Semiparametric Estimation in Observational Studies and Randomized Trials
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Researchers often seek robust inference for a parameter through semiparametric estimation. Semiparametric estimation is useful, for example, for survival analysis, for estimating growth parameters in longitudinal studies, and for estimating quantities under missing data, including treatment effects based on potential outcomes. In this dissertation we study semiparametric estimation from two design perspectives: observational studies and randomized trials. Traditional semiparametric estimation methods requires theoretical derivation of the efficient influence function, which can be a challenging and time-consuming task. To address this difficulty, we propose a new method, called ``deductive estimation'', for constructing semiparametric estimators for observational studies. The method is computerizable, meaning that it does not need theoretically deriving the functional form of the efficient influence function, and is guaranteed to produce semiparametric, locally efficient estimators even for complex parameters in nonparametric models. We apply the method to two designs: the two-phase design, and the double-sampling design. We demonstrate the method with a study on asthma care satisfaction and a study evaluating an HIV treatment in East Africa. In randomized trials, adjusting for baseline variables and short-term outcomes can lead to increased power and reduced sample size. We investigate the strengths and limitations of a semiparametric, locally efficient estimator compared to the standard unadjusted estimator in randomized trials context. We derive formulas for the precision gain from such covariate adjustment using semiparametric estimators for the average treatment effect, and give new results on what conditions lead to substantial power gains and sample size reductions. The theory is supported by two simulation studies: simulated group sequential trials based on data from the MISTIE Phase II trial, which is a trial of a new surgical intervention for stroke, and simulated adaptive enrichment trials based on data from the Alzheimer’s Disease Neuroimaging Initiative cohort study. Our results can be used in trial planning to predict the potential precision gain from covariate adjustment, which will translate to power gain or sample size reduction.