Estimating Treatment Effects and Identifying Optimal Treatment Regimes to Prolong Patient Survival.

Abstract

Motivated by an observational prostate cancer recurrence study, we investigate the effect of treatment on survival outcome. For studies such as these, it is important to properly handle the confounding effects, especially from longitudinal covariates. In addition, baseline covariates may also reflect the heterogeneity of the population in responding to the treatment. It is possible to recognize these differences and customize the treatment strategy accordingly.

In the first project, we formulate a generalized accelerated failure time (AFT) model to describe the treatment effect and the model includes a longitudinal covariate as a functional predictor, whose coefficient is a time-varying nonparametric function. We propose a spline-based sieve estimation for the time-varying coefficient of the functional predictor, and maximize the likelihood in the sieve space where we approximate the functional predictor and nonparametric coefficient using B-spline basis. Asymptotic properties of the proposed estimator are developed, and its performance is evaluated through simulation studies.

We further consider the interaction between treatment and other covariates, and explore the heterogeneity of the treatment effect and approaches to personalize the treatment assignment to optimize the survival outcome. In the second project, using the causal inference framework, we consider the counterfactual outcome as if every patient follows a given treatment regimen and develop a method to identify the optimal dynamic treatment regime from observational longitudinal data. We propose to use Random Forest to model the regime adherence of each subject, and use inverse probability weights to adjust for non-adherence to obtain the regime specific survival distribution. We study the theoretical properties of the proposed estimators, and its finite sample performance through simulation and real data analysis.

In the third project, we consider a more general class of candidate regimes through flexible models of the outcomes. We propose to use Random Survival Forest plus an inverse probability weighted bootstrap to estimate the causal outcome while marginalizing over the unavailable covariates. By comparing the restricted mean survival times, the optimal regime can be estimated for the target population. The performance of the proposed method is assessed through simulation studies.