Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
In chronic diseases such as cancer, physicians make multiple treatment decisions over the course of a patient's disease depending on his/her biological characteristics and accrued information. Essentially, the treatment rule at each decision point is a function which takes the patients' biomarker information, treatment and outcome history available up to that point as an input and returns the treatment choice as an output. In the single treatment setting, the optimal treatment decision can be obtained by a regression model on the mean outcome conditional on treatment and covariates, where the optimal treatment is the one that corresponds to the most desirable mean outcome. However, due to its overdependence on the outcome regression model, this method is heavily prone to model misspecification. Also, given data from an observational study, the usual regression method does not control for the confounding bias induced by the covariates affecting both treatment and outcomes. Causal inference provides a general framework to estimate the treatment causal effect by comparing the potential outcomes under each treatment group. However, for an individual patient, only one potential outcome is observed limiting the direct comparison of potential outcomes at the patient level. A handful number of methods have been proposed in the recent precision medicine literature where they employ semi-parametric estimation methods such as inverse probability weighting (IPWE) to predict the optimal treatment by maximizing a certain predefined value function. However, the likelihood based methods have received little attention in this area, partly due to making model assumptions. To fill this gap, in this dissertation, we develop two fully Bayesian semiparametric likelihood based methods to predict the optimal treatment for a new patient based on the treatment and covariate information from an observed group of patients. In the first approach (BayesG) we extend the idea of parametric g-formula to include a semiparametric mean function within a marginal structural model framework. In the second approach (PSBayes), we connect the treatment assignment mechanism to a missing data framework and build on the Penalized Spline of Propensity Prediction (PSPP) method in the missing data literature to develop a methodology to predict and compare the potential outcomes of the new patient. The posterior predictive potential outcome distribution is then analyzed to predict the optimal treatment. The performance of the proposed methodologies is illustrated in five different simulation studies covering a wide range of scenarios. Overall, the true specifications of inverse probability methods display comparable performance whereas the misspecified models perform poorly. In the additive mean function scenarios, PSBayes outperform all other methods in having higher accuracy in predicting true optimal treatments, whereas the inverse probability based methods show better performance in nonlinear mean function cases. In the presence of non-effect modifiers, the BayesG approach performs better than other methods. We conclude the dissertation by discussing the extension of our proposed methods to a dynamic treatment setting.
Chatterjee, Saptarshi, "Bayesian methods for optimal treatment allocation" (2018). Graduate Research Theses & Dissertations. 1610.
Northern Illinois University
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