A new framework for estimation and inference of optimal dynamic treatment regimes

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The proposed research endeavours to develop a new framework for estimation and inference of dynamic treatment regimes (DTRs), a modern implementation of experimental design, relevant to longitudinally recorded data arising from observational or randomized studies. This topic involves the statistical study of decision rules characterized by taking time-dependent characteristics as inputs such as a symptom score, and returning a treatment to be taken, such as initiation or augmentation of a therapy. Estimation and inference for optimal dynamic treatment rules are complicated by the potentially high-dimensionality of the problem, the presence of time-varying confounding, and the fact that regularity conditions often do not hold so that non-standard asymptotics are required. The proposed approach stems from an important insight that a particular form of weighted learning can be used to estimate decision rule parameters. The development of a complete framework for estimation and inference will include non-regular asymptotic theory, computational elements, and tools for trial design, including sample size and power formulae and programs. The impact of this work will be to change the manner in which researchers carry out estimation of dynamic regime parameters, and facilitate the use of a wider variety of outcomes, including discrete utilities, by providing a simple, weighed regression framework for estimation. The work will also provide important insights into the scope and nature of the non-regularity of the estimators, and consequent inferential challenges. More generally, the work will contribute to the important and growing literature on asymptotics at the boundary of the parameter space, which will be of use to a wider statistical audience.