Weighted trajectory analysis and application to clinical outcome assessment

The Kaplan-Meier estimator (KM) is widely used in medical research to estimate the survival function from lifetime data. KM is a powerful tool to evaluate clinical trials due to simple computational requirements, a logrank hypothesis test, and the ability to censor patients. However, KM has several constraints and fails to generalize to ordinal variables of interest such as toxicity and ECOG performance. We devised Weighted Trajectory Analysis (WTA) to combine the advantages of KM with the ability to 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 demonstrate the functionality of WTA through 1000-fold clinical trial simulations of unique stochastic models of chemotherapy toxicity and schizophrenia progression. At several increments of sample size and hazard ratio, we compare the performance of WTA to both KM and Generalized Estimating Equations (GEE). WTA generally required half the sample size to achieve comparable power to KM; advantages over GEE include its robust non-parametric approach and summary plot. We also apply 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 demonstrates that using traditional methods such as percent incidence and KM 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.