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Abstract:
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Causal inference from time-series data is a crucial problem in many fields. In particular, it allows tailoring interventions over time to evolving needs of a unit, painting a granular picture of the current status. In medicine, wealth of information available in time-series data hints at an exciting opportunity to explore the very definition of precision medicine- studies that focus on a single person. We present targeted maximum likelihood estimation (TMLE) of data-dependent and marginal causal effects based on observing a single time-series. A key feature of the estimation problem is that the statistical inference is based on asymptotics in time. We focus largely on the data-dependent causal effects that can be estimated in a double robust manner, therefore fully utilizing the sequential randomization. We propose a TMLE of a general class of averages of causal parameters, and establish asymptotic consistency and normality results. Finally, we demonstrate our general framework for the data-adaptive setting with a number of examples and simulations, including a sequentially adaptive design that learns the optimal treatment rule for the unit over time.
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