The thesis is divided in three sections of interconnected topics. Motivated by applications from precision medicine, we consider the problem of estimating an optimal treatment regime (or individual optimal decision rule) based on right-censored survival data. We consider a non-parametric approach that maximizes the expected mean restricted survival time of the potential outcome distribution. Comparing with existing methods, our approach does not need to assume the decision rule belongs to a restricted class (e.g., class of index rules) and can accommodate high-dimensional covariates. We investigate the theory of the estimated optimal treatment regime. Monte Carlo studies and a real data example are used to demonstrate the performance of our proposed method. Random forests are widely used today for various purposes such as regression classification, survival analysis however its theoretical properties are not yet explored completely. We propose a quantile random forest estimator which considers sub-sampling instead of complete bootstrap samples as in Meinshausen. We study the point wise asymptotics of quantile random forest estimator proposed by rendering it in the framework of U-statistics. We prove point-wise weak convergence to normality and also propose a consistent estimator of the variance. We further explore the asymptotic behavior of the proposed estimator via a simulation study. Measuring the efficacy of a treatment or policy can involve data heterogeneity. In such cases, the entire conditional distributional impact of the treatment is important rather than just a discrete metric such as the average treatment effect. Quantiles inform more about the distribution than an average and multiple quantiles can be used together to get an idea about the entire distribution. In the context of survival analysis with censored data, we propose a quantile regression model estimated using survival random forest. We further extend this to estimate quantile treatment effects under censoring. We show the efficacy of the proposed method via simulations. We also demonstrate using this method and interpreting quantile effect by analysing a colon cancer dataset.
University of Minnesota Ph.D. dissertation.June 2021. Major: Statistics. Advisor: Lan Wang. 1 computer file (PDF); xi, 129 pages.
Optimal Treatment Regimes Estimation with Censored Data and Related Topics.
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