Discussion on "Correct and logical causal inference for binary and time-to-event outcomes in randomized controlled trials" by Yi Liu, Bushi Wang, Miao Yang, Jianan Hui, Heng Xu, Siyoen Kil, and Jason C. Hsu.

In their paper, Liu et al. (2020) pointed out illogical discrepancies between subgroup and overall causal effects for some efficacy measures, in particular the odds and hazard ratios. As the authors show, the culprit is subgroups having prognostic effects within treatment arms. In response to their provocative findings, we found that the odds and hazard ratios are logic respecting when the subgroups are purely predictive, that is, the distribution of the potential outcome for the control treatment is homogeneous across subgroups. We also found that when we redefined the odds and hazards ratio causal estimands in terms of the joint distribution of the potential outcomes, the discrepancies are resolved under specific models in which the potential outcomes are conditionally independent. In response to other discussion points in the paper, we also provide remarks on association versus causation, confounding, statistical computing software, and dichotomania.