From Logic-respecting Efficacy Estimands to Logic-ensuring Analysis Principle for Time-to-event Endpoint in Randomized Clinical Trials with Subgroups

An important goal of precision medicine is to identify biomarkers that are predictive, and tailor the treatment according to the biomarker levels of individual patients. Differentiating prognostic vs. predictive biomarkers impacts important decision makings for patients and treating physicians. Using hazard ratio (HR) can mistake a purely prognostic biomarker for a predictive one leading to a disheartening possibility of depriving patients of beneficial treatment as demonstrated in the OAK trial. This stems from the illogical issue of HR at population level where marginal HR in the overall population can be larger than those in both subgroups. Instead of trying to circumvent this issue by discouraging comparisons between marginal and conditional HRs, we propose to directly fix it by using alternative logic-respecting efficacy estimands such as ratio of medians, ratio and difference of restricted mean survival times and milestone probabilities. These measures are straightforward, easy to interpret and clinically meaningful. More importantly, they will guarantee agreement between marginal and conditional efficacy and provide cohesive message around efficacy profile of the drug in the presence of subgroups.A step further is the application of Subgroup Mixable Estimation (SME) principle to ensure logical estimates when analyzing real clinical trial data. Detailed guidance is provided for the aforementioned logic-respecting estimands using either parametric, semi-parametric or non-parametric approaches. Simultaneous inference can be provided with proper multiplicity adjustment to facilitate joint decision making with user-friendly apps.