Using Auxiliary Sample Frame Information for Optimum Sampling of Rare Populations

We investigate disproportionate stratified sampling as a possibly efficient method of surveying members of a rare domain in circumstances in which there is no acceptable list of members. In this work, we assume that information is available at the sampling stage to stratify the general-population sampling frame into high- and low-density strata. Under a fixed constraint on the variance of the estimator of the domain mean, we make the optimum allocation of sample size to the several strata and show that, in comparison to proportional allocation, the optimum allocation requires (a) a smaller total sample size but (b) a larger number of interviews of members of the rare domain. We illustrate the methods using information about American consumers maintained by market-research companies. Such companies are able to develop lists of households that are thought to have a defined attribute of interest, such as at least one resident in a user-specified age range. The lists are imperfect, with false positives and negatives. We apply an age-targeted list to the National Immunization Survey (NIS), conducted by the Centers for Disease Control and Prevention, which targets the relatively rare population of children age 19-35 months. The age-targeted list comprises the high- density stratum and the rest of the survey's sampling frame comprises the low-density stratum. Given the optimum allocation, we demonstrate potential cost savings for the NIS in excess of ten percent.