Response to: ‘Methodological considerations in the analysis of time-to-event outcomes with MAIHDA by Bashir and Al-Kassab-Cordova

We thank Bashir and Al-kassab-Córdova for their thoughtful letter1 on our recent extension of multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) to time-to-event outcomes.2 Their discussion highlights important methodological considerations: scale dependence, informative censoring and competing risks.

First, we agree that interaction patterns in survival analysis are scale-dependent. As noted, the absence of hazard-scale interaction may appear as interaction on the survival probability scale due to the non-linear relationship between hazards and survival probabilities.3 In this regard, reporting interaction on multiple scales as recommended in epidemiology is also valuable for survival analysis. In our study, we evaluated several models—including accelerated failure time, parametric proportional hazards and Cox models—to examine this dependence. Testing interaction on the survival probability scale represents a welcome extension, though practical implementation will require accessible software tools.

Second, the authors correctly note that differential loss to follow-up across socially stratified groups…

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