An Interval Estimation Approach to Selection Bias in Observational Studies
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A persistent challenge in observational studies is that non-random participation in study samples can result in biased estimates of parameters of interest. To address this problem, we present a flexible interval estimator for a class of models encompassing population means, risk ratios, OLS and IV estimands which makes minimal assumptions about the selection mechanism. We derive valid confidence intervals and hypothesis tests for this estimator. In addition, we demonstrate how to tighten the bounds using a suite of population-level information commonly available to researchers, including conditional and unconditional survey response rates, covariate means and knowledge of the direction in which certain variables influence selection. We illustrate the performance of this method in practice using a realistic simulation and an applied example estimating the effect of education on income in UK Biobank.
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