Personalized Dynamic Treatment Regimes in Continuous Time: A Bayesian Approach for Optimizing Clinical Decisions with Timing

Accurate models of clinical actions and their impacts on disease progression are critical for estimating personalized optimal dynamic treatment regimes (DTRs) in medical/health research, especially in managing chronic conditions. Traditional statistical methods for DTRs usually focus on estimating the optimal treatment or dosage at each given medical intervention, but overlook the important question of "when this intervention should happen." We fill this gap by developing a two-step Bayesian approach to optimize clinical decisions with timing. In the first step, we build a generative model for a sequence of medical interventions-which are discrete events in continuous time-with a marked temporal point process (MTPP) where the mark is the assigned treatment or dosage. Then this clinical action model is embedded into a Bayesian joint framework where the other components model clinical observations including longitudinal medical measurements and time-to-event data conditional on treatment histories. In the second step, we propose a policy gradient method to learn the personalized optimal clinical decision that maximizes the patient survival by interacting the MTPP with the model on clinical observations while accounting for uncertainties in clinical observations learned from the posterior inference of the Bayesian joint model in the first step. A signature application of the proposed approach is to schedule follow-up visitations and assign a dosage at each visitation for patients after kidney transplantation. We evaluate our approach with comparison to alternative methods on both simulated and real-world datasets. In our experiments, the personalized decisions made by the proposed method are clinically useful: they are interpretable and successfully help improve patient survival

Essays in Financial and Insurance Mathematics.

This dissertation consists of the following three parts: (i) We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset. The price of the risky asset is assumed to follow a diffusion with stochastic volatility. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of outliving the wealth. Techniques from stochastic optimal control are used. (ii) We extend the Heston stochastic volatility model to include state-dependent jumps in the price and the volatility, and develop a method for the exact simulation of this model. The jumps arrive with a stochastic intensity that may depend on time, price, volatility and jump counts. The jumps may have an impact on the price or the volatility, or both. The random jump size may depend on the price and volatility. The exact simulation method is based on projection and point process filtering arguments. Numerical experiments illustrate the features of the exact method. (iii) We study the properties of sovereign credit risk using Credit Default Swap (CDS) spreads for U.S. and major sovereign countries. We develop a regime-switching two-factor model that allows for both global-systemic and sovereign-specific credit shocks, and use maximum likelihood estimation to calibrate model parameters to weekly CDS data. The preliminary results suggest that there is heterogeneity across different countries with respect to their sensitivity to system risk. Furthermore, the high-volatility and low-volatility regimes behave differently with asymmetric regime-shift probabilities.Ph.D.Applied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91381/1/xyhu_1.pd