Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models

Abstract

In both observational and randomized studies, subjects commonly drop out of the study (i.e., become censored) before end of follow-up. If, conditional on the history of the observed data up to t, the hazard of dropping out of the study (i.e., censoring) at time t does not depend on the possibly unobserved data subsequent to t, we say drop-out is ignorable or explainable (Rubin, 1976). On the other hand, if the hazard of drop-out depends on the possibly unobserved future, we say drop-out is non-ignorable or, equivalently, that there is selection bias on unobservables. Neither the existence of selection bias on unobservables nor its magnitude is identifiable from the joint distribution of the observables. In view of this fact, we argue that the data analyst should conduct a "sensitivity analysis" to quantify how one's inference concerning an outcome of interest varies as a function of the magnitude of non-identifiable selection bias.