Year: 2019
Type: dissertation
Abstract: Coarsened data, including a broad class of incomplete data structures, are ubiquitous in biomedical research. Various methods have been proposed when data are coarsened at random, where it is often required to specify working models for the coarsening mechanism, or the conditional outcome regression, or both. However, some practical issues emerge: for example, it is not unusual to have multiple working models that all fit the observed data reasonably well, or working model specification can be challenging in the presence of a large number of variables. In this dissertation, we propose new flexible statistical methods to tackle the challenges mentioned above with two types of coarsened data: missing data and counterfactual data when optimizing the dynamic treatment regime (DTR), which is a sequence of decision rules that adapt treatment to the time-varying medical history of each individual. In the first project, we develop a multiply robust kernel estimating equations (MRKEEs) method for nonparametric regression that can accommodate multiple working models for either the missing data mechanism or the outcome regression or both. The resulting estimator is consistent if any one of those models is correctly specified. When including correctly specified models for both, the proposed estimator achieves the optimal efficiency within the class of augmented inverse probability weighted (AIPW) kernel estimators. In the second project, we develop a stochastic tree-based reinforcement learning method, ST-RL, for estimating the optimal DTR in a multi-stage multi-treatment setting with data from either randomized trials or observational studies. At each stage, ST-RL constructs a decision tree by first modeling the mean counterfactual outcomes via Bayesian nonparametric regression models, and then stochastically searching for the optimal tree-structured regime using a Markov Chain Monte Carlo algorithm. We implement the proposed method in a backward inductive fashion through multiple decision stages. Compared to existing methods, ST-RL delivers the optimal DTR with better interpretability and does not require explicit working model specifications. Besides, ST-RL demonstrates stable and outstanding performance with moderately high dimensional data. In the third project, we propose a variable selection technique to screen potential tailoring variables for estimating the optimal DTR with large observational data. The proposed method is based on nonparametric sparse additive models and therefore enjoys superior flexibility. Also, it allows treatments with more than two levels, as well as continuous doses. In particular, the selection procedure enforces strong heredity constraint, i.e., the interactions can only be included when both of its main effects have already been selected.
Author: Yilun Sun
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2995698406