Bayesian sensitivity analyses for hidden sub‐populations in weighted sampling

Abstract

AbstractIn this paper, we propose several Bayesian model‐based approaches for sensitivity analyses on assessments of population averages and measures of association under complex models. In particular, the proposed methods adjust for a potential impact from a hidden sub‐population when weighted sampling from the non‐hidden sub‐population is possible. Bayesian models are presented for estimating population medical expenditure and health care utilization, as well as measures of association with a binary covariate. Large‐sample limiting versions of the posteriors are obtained for all the models. Using Medical Expenditure Panel Survey data, in which individuals with higher expenditures and more frequent health care visits are more likely to be included, we illustrate how the assumption about the hidden proportion of never‐respondents may impact the final estimates of expenditure, utilization, and measures of association with a binary covariate. The Canadian Journal of Statistics 42: 436–450; 2014 © 2014 Statistical Society of Canada