Title: Methods to Control for Overt and Hidden Biases in Comparative Studies
Co-Chair: Associate Professor Ben Hansen
Committee Members: Professor Robert Keener, Professor Edward Rothman, Associate Professor Michael Elliott (Biostatistics)
Abstract: When the goal of a comparative study is to ascertain the effect of some treatment condition, problems arise when it is not randomly assigned to units. In the absence of random assignment, units compared cannot be expected to be similar in terms of pretreatment covariates, yet the validity of resulting causal inferences relies on this resemblance. This thesis develops techniques that build upon existing methods to analyze observational studies, lifting certain of their limitations. To reduce bias in causal estimates from comparative studies, analysis procedures should ensure the likeness of the distributions of measured confounders across comparison groups. Methods such as matching or post-stratifying on the measured covariates group similar units, and analysis is performed within subgroups. We apply this bias-reducing idea to the Peters- Belson method, which estimates treatment effects in an experiment with regression models. By incorporating subgroups to restrict comparisons to groups of units with similar covariate distributions, bias induced by the application of the method to an observational study can be reduced. When analyzing observational data, units are commonly organized by similar propensity scores. In practice, the propensity score is estimated by a parametric model, and the literature is not unified regarding the selection of the best model. In line with one thread of the literature, we develop a method that improves the propensity score model by focusing it on covariates most relevant to an outcome of interest through the creation of what is called a multidimensional prognostic score. By improving the propensity score model, units compared are more similar, and resulting analyses have greater validity. While adjusting for measured confounders can sometimes suffice, additional methods to analyze comparative studies aim to quantify the potential impact of unmeasured confounders on the effect estimate. These methods, known broadly as sensitivity analyses, have roots in early literature that considered the addition or removal of a confounder. We introduce a new method of sensitivity analysis for a linear regression model that is unique in its simplicity and ability to assess the impact of unmeasured confounders on the entire confidence interval, rather than only the point estimate.