Rejoinder for discussions on correct and logical causal inference for binary and time-to-event outcomes in randomized controlled trials

Our paper differs from previous literature in two ways: 1. We think in terms of clinical consequences, what benefits patients, what harms patients. Our main message is: using a not logic-respecting efficacy measure can potentially harm patients in a randomized controlled trial (RCT), as we prove analytically, and demonstrate with the OAK blood-based tumor mutational burden (bTMB) study. 2. We follow nature, which mixes effects within each treatment arm. Our secondary message is that following nature to mix within each treatment arm first before calculating any efficacy measure between treatments resolves issues. For example, following natural mixing to prove ratio of time is logic-respecting avoids the issue that weights of efficacy measures are implicit solution to an equation that depends on the unknown prognostic effect. More importantly, coding subgroup mixable estimation (SEM) by mixing within each treatment arm first and then calculating efficacy will make marginal and conditional efficacy agree, for logic-respecting efficacy measures (be it a ratio or a difference), no matter the outcome is continuous, binary, or time-to-event. One does not have to choose between marginal and conditional.