Discussion on ‘Correct and logical causal inference for binary and time‐to‐event outcomes in randomized controlled trials'

We would like to thank Dr. Yi Liu and her coauthors for the insightful discussion of collapsibility and logic-respecting treatment effect measures in randomized controlled trials. There is a growing awareness in the pharmaceutical drug vdevelopment community about the need to precisely describe targeted treatment effects that are clinically relevant and this paper is a timely contribution to this discussion. To properly inform decision making by pharmaceutical companies, regulators, patients, physicians and other stakeholders, clear descriptions of the benefits and risks of a medicinal treatment for a given disease condition should be made available. As argued in the recent ICH (2019) guideline, there is a concern that the reported ‘treatment effect’ will be misunderstood without such clarity: How the outcome of treatment compares to what would have happened to the same patients under alternative treatment (i.e. had they not received the treatment, or had they received a different treatment). While the guideline does not use the term ‘causal’ or provides a formal definition of ‘treatment effect’, it has been written with causal reasoning in mind. Importantly, the ICH (2019) guideline invites readers to differentiate between conditional and marginal estimands. This distinction has been largely neglected in pharmaceutical drug development. For example, a marginal estimand for a binary outcome could be defined as a marginal odds ratio, which is a contrast of response probabilities obtained by averaging over the covariate space. On the other hand, a conditional estimand could be the treatment effect parameter in a standard logistic regression with covariates, which should be interpreted as an odds ratio conditioning on certain values of the covariates (e.g. their mean values). It is neither right nor wrong to favour one estimand over another, much like one cannot favour apples over oranges (or vice versa). Both estimands allow for a causal interpretation in the sense of ICH (2019), and the choice between them should be guided by the clinical meaningfulness of the resulting treatment effects. The distinction between conditional andmarginal estimands is closely related to the non-collapsibility of odds ratios and hazard ratios (FDA, 2021). As pointed out by Liu et al. (2021) and many other authors before (see, e.g. Daniel et al. (2021), and the references therein), the odds ratio and the hazard ratio, using logistic and Cox proportional hazard regression respectively, are non-collapsible. Even in an ideal randomized controlled trial without loss to follow-up or confounding due to intercurrent events, the odds ratio or risk ratio comparing two treatments would change when a baseline covariate associated with the outcome were to be included in the logistic regression and Cox proportional hazard regression, respectively. This reminds us that confounding and non-collapsibility are two separate issues: Conditioning on the covariates changes the expected treatment effect and this difference between conditional and marginal estimands refers to odds ratios and hazard ratios being non-collapsible. It is instructive to compare the collapsibility definition in Liu et al. (2021) with other definitions in the literature. Using their notation, let A ∈ {Rx, C} denote a binary exposure (i.e. treatment and control), Y a binary outcome (i.e. success yes/no) and X ∈ {g, g} a covariate with two levels (i.e. subgroup defined through biomarker status positive/negative).