STORM Mexico: quantify the recruitment needed for genotype subgroup evaluation

Build a reproducible recruitment feasibility analysis for evaluating methotrexate outcomes in genetic subgroups. Use the published genotype counts from a Mexican rheumatoid arthritis cohort to show how total cohort size affects the chance of obtaining adequately represented subgroups. The useful result is a defensible planning calculator and a clear account of what remains unknown before a calibrated prediction model could be evaluated.

The public STORM project seeks risk and response probabilities with uncertainty bands for Mexican and Indigenous patients. A necessary prior decision is whether a proposed evaluation cohort would contain enough people in each genetic subgroup to estimate its outcomes at all. This task purchases that planning analysis, not validation of STORM or recommendations about patient treatment.

Use Table 1 in the primary study below. The analysis covers the RA cohort's three reported genotypes at each of its four polymorphisms: MTRR A66G, RFC1 G80A, MTHFR C677T and MTHFR A1298C. Do not substitute healthy control counts or allele counts for patient genotype counts. Analyze each of the 12 subgroups separately, then bound simultaneous coverage of all 12 without assuming independence across loci.

Evaluate minimum subgroup counts m = 20 and 50, and assurance targets q = 0.90 and 0.95. These are explicit planning scenarios chosen for this task, not validated clinical sample-size standards. For each scenario calculate the smallest total recruitment N satisfying P(Binomial(N,p) >= m) >= q for every separately reported subgroup under its plug-in frequency. Also calculate a sufficient N for all 12 groups jointly using a union bound with equal per-group failure budgets (1-q)/12. Label the latter sufficient, not the exact minimum joint sample size. The article does not provide joint genotypes; do not manufacture linkage information.

Propagate frequency uncertainty in two ways: individual two-sided 95% Clopper–Pearson intervals for each subgroup proportion, and family-wise lower confidence bounds constructed using one-sided exact Clopper–Pearson bounds with a Bonferroni allocation of alpha=0.05/12 per subgroup. For a subgroup count x out of n, define the lower bound as 0 if x=0, and otherwise as the alpha quantile of a Beta(x, n-x+1) distribution. This exact definition governs the simultaneous lower bounds; Wilson, Wald, Bayesian and other alternative bounds do not replace it. Repeat the marginal planning calculation at each individual lower bound, and the joint sufficient-size calculation at the simultaneous lower bounds. A lower bound of zero means no finite guaranteed N under that bound, not a numerical failure or a finite substituted value. Keep confidence about p separate from recruitment assurance conditional on p.

For each subgroup, additionally calculate the smallest subgroup sample size needed for at least 10 events AND 10 non-events with 90% probability when a binary outcome prevalence is assumed to be 0.10, 0.30 or 0.50. Use the exact binomial probability P(10 <= X <= n-10). These prevalence values are hypothetical sensitivity scenarios, not measured methotrexate response rates. Explain why satisfying these event counts still does not establish calibration, adequate power, or utility.

All five outputs below are required as files inside the Submission; links do not replace them.

1. genotypes.csv: all 12 RA genotype records, with locus, genotype spelling, count, denominator, plug-in frequency, exact source locator and any transcription ambiguity. Include a separate column preserving the source's allele-1/allele-2 convention.
2. recruitment_results.csv: scenario inputs and calculated subgroup sample sizes, marginal recruitment minima, and joint sufficient recruitment sizes, including uncertainty-bound scenarios. Include unrounded probabilities at the selected N and N-1 for every claimed minimum; record whether a value is marginal-minimal or joint-sufficient.
3. analysis.py or analysis.R, with a plain-text dependency/version list and run instructions. The code must read the submitted extraction, perform the calculations and regenerate the submitted result tables. Any additional required code or numeric input must be included as files. Ordinary laptop execution with freely available software must suffice; no paid services or unavailable patient data may be required.
4. verification.md: verify locus totals against the reported RA cohort; document handling of zero/one probabilities, a small manually checkable binomial case, the N versus N-1 minimum checks, and cross-check at least two recruitment calculations using an independently implemented tail calculation or separate established statistical implementation. State the numeric tolerance used and investigate any larger discrepancy.
5. decision_memo.md: explain which subgroups constrain recruitment and how frequency uncertainty changes the planning decision, using the result tables. Distinguish the source population from the proposed target population; identify the exact missing information required to turn this feasibility calculation into an external calibration study (including a frozen model, prediction time, endpoint and horizon, intended target cohort, and individual predictions/outcomes). Explain what recruitment conclusions survive and fail under population shift. Include a sensitivity figure or table in this file or as an additional submitted image/data file.

Required input: Table 1 and the cohort description of *MTRR A66G, RFC1 G80A, and MTHFR C677T and A1298C Polymorphisms and Disease Activity in Mexicans with Rheumatoid Arthritis Treated with Methotrexate*, published in 2017, DOI 10.1089/gtmb.2017.0124, PMCID PMC5695735. The governing version is the original 2017 article and its Table 1, as publicly available on 17 September 2026; later revisions are outside scope. Full text is available through PMC and its Europe PMC XML mirror. If the two transcriptions differ, identify both readings and resolve them against the original article table; never silently choose a favorable result.

Background only: STORM: Stochastic Therapeutic Outcome & Risk Model. This page establishes the planning context but supplies no private model, patient records or further acceptance requirements. Neither project access nor new data collection is required.

Only Submissions meeting every acceptance criterion are eligible. Compare eligible Submissions in this order: (1) correctness and independently supported numerical verification; (2) traceability from every planning conclusion to its input and result, including explicit separation of conditional assurance from confidence about frequencies; (3) decision usefulness, meaning a clear explanation of which recruitment constraint binds and what specific missing input would change it. Extra literature volume, favorable results and unsupported precision do not improve rank. If still tied, the earlier submitted eligible Submission wins. If only one qualifies, it wins; if none qualifies, the outcome is no_valid_submission.

No recruitment, patient data acquisition, clinical advice, treatment selection, model training, invented patient-level records, STORM performance claims or wet-lab work. No pooling the study's controls with RA patients and no independence assumption for genotypes across loci.