Steam Collective: size a credible mortality follow-up study

Build a reproducible event and recruitment calculator to help Steam Collective decide whether a future community-sauna cohort could meaningfully evaluate all-cause mortality associations. Ground the comparison in the published Finnish cohort, then show how weaker associations, exposure imbalance and lower event rates change feasibility. This is a research-planning purchase, not a claim that sauna prevents death.

The project proposes community saunas that contribute research data and cites long-term mortality associations. Determine what an independently evaluated mortality association would require under explicit planning assumptions, and what a smaller pilot would need to measure before a defensible study could be designed.

The fixed historical extraction is the original 2015 Laukkanen paper's frequency analysis: all three sauna-frequency category sizes, their all-cause death counts, follow-up description, and every all-cause hazard ratio and confidence interval in Table 2 across adjustment levels. Extract adjustment sets, baseline exposure measurement, participant eligibility, and outcome ascertainment. Duration-of-session analyses and other endpoints are outside the quantitative scope.

The planning comparison is high frequency (4–7 sessions/week) versus once weekly, excluding the middle category. Evaluate both balanced exposure allocation p=0.5 and the high-frequency proportion among these two published categories, derived from their counts. These are hypothetical recruitment scenarios; the original exposure groups were not randomized.

Calculate approximate required observed deaths using Schoenfeld's two-group proportional-hazards formula, D=(z_(1-alpha/2)+z_power)^2/[p(1-p)(log(HR))^2], with two-sided alpha=0.05, power 0.80 and 0.90, and HR scenarios 0.60, 0.80 and 0.90. Explain which published value motivates the first scenario and why weaker-effect scenarios are necessary. Round required events upward only after preserving the unrounded result. This formula is an approximation under the specified proportional-hazards comparison, not an exact guarantee for an adjusted observational model.

Convert D to approximate recruitment under control-group cumulative event-risk scenarios r0=0.01, 0.05 and 0.20 at an unspecified fixed study horizon. Under proportional hazards, use r1=1-(1-r0)^HR and average risk (1-p)r0+p*r1. Apply initial nonparticipation/zero-follow-up fractions 0 and 0.15 by dividing expected usable event yield by the corresponding retained fraction. Let D_int=ceil(D) be the required integer deaths, let a be the initial exclusion fraction, and let r_bar=(1-p)r0+p*r1. Define unrounded recruitment as N_raw=D_int/[(1-a)*r_bar], and the required integer recruitment as N=ceil(N_raw). Preserve D, D_int, N_raw and N as separate output fields. For each simulation, assign n_high=floor(N*p+0.5) participants to the high-frequency group (nearest integer, with exact halves rounded up), and n_control=N-n_high to the control group. Use this integer allocation without re-solving the analytic formula; report the realized allocation n_high/N alongside the nominal p. This simple exclusion scenario is not time-dependent censoring. Do not attach calendar years to these hypothetical event risks or treat raw historical death fractions over variable follow-up as fixed-horizon Kaplan–Meier estimates.

Add an executable simulation check of the analytic approximation for the four combinations of HR=0.60/0.80 and the two allocations, at power target 0.80, r0=0.20, and no initial exclusion. Use independent exponential event times, a common administrative horizon normalized to 1, baseline hazard -log(1-r0), and the alternative hazard HR times baseline. Simulate the rounded analytic recruitment size and compare empirical two-sided log-rank rejection probability with nominal power. At least 1000 replicates per scenario, reproducible seeds, actual integer group counts and Monte Carlo uncertainty intervals are required. Retain departures from nominal power as findings; do not alter scenarios to force agreement.

All outputs are required as files inside the Submission. A source URL does not replace a required artifact.

• source_extraction.csv: the defined historical extraction with row-level table/paragraph locators, denominators, effect scale, confidence bounds and adjustment-set identifiers; a companion plain-text adjustment table is allowed.
• planning_grid.csv: every defined analytic scenario, its unrounded event requirement, rounded deaths and recruitment, exposure allocation, assumed event probabilities and exclusions. Include enough intermediate values to trace each result.
• simulation_results.csv: the four required simulation scenarios with sample sizes, replicates, seed, observed rejection count, estimated power and binomial Monte Carlo interval; record the chosen interval method.
• Executable Python or R code and dependency versions/run instructions that regenerate the results from the submitted input. Include all required code and numeric inputs. Ordinary laptop computation with freely available software must suffice; no private cohort, paid service or API may be needed.
• decision_memo.md: a source-linked interpretation of which assumptions dominate feasibility, a proposed pilot measurement list tied to those uncertainties, and a precise account of the confounding, exposure-change, follow-up, target-population and proportional-hazards limitations. Include at least one visual or compact table comparing required recruitment across effects and event risks. Explain whether the historical all-cause claim supports the same wording for the proposed target population, and distinguish that evidence judgment from the hypothetical power calculation.
• checks.md: source-count reconciliation, two manually inspectable formula substitutions, verification of simulation event/censoring logic, Monte Carlo uncertainty calculation, and an independent numerical check of at least one log-rank statistic against an established implementation or a separate implementation. Explain mismatches instead of hiding them.

Required historical input: Laukkanen et al., *Association Between Sauna Bathing and Fatal Cardiovascular and All-Cause Mortality Events*, JAMA Internal Medicine 2015;175:542–548, DOI 10.1001/jamainternmed.2014.8187. Governing content is the original 2015 article, Table 2 and associated cohort methods/results, as available on 17 September 2026. Publisher full text and tables; PubMed bibliographic record and abstract. The publisher table governs over rounded abstract language; later studies do not replace it.

The required method is specified completely by the mathematical formula and simulation conditions above. Background bibliographic reference is Schoenfeld, *Sample-Size Formula for the Proportional-Hazards Regression Model*, Biometrics 1983;39:499–503, DOI 10.2307/2531021. Bibliographic record and abstract. Full-text access to that methods article is not required; the formula and scenarios stated in this challenge govern rather than software defaults.

Background only: Steam Collective project. It supplies the community-research motivation and no private data or additional acceptance conditions.

Among fully eligible Submissions, rank first by verified computational correctness and reproducibility; next by traceability of historical inputs and clear separation of observed versus assumed quantities; then by practical decision value, defined as explaining which feasibility constraints bind and which pilot measurements would resolve them. More favorable effect estimates or more confident conclusions do not improve rank. Remaining ties go to the earlier submitted eligible Submission. If one qualifies, it wins; if none qualifies, the outcome is no_valid_submission.

No recruitment, health intervention, sauna-use advice, actual clinical protocol approval, new mortality records, individual-data reconstruction, causal efficacy proof, dementia claims or extrapolated benefits for women or other heat modalities.