A non-probability sampling mechanism 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 a recently published statistic, the so-called 'standardized measure of unadjusted bias', which explicitly quantifies the extent of bias under the assumption that a specified amount of non-ignorable selection exists. Our findings suggest that this new sensitivity diagnostic is considerably 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.
Applied Statistics | Design of Experiments and Sample Surveys
Boonstra, Philip S.; Little, Roderick JA; West, Brady T.; Andridge, Rebecca R.; and Alvarado-Leiton, Fernanda, "A simulation study of diagnostics for bias in non-probability samples" (March 2019). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 125.