Evidence Factors for Observational Studies: Design, Analysis and Computation

This thesis includes five chapters on evidence factors analysis of causal effect in various observational study settings. Each of these chapters can be read independently without knowledge of the content of any of the other chapters. Evidence factors allow for two independent analyses to be constructed from the same data set. When combining the evidence factors, the type-I error rate must be controlled to obtain valid inference. A powerful method is developed for controlling the familywise error rate for sensitivity analyses to unmeasured confounding with evidence factors. It is shown that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for either evidence factor alone. The popular strategy of matching, for controlling the observed covariates, before inferring about the treatment effect, requires solving an optimization problem. This problem can be solved in polynomial time. In an evidence factors analysis we must consider multiple comparisons, thus the matching problem is often of matching at least three groups. This slightly different problem is much more difficult to solve. The third chapter proposes an approximation algorithm to solve this (and more practical versions of this) problem. We prove that the proposed algorithm provides a solution fast, that is provably not a lot further than the optimal solution that is difficult calculate. Two chapters that follow show the applicability of evidence factors analysis in more complicated study designs. The first of these two chapters considers a case-control study with multiple case definitions and the latter one considers studies with instrumental variables, where the instrument(s) may become invalid. The final chapter of the thesis develops a frequentist method for quantification of the degree of corroboration of causal hypothesis using the tool of evidence factors