Nonparametric Tests for Treatment Effect Leveraging Information on Recurrent and Terminal Events and Physiological Decline

ABSTRACT When evaluating treatment effects in progressive disease clinical trials, analyses of time to recurrent or terminal events largely ignore (or separately analyze) functional measures of disease progression over time. For instance, in pulmonary research settings, treatment may impact recurrent times‐to‐hospitalization, mortality and pulmonary function during follow‐up. Ignoring longitudinal pulmonary function in two‐sample tests for recurrent and terminal events is not only a potential waste of statistical information that could help power the study, but also misses the daily impact of treatment on the ability to breathe that comprises the majority of the follow‐up period. In this manuscript, we develop a two‐sample testing procedure that analyzes recurrent and terminal events, also taking into account pulmonary health over time as a health history state with a corresponding utility function. Our proposed test compares the longitudinal profiles of ‐restricted, utility‐adjusted event‐free times across multiple follow‐up windows. Asymptotic limiting behavior of our test statistic is given along with finite sample formulas and graphical summaries convenient for use in data analysis. Simulations demonstrate good performance of the testing procedure. Simulated power results give insight into strengths and limitations of incorporating health history utilities into the analysis with gains demonstrated when treatment improves both event rates and health history. We further apply this method to the Azithromycin for Prevention of COPD Exacerbation Trial to show its practical use.