Methodological challenges for the estimation of optimal dynamic treatment regimes from observational studies

This thesis contributes to methodology for estimating the optimal dynamic treatment regime (DTR) from longitudinal data collected in an observational study. In Chapter 1, we discuss assumptions under which it is possible to use observational data to estimate the optimal DTR in a class of prespecified logistically feasible dynamic regimes. We introduce a new class of structural model, the so called dynamic marginal structural models (MSMs), which are specially suitable for estimating the optimal regime in a smooth class because they allow borrowing of information across DTR thought to have similar effects. We derive a class of consistent and asymptotically normal estimators of the optimal DTR and derive a locally efficient estimator in the class. Chapter 1 proposals assume that the frequency of clinic visits is the same for all patients. However, often in the management of chronic diseases, doctors indicate the next visit date according to medical guidelines and patients return earlier if they need to do so. At every visit, whether planned or not, treatment decisions are made. It is of public health interest to estimate the effect of DTRs that are to be implemented in settings in which: (i) doctors indicate next visit date using medical guidelines and these indications may depend on the patient health status, (ii) patients may come to the clinic earlier than the indicated return date and (iii) doctors have the opportunity to intervene and alter the treatment each time the patient comes to the clinic. In Chapter 2 we derive an extension of the MSM model of Murphy, van der Laan and Robins (2001), which allows estimation from observational data of the effects of DTRs that are to be implemented in settings in which (i)-(iii) hold. We derive consistent and asymptotically normal estimators of the model parameters. In Chapter 3 we apply the methodology proposed in Chapter 1 and 2 to the French Hospital Database on HIV cohort. The goal is to estimate the optimal CD4 cell count at which to start antiretroviral therapy in HIV patients. We discuss a number of difficult practical problems for this specific problem and we argue that available observational data may not satisfy the requirements for answering the "When to start" question.