
FDA Draft Guidance (January 12, 2026)
“Bayesian methodologies help address two of the biggest problems of drug development: high costs and long timelines.”
— FDA Commissioner Marty Makary, on the draft guidance extending Bayesian methodology to drugs and biologics
6Validation Framework
6.1 Overview and Methodology
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. This enables independent verification, continuous validation via GitHub Actions, and community contribution.
View Validation RepositoryValidation Summary
Table 8
Validation Results Summary
| Calculator | Tests | Status | Max Deviation | Reference |
|---|---|---|---|---|
| GSD | 30 | ✓ 100% | 0.0046 z-score | gsDesign R package |
| CUPED | 12 | ✓ 100% | Exact | Analytical VRF = 1-ρ² |
| Bayesian | 9 | ✓ 100% | Exact | Conjugate prior formulas |
| Total | 51 | 100% | 0.0046 | Multiple benchmarks |
6.2 Clinical Trial Replications
HPTN 083
Phase 3 HIV prevention trial. 4-look O'Brien-Fleming design replicated within 0.000 z-score deviation.
✓ All boundaries exact matchHeartMate II
LVAD trial with unequal information fractions [0.27, 0.67, 1.00]. All boundary properties verified.
✓ Unequal spacing validated7Case Studies
These case studies represent realistic scenarios constructed from published trial parameters and literature-supported assumptions. Actual benefits vary by trial characteristics.
Oncology Phase II: Sample Size Reduction via CUPED
HER2-positive breast cancer trial. Baseline tumor burden (SLD) correlation ρ = 0.55 with response.
| Metric | Standard | CUPED | Savings |
|---|---|---|---|
| Sample Size | 240 | 168 | 72 (30%) |
| Duration | 14 mo | 10.4 mo | 3.6 mo |
| Total Cost | $12.0M | $8.4M | $3.6M |
Cardiovascular Phase III: Early Stopping with GSD
PCSK9 inhibitor for MACE prevention. 4-look O'Brien-Fleming design with 2,400 patients.
| Metric | Fixed | GSD (Stopped) | Savings |
|---|---|---|---|
| Duration | 48 mo | 36 mo | 12 mo (25%) |
| Events | 430 | 220 | 210 events |
| Cost | $76.8M | $58.7M | $18.1M |
Outcome: Stopped at Interim 2 (HR = 0.68). FDA Priority Review granted, 12 months earlier approval.
Rare Disease Trial: Bayesian Go/No-Go Decision
Gene therapy for Duchenne muscular dystrophy. N = 30 patients (limited by prevalence).
Outcome: Breakthrough Therapy Designation granted. Accelerated Approval obtained 18 months earlier than traditional pathway.
Comparative Analysis: Full Program Integration
NSCLC immunotherapy Phase II/III program with all three methodologies integrated.
| Metric | Traditional | Zetyra-Optimized | Savings |
|---|---|---|---|
| Total Duration | 66 months | 50 months | 16 mo (24%) |
| Total Cost | $104M | $89.9M | $14.1M (14%) |
| Time to BLA | Month 72 | Month 56 | 16 mo earlier |
8Conclusions
8.1 Summary of Capabilities
Zetyra provides a validated, integrated platform of three statistical calculators addressing complementary inefficiencies in clinical trial design:
CUPED
- • Leverages baseline-outcome correlations to reduce sample size by 15-35%
- • Validated against analytical VRF formula with exact matches
- • Supported by FDA May 2023 guidance on covariate adjustment
Group Sequential Design
- • Enables interim efficacy/futility monitoring with Type I error control
- • Validated against gsDesign (max deviation 0.0046 z-score)
- • O'Brien-Fleming requires only 2-3% inflation, enables 15-40% expected reduction
Bayesian Predictive Power
- • Computes probability of success given interim data and prior beliefs
- • Validated against analytical conjugate prior formulas (exact matches)
- • Enables quantitative go/no-go decisions vs. binary p-value thresholds
8.2 Competitive Positioning
Table 9
Feature Comparison
| Capability | Zetyra | East | PASS | nQuery |
|---|---|---|---|---|
| CUPED Calculator | ✓ | — | — | — |
| Group Sequential | ✓ | ✓ | ✓ | — |
| Bayesian Predictive | ✓ | — | — | — |
| Public Validation | ✓ | — | — | — |
| Web-Based | ✓ | — | — | — |
| Annual Cost | $1,188 | $15,000 | $8,000 | $6,000 |
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, and Bayesian predictive power will transition from competitive advantage to industry standard.
