Longitudinal Modeling of Rank-based Global Outcome

Many chronic diseases exhibit multifaceted symptoms that cannot be comprehensively characterized by one outcome. To address this, researchers often adopt a global outcome to combine information from multiple individual outcomes. The global rank-sum facilitates robust integration of multiple outcomes and has been applied in many clinical studies. We consider longitudinal settings and devise a global percentile outcome for depicting patients' time-varying global disease burden. We develop useful regression strategies for the longitudinal global percentile outcome based on a flexible regression framework of the monotonic index model. Posing minimal restrictions, we propose a maximum rank correlation type estimator and show that it entails desirable asymptotic properties. The methods are also extended to accommodate the common missing at random dropout scenarios. We propose a computationally stable and efficient procedure for parameter estimation, as well as a perturbation scheme for consistent variance estimation. Numerical studies show that our method performs well under realistic settings. We apply the proposed method to data from a Parkinson's disease clinical trial to examine risk factors associated with elevated global disease burden and accelerated disease progression.