Predict Risk of Relapse for Patients with Multiple Stages of Treatment of Depression

Depression is a serious mood disorder afflicting millions of people around the globe. Medications of different types and with different effects on neural activity have been developed for its treatments during the past few decades. Due to the heterogeneity of the disorder, many patients cannot achieve symptomatic remission from a single clinical trial. Instead they need multiple clinical trials to achieve remission, resulting in a multiple stage treatment pattern. Furthermore those who indeed achieve symptom remission are still faced with substantial risk of relapse. One promising approach to predicting the risk of relapse is censored regression. Traditional censored regression typically applies only to situations in which the exact time of event of interest is known. However, follow-up studies that track the patients' relapse status can only provide an interval of time during which relapse occurs. The exact time of relapse is usually unknown. In this paper, we present a censored regression approach with a truncated $l_1$ loss function that can handle the uncertainty of relapse time. Based on this general loss function, we develop a gradient boosting algorithm and a stochastic dual coordinate ascent algorithm when the hypothesis in the loss function is represented as (1) an ensemble of decision trees and (2) a linear combination of covariates, respectively. As an extension of our linear model, a multi-stage linear approach is further proposed to harness the data collected from multiple stages of treatment. We evaluate the proposed algorithms using a real-world clinical trial dataset. Results show that our methods outperform the well-known Cox proportional hazard model. In addition, the risk factors identified by our multi-stage linear model not only corroborate findings from recent research but also yield some new insights into how to develop effective measures for prevention of relapse among patients after their initial remission from the acute treatment stage.