Optimal dynamic treatment strategies

Abstract

Dynamic treatment regimes are functions of treatment and covariate history which are used to advise on decisions to be taken. Murphy (2003) and Robins (2004) have proposed models and developed semi-parametric methods for making inferences about the optimal dynamic treatment regime in a multi-interval study that provide clear advantages over traditional parametric approaches. The main part of the thesis investigates the estimation of optimal dynamic treatment regimes based on two semi-parametric approaches: G-estimation by James Robins and Iterative Minimization by Susan Murphy. Moodie et al. (2006) show that Murphy's model is a special case of Robins' and that the methods are closely related but not equivalent. In this thesis we rst describe and demonstrate the current theory, then present an alternative method. This method proposes a modelling and estimation strategy which incorporates the regret functions of Murphy (2003) into a regression model for observed responses. Estimation is fast and diagnostics are available, meaning a variety of candidate models can be compared. The method is illustrated using two simulation scenarios taken from the literature and using a two-armed bandit problem. An application on determination of optimal anticoagulation treatment regimes is presented in detail.