How much can missing diary outcomes change the colic trial's treatment contrast?

Build a reproducible missing-outcome sensitivity analysis for the 2014 randomized trial of Lactobacillus reuteri DSM 17938 in infant colic. Deliver a decision brief identifying which treatment and subgroup claims the aggregate evidence can support, and which diary-retention uncertainties should shape a future objectively measured trial. A negative or inconclusive conclusion is eligible.

The listed OpenLabs colic project seeks subgroup phenotyping and objective crying measurement. This bounty addresses a concrete prerequisite: determine whether conclusions from a major diary-based trial are robust to unavailable outcomes, and whether its feeding subgroup evidence establishes treatment-effect heterogeneity. It does not purchase a new treatment recommendation or a meta-analysis of all probiotics.

Use the fixed public trial below. Its participant flow and Table 3 contain randomized counts, observed outcome counts, and observed means and standard deviations. Analyze the one-month total daily cry-or-fuss endpoint in minutes/day. The primary sensitivity estimand is an unadjusted mean contrast among all randomized infants, probiotic minus placebo. It is deliberately distinct from the paper's covariate-adjusted estimate. Participant records are unavailable and must not be invented.

For each arm j, define N_j as randomized count, n_j as observed one-month endpoint count, y_j as its reported observed mean, and m_j as an assumed mean for missing outcomes. Calculate M_j = (n_j*y_j + (N_j-n_j)*m_j)/N_j and contrast D=M_probiotic-M_placebo. Treat missing means as unknown sensitivity parameters, not measured data. Lower cry-or-fuss time is favorable.

• inputs.csv: sourced randomized and observed counts, one-month cry-or-fuss means and SDs, adjusted overall estimate/CI, and all reported one-month feeding-subgroup cry-or-fuss contrasts/CI/sample counts. Each row needs a table/figure/paragraph location, units and exact reported text beside parsed values. Preserve unavailable values as missing with explanation.
• analysis.py or analysis.R, README.md, and generated sensitivity.csv: (a) observed-case unadjusted contrast and its normal-approximation 95% interval using sqrt(SD_P²/n_P + SD_C²/n_C); (b) full-randomized-cohort contrast over every pair of missing means in {0,10,...,1440} minutes/day; (c) a labeled local sensitivity grid where each missing-arm mean equals its observed-arm mean plus a shift in {-180,-90,0,90,180}, clipped to [0,1440]; (d) exact algebraic zero-contrast threshold for one missing-arm mean as a function of the other, identifying which part lies in the physical [0,1440] range; and (e) sharp arithmetic bounds on D from that range. The physical range is a worst-case bound, not a claim of clinical plausibility.
• sensitivity.svg or sensitivity.png: readable surface or contour plot displaying the sign of D, zero contour and observed-mean missingness assumption. Clearly identify hypothetical axes and minutes/day units.
• decision.md: explain which conclusions change under which assumptions, compare the unadjusted and published adjusted estimands without pretending to reproduce the latter, and distinguish an arithmetic tipping point from evidence that the assumed missingness occurred. Evaluate the feeding-subgroup evidence, including whether a treatment-by-feeding interaction is reported or recoverable and why different within-subgroup significance does not alone prove heterogeneity. Give a concrete future measurement/retention design recommendation grounded in the observed missing-data mechanism, with the additional data needed to resolve the leading uncertainty. Explain the limits of applying this one trial to the project's breastfed-infant proposition. All required file bytes must be included; citations alone do not replace artifacts.

Fixed evidence set: Sung et al., *Treating infant colic with the probiotic Lactobacillus reuteri: double blind, placebo controlled randomised trial*, BMJ 2014;348:g2107, DOI 10.1136/bmj.g2107, PMCID PMC3972414, public PMC article version available on 17 September 2026: https://pmc.ncbi.nlm.nih.gov/articles/PMC3972414/ . Use participant flow, Table 3, statistical analysis, subgroup results, discussion and data-sharing statement. No supplementary file, individual participant data, new diary recording or author response is required. Any additional source is optional context and cannot replace this fixed input.

Project context: https://openlabs-git-codex-openlabs-elgora-adapter-bio-xyz.vercel.app/projects/30fc0365-3b96-4ea4-ae4b-ed352ff22880 . This is an independent research contribution without claimed project-owner endorsement.

Only submissions meeting every acceptance criterion are eligible. Among eligible submissions, prefer fewer material scientific or numerical errors, then the clearest defensible connection between quantified sensitivity and a concrete future measurement/retention decision, then stronger source traceability and reproducibility. Longer reports or stronger claims do not score better. If still tied, earlier on-chain submission timestamp wins, then lower numeric submission ID. If none meets the criteria, no winner is required.