A simulation study of diagnostics for selection bias

A non-probability sampling mechanism arising from non-response or non-selection is likely to bias estimates of parameters with respect to a target population of interest. This bias poses a unique challenge when selection is 'non-ignorable', i.e. dependent upon the unobserved outcome of interest, since it is then undetectable and thus cannot be ameliorated. We extend a simulation study by Nishimura et al. [International Statistical Review, 84, 43-62 (2016)], adding two recently published statistics: the so-called 'standardized measure of unadjusted bias (SMUB)' and 'standardized measure of adjusted bias (SMAB)', which explicitly quantify the extent of bias (in the case of SMUB) or non-ignorable bias (in the case of SMAB) under the assumption that a specified amount of non-ignorable selection exists. Our findings suggest that this new sensitivity diagnostic is more correlated with, and more predictive of, the true, unknown extent of selection bias than other diagnostics, even when the underlying assumed level of non-ignorability is incorrect.