Selection bias and multiple inclusion criteria in observational studies

Abstract Objectives Spurious associations between an exposure and outcome not describing the causal estimand of interest can be the result of selection of the study population. Recently, sensitivity parameters and bounds have been proposed for selection bias, along the lines of sensitivity analysis previously proposed for bias due to unmeasured confounding. The basis for the bounds is that the researcher specifies values for sensitivity parameters describing associations under additional identifying assumptions. The sensitivity parameters describe aspects of the joint distribution of the outcome, the selection and a vector of unmeasured variables, for each treatment group respectively. In practice, selection of a study population is often made on the basis of several selection criteria, thereby affecting the proposed bounds. Methods We extend the previously proposed bounds to give additional guidance for practitioners to construct i) the sensitivity parameters for multiple selection variables and ii) an alternative assumption free bound, producing only logically feasible values. As a motivating example we derive the bounds for causal estimands in a study of perinatal risk factors for childhood onset Type 1 Diabetes Mellitus where selection of the study population was made by multiple inclusion criteria. To give further guidance for practitioners, we provide a data learner in R where both the sensitivity parameters and the assumption-free bounds are implemented. Results The assumption-free bounds can be both smaller and larger than the previously proposed bounds and can serve as an indicator of settings when the former bounds do not produce feasible values. The motivating example shows that the assumption-free bounds may not be appropriate when the outcome or treatment is rare. Conclusions Bounds can provide guidance in a sensitivity analysis to assess the magnitude of selection bias. Additional knowledge is used to produce values for sensitivity parameters under multiple selection criteria. The computation of values for the sensitivity parameters is complicated by the multiple inclusion/exclusion criteria, and a data learner in R is provided to facilitate their construction. For comparison and assessment of the feasibility of the bound an assumption free bound is provided using solely underlying assumptions in the framework of potential outcomes.