Is the shift in a prognostic gene expression association produced by adjustment for tumor proliferation governed by the prognostic strength of proliferation itself? A confirmatory test in cohorts not yet examined

This is the second registration for this project. It follows an earlier registration, doi:10.17605/OSF.IO/X5DCF, and it is a new study rather than an amendment to that one. I have not edited, withdrawn, or reinterpreted the earlier registration, and its result stands as recorded there. The first registration predicted that adjusting a prognostic gene expression model for a score of tumor proliferation would shift the estimated hazard ratios in a direction set by each gene's correlation with that score, and that the slope describing this would be negative in every cancer type. It also predicted that the shift estimated for a given gene in one cancer type would agree with the shift estimated for the same gene in another. Both predictions were tested in ten cancer types and both were refuted. The slope was negative in five cancer types and positive in five, and the median pairwise agreement of the shift across cancer types was negative rather than positive. This registration differs in its hypotheses, in its data, and in what it treats as the unit of analysis. Its hypotheses are quantitative rather than directional. Writing the within-cohort slope as b and the log hazard ratio of the proliferation score in that same cohort as L, I predict that the coefficient of L in a regression of b on L across cohorts is negative, that the intercept of that regression does not differ from zero, and that the sign of b follows the sign of L within each cohort. The unit of analysis is the cohort rather than the gene, which is what the first registration got wrong. The data are cohorts that have not been examined. Fifteen cancer types in The Cancer Genome Atlas were excluded from the first registration before any model was fitted in them, so no slope and no proliferation hazard ratio from those cancer types has been seen. They enter here under thresholds set for a cohort-level analysis. To test the claim against the possibility that it is a property of one processing pipeline, cohorts from outside The Cancer Genome Atlas are added under a rule that is fixed in the attached document, with a verification of each matrix reported before any contrast is computed in it. The candidate accessions are deliberately not named, because I have not yet verified any of them. I want one point on the record before the result exists. The prediction that the intercept is zero is the one I consider most likely to fail. A nonzero intercept would mean that a shift remains in cohorts where proliferation carries no prognostic information, which would point away from confounding and toward non-collapsibility or some other consequence of adding a covariate. That outcome would not overturn the first hypothesis, but it would narrow what the work is entitled to claim, and I have written the decision rule so that it cannot be read any other way afterward. The attached document, PREREG2_ConfoundingLaw_20260920.docx, is the full preregistration and contains the inclusion rules, the analysis, the handling of measurement error in L, and the numeric thresholds at which each hypothesis is treated as confirmed, refuted, or equivocal.