Statistical Methods for Effect Estimation in Biomedical Research

Practical application of statistics in biomedical research is predicated on the notion that one can readily return valid effect estimates of the health consequences of treatments (exposures) that are being studied. The goal as statisticians should be to provide results that are scientifically useful, to use the available data as efficiently as possible, to avoid unnecessary assumptions, and, if necessary, develop methods that are robust to incorrect assumptions. In this dissertation, I provide methods for effect estimation that meet these goals. I consider three scenarios: (1) clustered binary outcomes; (2) continuous outcomes with a binary treatment; and (3) continuous outcomes with potentially missing continuous exposure. In each of these settings, I discuss the shortfalls of current statistical methods for effect estimation available in the literature and propose new and innovative methods that meet the previously stated goals. The validity of each proposed estimator is theoretically verified using asymptotic arguments, and the finite sample behavior is studied through simulation.