All Times EDT
Keywords: companion diagnostic, confounding, estimand, prognostic and predictive biomarkers, subgroup analysis
Causal effects are statements about the joint distribution of potential outcomes Y(C) and Y(Rx), where C and Rx are treatments. However, the causal odd ratio and the causal hazard ratio have been defined in literature as functions of the marginal distributions of Y(C) and Y(Rx), leading to non-collapsibility of these measures over subgroups, even when the treatments are randomized to subjects. To address the problem, we propose a new probability ratio defined on the joint distribution of potential binary outcomes that is collapsible and equivalent to the odds ratio when the potential outcomes are conditionally independent given the subgroup. We also consider the odds of living longer on C than Rx and show it is collapsible and is equivalent to the hazard ratio when the potential time-to-event outcomes are conditionally independent given the subgroup. We illustrate the new measures on a numerical example given in Liu et al. (Biometrical J, 2021) and a clinical trial in which treatments gefitinib and carboplatin+paclitaxel for non-small cell lung cancer are compared on progression-free survival within EGFR tumor status subgroups and overall.