9References
Statistical Methodology
1. Deng A, Xu Y, Kohavi R, Walker T. Improving the sensitivity of online controlled experiments by utilizing pre-experiment data. WSDM 2013.
2. Frison L, Pocock SJ. Repeated measures in clinical trials. Statistics in Medicine 1992.
3. O'Brien PC, Fleming TR. A multiple testing procedure for clinical trials. Biometrics 1979.
4. Lan KKG, DeMets DL. Discrete sequential boundaries for clinical trials. Biometrika 1983.
5. Jennison C, Turnbull BW. Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall, 2000.
6. Berry SM, et al. Bayesian Adaptive Methods for Clinical Trials. CRC Press, 2010.
7. Spiegelhalter DJ, Freedman LS. Monitoring clinical trials: conditional or predictive power? Controlled Clinical Trials 1986.
Empirical Studies
8. Walters SJ, et al. Sample size estimation for RCTs with repeated assessment of PROs. Trials 2019. [464 correlations, mean ρ=0.50]
9. DiMasi JA, et al. Innovation in the pharmaceutical industry: New estimates of R&D costs. J Health Economics 2016. [$2.6B average]
10. Moore TJ, et al. Estimated costs of pivotal trials. JAMA Internal Medicine 2018.
Regulatory Guidance
11. FDA. Adjusting for Covariates in Randomized Clinical Trials. May 2023.
12. FDA. Adaptive Designs for Clinical Trials of Drugs and Biologics. November 2019.
13. FDA. Use of Bayesian Methodology in Clinical Trials (Draft). January 12, 2026.
14. EMA. Guideline on Adjustment for Baseline Covariates. EMA/CHMP/295050/2013.
15. ICH E9(R1). Estimands and Sensitivity Analysis. November 2019.
Published Clinical Trials
16. Landovitz RJ, et al. Cabotegravir for HIV prevention. NEJM 2021. [HPTN 083]
17. Slaughter MS, et al. HeartMate II LVAD trial. NEJM 2009.
18. Barker AD, et al. I-SPY 2: Adaptive breast cancer trial design. Clin Pharmacol Ther 2009.
19. Maude SL, et al. Tisagenlecleucel in pediatric ALL. NEJM 2018.
Software
20. Anderson K. gsDesign: Group Sequential Design. R package v3.6.4. 2024.
Full 60-reference bibliography available in PDF version, including foundational statistical works, computational methods, and additional regulatory documents.
10Appendices
Appendix A: API Documentation
Zetyra provides a RESTful API for programmatic access to all calculators.
POST https://zetyra-backend.../api/v1/cuped
POST https://zetyra-backend.../api/v1/gsd
POST https://zetyra-backend.../api/v1/bayesian/binaryFull API documentation with Python/R client examples available in PDF version.
Appendix B: Validation Test Results
Complete validation results available at GitHub repository:
github.com/evidenceinthewild/zetyra-validation/resultsAppendix C: Regulatory Guidance Quick Reference
• CUPED: FDA-2023-D-1711 (May 2023), EMA/CHMP/295050/2013
• GSD: FDA-2018-D-3124 (November 2019), CHMP/EWP/2459/02
• Bayesian: FDA-2024-D-5829 (Draft, January 12, 2026)
• Estimands: ICH E9(R1) (November 2019)
Appendix D: Glossary
Full glossary with 30+ terms available in PDF version.
Appendix E: Platform Architecture
Frontend
React 18 + TypeScript, Tailwind CSS, Recharts
Backend
Python FastAPI, NumPy/SciPy, gsDesign via rpy2
Infrastructure
Google Cloud Run, PostgreSQL, 99.9% SLA
Security
OAuth 2.0, TLS 1.3, AES-256, SOC 2 in progress
Suggested Citation
Qian, Lu. (2026). Zetyra: A Validated Suite of Statistical Calculators for Efficient Clinical Trial Design (Version 1.0). Zenodo. https://doi.org/10.5281/zenodo.18253308
DOI: 10.5281/zenodo.18253308Ready to design more efficient trials?
Try Zetyra's validated calculators today.