Optimal dynamic treatment regimes :regret-regression method with myopic strategies

Abstract

Optimal dynamic treatment strategies provide a set of decision rules that are based on a patient’s history. We assume there are a sequence of decision times j = 1,2,...,K. At each time a measurement of the state of the patient Sj is obtained and then some action Aj is decided. The aim is to provide rules for action choice so as to maximise some final value Y . In this thesis we will focus on the regret-regression method described by Henderson et al. (2009), and the regret approach to optimal dynamic treatment regimes proposed by Murphy (2003). The regret-regression method combines the regret function with regression modelling and it is suitable for both long term and myopic (short-term) strategies. We begin by describing and demonstrating the current theory using the Murphy and Robins G-estimation techniques. Comparison between the regret-regression method and these two methods is possible and it is found that the regret-regression method provides a better estimation method than Murphy’s and Robins G-estimation. The next approach is to investigate misspecification of the Murphy and regret-regression models. We consider the effect of misspecifying the model that is assumed for the actions, which is required for the Murphy method, and of the model for states, which is required for the regret-regression approach. We also consider robustness of the fitting algorithms to starting values of the parameters. Diagnostic tests are available for model adequacy. An application to anticoagulant data is presented in detail. Myopic one and twostep ahead strategies are studied. Further investigation involves the use of Generalised Estimating Equations (GEEs) and Quadratic Inference Functions (QIF) for estimation. We also assess the robustness of both methods. Finally we consider the influence of individual observations on the parameter estimates.