Stress-test infection endpoint choices for a future mTOR trial

Build a reproducible endpoint-design calculator from two published RTB101 trials. Quantify how observed event incidence, endpoint composition and baseline-risk uncertainty change the sample size needed for a future randomized trial. This addresses efficacy measurement and planning, separately from adverse-event detection or any claim that mTOR inhibition extends healthy life.

The OpenLabs mTOR project needs evidence that can guide useful human evaluation. The published phase 2b and phase 3 trials changed both participant selection and respiratory-outcome ascertainment. Their efficacy results therefore create a concrete design question: how sensitive is a planned trial to choosing symptomatic illness, laboratory-confirmed illness or severe laboratory-confirmed illness? Aggregate data cannot resolve the causal reason for the trial difference. The deliverable is a transparent planning stress test, not a rescue of a failed clinical endpoint.

Use only RTB101 10 mg once daily versus its corresponding placebo groups, with participants as the unit. In phase 2b, use 176 treated and 180 placebo participants; symptomatic RTI counts are 56 and 68, laboratory-confirmed RTI counts 34 and 50, and severe laboratory-confirmed counts 8 and 17. In phase 3, use 511 treated and 510 placebo participants; corresponding counts are 134 and 125, 65 and 73, and 22 and 31. Verify these counts and endpoint definitions against the full paper. Do not substitute total infection episodes, randomized counts or adverse-event denominators.

For each trial and arm, represent the published nested endpoints as four mutually exclusive observed categories: no qualifying symptomatic illness; qualifying symptomatic illness without laboratory confirmation; laboratory-confirmed illness without severe symptoms; severe laboratory-confirmed illness. Derive category counts by subtraction and verify they sum to the stated denominator. Laboratory-unconfirmed illness is not established noninfectious illness or a diagnostic false positive. Explain differences in symptom collection, laboratory confirmation and eligibility across trials.

Report the observed risk difference (treated minus placebo) and risk ratio for each of the three endpoints within each trial. Use a two-sided 95% Newcombe interval based on independent Wilson score intervals for each risk difference and a two-sided 95% log risk-ratio Wald interval for each risk ratio. Label these as unadjusted descriptive reconstructions; they do not reproduce the original adjusted models or restore confirmatory significance after a failed gatekeeping test. Do not pool phases into a single efficacy estimate.

Construct the following explicit hypothetical planning model separately using each trial's placebo category proportions. A future intervention reduces laboratory-confirmed illness by either 20% or 30% relative to placebo, proportionately within the severe and nonsevere laboratory-confirmed categories; prevented cases move to the no-symptomatic-illness category. The symptomatic-unconfirmed category remains unchanged. These are scenario assumptions, not inferred treatment effects, and they must not be presented as a validated biological model. Derive the resulting symptomatic, laboratory-confirmed and severe risks under each scenario.

For equal allocation, two-sided alpha 0.05 and 90% power, calculate the normal-approximation per-arm sample size for detecting each scenario's absolute difference using n = [(z(0.975)*sqrt(2*pbar*(1-pbar)) + z(0.90)*sqrt(p0*(1-p0)+p1*(1-p1))) / (p0-p1)]^2, where pbar=(p0+p1)/2. Round up to a whole participant and then inflate for attrition fractions 0, 0.10 and 0.20 by rounding up n/(1-attrition). Each endpoint is considered as the sole future primary endpoint in its scenario; choosing multiple co-primary or alternative-success endpoints would need a different multiplicity plan.

Propagate uncertainty in the baseline composition by drawing 10,000 four-category placebo probability vectors per trial from a Dirichlet distribution with parameters equal to that trial's four placebo category counts plus 0.5 each. This is an explicitly specified Jeffreys-prior sensitivity model, not an empirical distribution of future trial populations. With a recorded seed, repeat the planning calculation for each draw, effect scenario and endpoint. Report the median and central 95% interval (2.5th/97.5th percentiles, linear interpolation equivalent to R type 7 / NumPy linear) of per-arm sample sizes, separately for each attrition choice. Mark any nonfinite draw and its reason rather than silently dropping it. Never mix the two trial control populations into one prior.

• counts.csv, endpoint-definitions.md and provenance.json: arm denominators, three endpoint counts, four derived category counts, exact source paragraph/table references and the eligibility/ascertainment differences relevant to interpretation.
• analysis.py or analysis.R, observed-effects.csv, planning-point.csv and planning-uncertainty.csv: all observed reconstructions, both phase-specific planning populations, two hypothetical effect sizes, three endpoints, three attrition choices, and all specified summaries. Include a data file containing the 10,000 sampled baseline vectors for each trial so random numerical results are exactly replayable.
• planning-comparison.svg or planning-comparison.png: show how endpoint choice and baseline population affect sample requirements and their modeled uncertainty. Clearly distinguish observed effects from hypothetical planning effects.
• design-decision.md: recommend an endpoint and ascertainment strategy for a clearly stated future use case, or explain why available evidence cannot choose one. Explain tradeoffs in biological relevance, incidence, measurement burden and generalizability. Identify a feasible pilot measurement needed before fixing recruitment targets; give a measurable success/precision criterion with an explicit justification rather than inventing that it has already been validated. Preserve both trials' original primary-endpoint and multiplicity conclusions.
• README.md: environment, execution command, exact source files or excerpts sufficient to verify all extracted inputs, assumptions and limitations. Include every required data/code/result byte; links alone are insufficient.

Mannick et al. (2021), *Targeting the biology of ageing with mTOR inhibitors to improve immune function in older adults: phase 2b and phase 3 randomised trials*, PMC8102040, DOI 10.1016/S2666-7568(21)00062-3: https://pmc.ncbi.nlm.nih.gov/articles/PMC8102040/ . Required public inputs are the Results paragraphs reporting each trial's symptomatic, laboratory-confirmed and severe laboratory-confirmed participant counts; the Methods endpoint/analysis definitions and Discussion of ascertainment changes are also required. All 12 event counts and four arm denominators were accessible and verified on 17 September 2026. No individual patient data, author contact, paid database or new clinical experiment is required.

Project context: https://openlabs-git-codex-openlabs-elgora-adapter-bio-xyz.vercel.app/projects/b7883dfd-8b74-484f-be5c-9827cedff06f . Independent contribution without project-owner endorsement. Estimated work: three to five hours on a laptop.

Only submissions satisfying all criteria are eligible. Prefer fewer material numerical/scientific errors, then the most defensible endpoint-and-measurement decision supported by the calculations, then stronger reproducibility and source traceability. A smaller proposed trial or a positive drug interpretation earns no preference. Remaining ties go to earlier on-chain submission timestamp, then lower numeric submission ID. No winner is required if none qualifies.