---
profile: elgora_markdown_bounty_challenge_v0
escrow_amount: "1000000"
submission_deadline: 1789624800
payout_policy: winner_take_all
---

# Quantify the precision needed to test an acute UVA blood-pressure hypothesis

## Summary
Build a reproducible covariance-sensitivity and recruitment calculator using the public aggregate blood-pressure data from a randomized crossover UVA experiment. Determine what its published means can establish, what depends on unknown within-person covariance, and which covariance measurements a future pilot should collect. This supports the Sun-Human Interface project's hypothesis-driven UVA/nitric-oxide research; it is not an exposure recommendation.

## Challenge details
The project separates visible-light, UVB, UVA and heat pathways and treats vitamin-D-independent biology as an open hypothesis. This task addresses a practical study-design decision: how many complete paired observations could be needed to distinguish a small acute blood-pressure contrast, and how strongly that answer depends on unpublished covariance and rounded standard errors.

Use Table 1 of the fixed study below for systolic BP, diastolic BP and mean arterial pressure (MAP), in CON, UVA10 and UVA20, at baseline, immediate cessation and 30 minutes. The twelve target contrasts are the change from baseline in each active condition minus the corresponding change in CON, for each BP endpoint and post-exposure time. These are aggregate difference-in-change calculations, not a reproduction of the original repeated-measures analysis.

For each contrast use measurement order (active post, active baseline, CON post, CON baseline) and coefficient vector c=(1,-1,-1,1). Recover individual marginal SDs as reported SEM times sqrt(the study sample count). For hypothetical correlation r in {0,0.25,0.5,0.75,0.9}, form covariance matrix S=diag(SD) R diag(SD), where R has diagonal 1 and every off-diagonal entry r. Calculate individual contrast variance V=c'Sc and contrast standard error sqrt(V/n). This common-correlation model is a transparent sensitivity assumption, not an estimate from the paper.

Compute point contrasts and approximate 95% normal intervals under each r. For hypothetical future differences of 2, 3 and 5 mmHg, compute n_complete=ceil((z_0.975+z_0.80)^2 V/difference^2) for a two-sided 5% test and 80% power, and n_enroll=ceil(n_complete/(1-dropout)) for dropout 0%, 10% and 20%. Use full-precision normal quantiles. These are normal-approximation planning scenarios, not final clinical sample-size recommendations; discuss small-n, covariance estimation, endpoint multiplicity, order/carryover and population limitations.

## What you need to submit (Deliverables)
- `inputs.csv`: all 27 BP condition/time/endpoint entries with reported mean, SEM, units, sample count, source location and exact source text. Record the crossover population and timing in a separate metadata section of `README.md`.
- `analysis.py` or `analysis.R`, `contrasts.csv`, `planning.csv`: reproducible calculations for every specified contrast, correlation, target difference and dropout combination. Include the covariance assumptions and an explicit positive-semidefinite check. No guessed participant correlations or fabricated raw records.
- `rounding.csv`: repeat the planning variance calculation at every corner of the four marginal SEM intervals [max(0,reported SEM−0.5),reported SEM+0.5], reflecting Table 1's integer reporting. For each contrast/r combination report the minimum and maximum V over those 16 corners and corresponding planning counts for a 3 mmHg target and 10% dropout. These are corner-sensitivity ranges, not asserted global bounds or confidence intervals; do not treat them as rounding-error probabilities.
- `precision.svg` or `precision.png`: an interpretable display of how required complete participants change with correlation for all endpoints, active conditions and post-exposure times, with a clearly stated target difference.
- `decision.md`: identify which design decisions remain unstable under covariance and rounding assumptions; recommend the specific repeated measurements, retention reporting and covariance outputs required from a future pilot before fixing recruitment. Assess whether Table 1 establishes a treatment effect, distinguish BP from nitric-oxide biomarker claims, and explain which UVA/heat/exposure-control limitations remain. Give an explicit conclusion on what this study can and cannot contribute to the project's hypothesis. `README.md` must give provenance, environment and a command that regenerates all numeric outputs. Include all artifact bytes in the Submission.

## Inputs, Materials and References
Monaghan et al. (2018), *The effects of two different doses of ultraviolet-A light exposure on nitric oxide metabolites and cardiorespiratory outcomes*, DOI 10.1007/s00421-018-3835-x, PMC5959980: https://pmc.ncbi.nlm.nih.gov/articles/PMC5959980/ . Fixed input is its public PMC version available 17 September 2026, Table 1 and relevant participant, protocol, analysis and results sections. Table 1 identifies its dispersion as SEM; text or figures may use other conventions. No participant data, supplementary files, UV exposure or lab work is required.

Project context: https://openlabs-git-codex-openlabs-elgora-adapter-bio-xyz.vercel.app/projects/7ed1e5eb-20d6-4943-9fd7-5548f45e8bf4 . Independent contribution, with no claimed project endorsement.

## Acceptance Criteria
1. The full 27-entry input scope matches Table 1, correctly distinguishing SEM from SD and mmHg from other units. Sample size and exposure timing are sourced accurately.
2. All twelve contrasts and every specified scenario are present. Code reproduces point estimates, V, standard errors, normal intervals and recruitment calculations to 0.000001 before rounding; participant counts use ceilings at the specified steps. Matrices are checked as positive semidefinite within declared numerical tolerance.
3. The 16-corner rounding analysis is complete for each contrast/r pair and labeled accurately. No confidence level or probability is attributed to it. The visualization agrees with output tables.
4. The report distinguishes calculated point contrasts from conditional precision, physical observed data from hypothetical covariance, and a within-condition change from a between-condition treatment effect. It does not present common correlation, dropout or target differences as measured facts, nor report these scenarios as the original study's p values.
5. The pilot recommendation names the covariance and retention data needed to replace the sensitivity assumptions, addresses order/carryover and multiplicity, and identifies the study's population/acute-endpoint limits. It makes no clinical, chronic-benefit or safe-dose claim and does not infer that absence of statistical significance proves absence of effect.

## How is the winner selected?
Only submissions satisfying all criteria are eligible. Prefer fewer material numerical or scientific errors, then the most defensible interpretation of uncertainty for the pilot's measurement and recruitment decision, then stronger reproducibility and provenance. Remaining ties go to earlier on-chain submission timestamp, then lower numeric submission ID. No winner is required if none qualifies.