Estimating causal contrasts involving intermediate variables in the presence of selection bias.

An important goal across the biomedical and social sciences is the quantification of the role of intermediate factors in explaining how an exposure exerts an effect on an outcome. Selection bias has the potential to severely undermine the validity of inferences on direct and indirect causal effects in observational as well as in randomized studies. The phenomenon of selection may arise through several mechanisms, and we here focus on instances of missing data. We study the sign and magnitude of selection bias in the estimates of direct and indirect effects when data on any of the factors involved in the analysis is either missing at random or not missing at random. Under some simplifying assumptions, the bias formulae can lead to nonparametric sensitivity analyses. These sensitivity analyses can be applied to causal effects on the risk difference and risk-ratio scales irrespectively of the estimation approach employed. To incorporate parametric assumptions, we also develop a sensitivity analysis for selection bias in mediation analysis in the spirit of the expectation-maximization algorithm. The approaches are applied to data from a health disparities study investigating the role of stage at diagnosis on racial disparities in colorectal cancer survival.