Counting Process Based Dimension Reduction Methods for Censored Outcomes

We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. The proposed method addresses two fundamental limitations of existing approaches. First, using the counting process formulation, it does not require any estimation of the censoring distribution to compensate the bias in estimating the dimension reduction subspace. Second, the nonparametric part in the estimating equations is adaptive to the structural dimension, hence the approach circumvents the curse of dimensionality. Asymptotic normality is established for the obtained estimators. We further propose a computationally efficient approach that simplifies the estimation equation formulations and requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that our new approaches exhibit significantly improved performance for estimating the true dimension reduction subspace. We further conduct a real data analysis on a skin cutaneous melanoma dataset from The Cancer Genome Atlas. The proposed method is implemented in the R package "orthoDr".Comment: First versio

Tree-based methods for survival analysis and high-dimensional data

Machine learning techniques have garnered significant popularity due to their capacity to handle high dimensional data. Tree-based methods are among the most popular machine learning approaches. My dissertation aims on improving existing tree-based methods and developing statistical framework for understanding the proposed methods. It contains three topics: recursively imputed survival tree, reinforcement learning trees and reinforcement learning trees for right censored survival data. A central idea of my dissertation is focused on increasing the chance of using signaled variables as splitting rule during the tree construction while not losing the randomness/diversity, hence a more accurate model can be built. However, different methods achieve this by using different approaches. Recursively imputed survival tree recursively impute censored observations and refit the survival tree model. This approach allows better use of the censored observations during the tree construction, it also changes the dynamic of splitting rule selections during the tree construction so that signaled variables can be emphasized more in the refitted model. Reinforcement learning trees takes a direct approach to emphasize signaled variables in the tree construction. An embedded model is fitted at each internal node while searching for splitting rules. The variable with the largest variable importance measure is used as the splitting variable. A new theoretical framework is proposed to show consistency and convergence rate of this new approach. In the third topic, we further extend reinforcement learning trees to right censored survival data. Brier score is utilized to calculate the variable importance measures. We also show a desirable property of the proposed method that can help correct the bias of variable importance measures when correlated variables are present in the model.Doctor of Philosoph

Quasi-optimal Learning with Continuous Treatments

Many real-world applications of reinforcement learning (RL) require making decisions in continuous action environments. In particular, determining the optimal dose level plays a vital role in developing medical treatment regimes. One challenge in adapting existing RL algorithms to medical applications, however, is that the popular infinite support stochastic policies, e.g., Gaussian policy, may assign riskily high dosages and harm patients seriously. Hence, it is important to induce a policy class whose support only contains near-optimal actions, and shrink the action-searching area for effectiveness and reliability. To achieve this, we develop a novel \emph{quasi-optimal learning algorithm}, which can be easily optimized in off-policy settings with guaranteed convergence under general function approximations. Theoretically, we analyze the consistency, sample complexity, adaptability, and convergence of the proposed algorithm. We evaluate our algorithm with comprehensive simulated experiments and a dose suggestion real application to Ohio Type 1 diabetes dataset.Comment: The first two authors contributed equally to this wor

Policy Learning for Individualized Treatment Regimes on Infinite Time Horizon

With the recent advancements of technology in facilitating real-time monitoring and data collection, "just-in-time" interventions can be delivered via mobile devices to achieve both real-time and long-term management and control. Reinforcement learning formalizes such mobile interventions as a sequence of decision rules and assigns treatment arms based on the user's status at each decision point. In practice, real applications concern a large number of decision points beyond the time horizon of the currently collected data. This usually refers to reinforcement learning in the infinite horizon setting, which becomes much more challenging. This article provides a selective overview of some statistical methodologies on this topic. We discuss their modeling framework, generalizability, and interpretability and provide some use case examples. Some future research directions are discussed in the end

Recursively Imputed Survival Trees

We propose recursively imputed survival tree (RIST) regression for right-censored data. This new nonparametric regression procedure uses a novel recursive imputation approach combined with extremely randomized trees that allows significantly better use of censored data than previous tree based methods, yielding improved model fit and reduced prediction error. The proposed method can also be viewed as a type of Monte Carlo EM algorithm which generates extra diversity in the tree-based fitting process. Simulation studies and data analyses demonstrate the superior performance of RIST compared to previous methods

Stage-Aware Learning for Dynamic Treatments

Recent advances in dynamic treatment regimes (DTRs) provide powerful optimal treatment searching algorithms, which are tailored to individuals' specific needs and able to maximize their expected clinical benefits. However, existing algorithms could suffer from insufficient sample size under optimal treatments, especially for chronic diseases involving long stages of decision-making. To address these challenges, we propose a novel individualized learning method which estimates the DTR with a focus on prioritizing alignment between the observed treatment trajectory and the one obtained by the optimal regime across decision stages. By relaxing the restriction that the observed trajectory must be fully aligned with the optimal treatments, our approach substantially improves the sample efficiency and stability of inverse probability weighted based methods. In particular, the proposed learning scheme builds a more general framework which includes the popular outcome weighted learning framework as a special case of ours. Moreover, we introduce the notion of stage importance scores along with an attention mechanism to explicitly account for heterogeneity among decision stages. We establish the theoretical properties of the proposed approach, including the Fisher consistency and finite-sample performance bound. Empirically, we evaluate the proposed method in extensive simulated environments and a real case study for COVID-19 pandemic