Abstract

Selection bias is a systematic error that can occur when subjects are included or excluded in the analysis based on some selection criteria for the study population. This type of bias can jeopardize the validity of the study, not only in the case of generalization to the total population but also for the selected study population. Thus, methods for assessing the effect of selection bias are desired. One method of estimating the effect of selection bias is through sensitivity analysis, and one type of sensitivity analysis is bounding the bias.

In this work, we investigate a previously proposed bound, referred to as the SV bound, that is based on assumptions of values of sensitivity parameters. Furthermore, we derive feasible regions for the sensitivity parameters as well as conditions for the SV bound to be sharp, where sharp means that the bias can be equal to the value of the bound. It can sometimes be difficult to specify the unknown sensitivity parameters and thus, as an alternative, we present a second bound that is based solely on the observed data and is therefore referred to as the assumption-free (AF) bound. Furthermore, we develop an R package for calculating the SV and AF bounds. The theoretical properties of the bounds as well as the R package are illustrated with a simulated dataset that emulates a study on the effect of the zika virus on microcephaly in Brazil. The methods, code, and results developed in this work are of interest to researchers in observational studies.