"Days alive and at home" (DAH) is a recent patient-centered outcome measure for perioperative trials, defined as the number of days a patient spends at home during the follow-up period. DAH typically follows a zero-inflated, left-skewed, bi-modal distribution. Other increasingly used complex endpoints, such as days alive without a ventilator, share these statistical features arising from combining survival with another clinically relevant count outcome into a single, comprehensive measure. A key challenge for DAH and similar endpoints is the lack of a readily identifiable distributional form, which complicates the statistical design of trials using it as the primary endpoint, particularly regarding the robustness of sample size calculations and final analyses where the central limit theorem might not be suitable. Using 200 data points from the interim data of the NOTACS trial (ISRCTN14092678), whose primary endpoint was DAH, we developed a novel 'Divide & Conquer' model that breaks DAH into distinct parts modeled individually. To our knowledge, such a model has not been used before for DAH. We demonstrate that our approach significantly improves model fit compared to existing alternatives, enabling more suitable DAH data generation that can be used for simulation-based sample size calculations and evaluation of operating characteristics of the statistical test(s). Beyond NOTACS, our work has large potential to inform the design and analysis of other trials using DAH or similar complex endpoints.

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