Getting the same answer in R and Python is a useful checkpoint. It makes a result easier to inspect and gives a research team more confidence in the calculation. It also leaves some of the most consequential questions open: which participants the result describes, what happened at later follow-ups, and how missing outcomes were handled.
Our Beating the Blues methods case study follows those questions through a public depression-trial teaching dataset. The example shows how computational verification fits into the wider work of deciding what an analysis can support.
The HSAUR3 teaching release contains 100 records attributed to a trial of Beating the Blues, a computerized cognitive-behavioural programme. The cited original trial randomized 167 adults. How the 100 released records were selected remains unresolved in the documentation we inspected.
That matters before a model is fitted. An analysis of the released records cannot automatically stand in for an analysis of everyone randomized. Handling missing follow-up scores within those records does not recover the other trial participants.
We therefore describe this work as a reanalysis of a public teaching release. Exact numerical reproduction of the original clinical paper has not been established. Keeping that scope explicit helps readers understand whose outcomes the estimates describe.
We first analyzed the observed two-month scores, adjusting for baseline symptoms. We then fitted a longitudinal model with a separate treatment estimate at each visit, using the available follow-up measurements.
Independent Python and R implementations refitted the longitudinal model and all 999 patient bootstrap samples. The samples were shared so that the two implementations faced the same numerical task; each language performed its own fitting. The estimates and sensitivity summaries met the specified comparison tolerances.
This is evidence about implementation. The second calculation is valuable for finding coding or specification errors. Both implementations still use the same released data and modeling assumptions, so their agreement cannot establish whether those assumptions describe the study adequately.
At two months, the longitudinal estimate was 3.95 depression-score points lower for Beating the Blues than usual care. The 95% patient-bootstrap interval ran from 7.13 points lower to 0.77 points lower. At eight months, the estimate was 1.54 points lower, with an interval from 5.16 points lower to 2.42 points higher.
The early estimate is clearer in this release. The later interval includes no difference, and the later visits were exploratory. Those facts do not establish that the benefit declined: a claim about change in the treatment effect needs a direct comparison between visits. Looking at which individual intervals include zero is not that comparison.
The longitudinal model assumes outcomes are missing at random: after accounting for treatment, baseline symptoms, and observed follow-up scores, missingness does not additionally depend on the unobserved scores. Agreement between programs cannot verify that assumption.
We also examined 25 illustrative scenarios that shifted expected missing scores separately in each treatment group. The two-month interval stayed below zero throughout that grid; limited missingness at that visit helps explain its stability. Later estimates were more sensitive. The shifts were examples for exploring assumptions, not clinically established bounds on what the missing scores could have been.
A reproducible analysis is easier to assess when readers can follow the data version, model, uncertainty calculation, and interpretation together. The full case study includes the results figure, methods, and a curated reproducibility download. It explains how to obtain the pinned public data separately and rerun the numerical checks.
For a manuscript or evaluation report, the same discipline is useful: identify the analysis population, state how missing outcomes were handled, keep uncertainty beside the estimate, and document which checks were actually completed. Readers can then judge how closely the reported conclusion follows from the evidence.
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