Dynamic treatment regimens (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. The ultimate goal is to accommodate heterogeneity among patients and find the DTR which will produce the best long term outcome. The patients receive treatments are often at multiple decision times. The effects of the covariates are often complex and the dimension of covariates are often very high. The broad, long-term objectives of this project are to develop statistical learning methodologies for optimal, personalized and single-stage or dynamic treatment regimens. Specifically, this project aims 1) to develop flexible semiparametric modeling tailored in single-stage or dynamic treatment regimens; 2) to develop a penalized Q-learning and valid statistical inference for estimating optimal dynamic regimens with censored outcome; 3) to develop effective variable selection strategies which can simplify and improve implementation and reproducibility of personalized treatment regimens. For all the goals, the desired asymptotic properties will be established rigorously and suitable numerical algorithms will be provided.
The outlined research project will bring more insights into multi-stage, high-dimensional statistical learning and will benefit future studies in this area. This study will develop flexible models and Q-learning methods in estimating personalized treatment regimens. A successful completion of this research will not only fill important gaps in statistical theory, but will also yield new tools for applied statisticians and other scientists. This project will foster more intensive collaborations among investigators from the Department of Statistics, the Department of Mathematics and the Health Systems Research Group in the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. The proposed study will promote teaching, training and learning at North Carolina State University. Research conducted in this study will help develop advanced graduate courses in statistical learning and semiparametric methodology. It will create challenging statistical projects for graduate students. The results will be disseminated broadly through presentations at seminars, conferences and the internet, which may promote interdisciplinary research among scientists from diverse fields.