Weighted Trajectory Analysis and Application to Clinical Outcome Assessment

Abstract

The Kaplan–Meier (KM) estimator is widely used in medical research to estimate the survival function from lifetime data. KM estimation is a powerful tool to evaluate clinical trials due to simple computational requirements, its use of a logrank hypothesis test, and the ability to censor patients. However, KM estimation has several constraints and fails to generalize to ordinal variables of clinical interest, such as toxicity and ECOG performance. We devised weighted trajectory analysis (WTA) to combine the advantages of KM estimation with the ability to visualize and compare treatment groups for ordinal variables and fluctuating outcomes. To assess statistical significance, we developed a new hypothesis test analogous to the logrank test. We demonstrated the functionality of WTA through 1000-fold clinical trial simulations of unique stochastic models of chemotherapy toxicity and schizophrenia disease course. With increments in sample size and hazard ratio, we compared the performance of WTA to KM estimation and the generalized estimating equation (GEE). WTA generally required half the sample size to achieve comparable power to KM estimation; advantages over the GEE included its robust nonparametric approach and summary plot. We also applied WTA to real clinical data: the toxicity outcomes of melanoma patients receiving immunotherapy and the disease progression of patients with metastatic breast cancer receiving ramucirumab. The application of WTA demonstrated that using traditional methods such as KM estimation can lead to both type I and II errors by failing to model illness trajectory. This article outlines a novel method for clinical outcome assessment that extends the advantages of Kaplan–Meier estimates to ordinal outcome variables.