Stina Zetterström: Bounds for selection bias in causal inference

Abstract

This thesis consists of four papers that study and propose several bounds of causal estimands under selection bias.

Paper I investigates previously reported bounds. Importantly, we study the impact on the bounds when additional selections are made. This study highlights practical challenges when using the reported bounds. Additionally, Paper I also presents assumption-free bounds that are based on the observed data and the standard assumptions. These bounds are in many cases easier to use than the previously reported bounds, although they are sometimes conservative.

Paper II proposes two alternative bounds for selection bias. These bounds utilize the observed data but requires the specification of unknown sensitivity parameters and additional assumptions. The bounds equal the corresponding assumption-free bound in Paper I when the sensitivity parameters are set to their most conservative values. For other choices of the sensitivity parameters, these bounds are tighter than the assumption-free bound.

Paper III summarizes the results from Paper I and II in the R package SelectionBias to make the bounds easily accessible for practitioners, and compares the R package SelectionBias to existing software for calculating some of the bounds.

Paper IV investigates properties of previously reported bounds. First, variation independence of the sensitivity parameters is shown, implying that the sensitivity parameters can be considered separately. Second, it is shown that the considered bounds are sharp under certain conditions, meaning that the bias can be as large as the bounds. Lastly, improved versions of the bounds in the non-sharp regions are presented.

The bounds discussed in this thesis are valid for causal effects measured on a difference or ratio scale. The bounds can be used in different situations depending on the knowledge and/or data available. The presented R package is intended to make the research accessible to practitioners.