Sampling of subpopulations in two-stage surveys

Many health and other surveys aim to produce statistics on small subpopulations, such as specific ethnic groups or the indigenous population of a country. In most countries, there is no reliable sampling frame of the subpopulations of interest, hence it is necessary to sample from the general population, which can be very expensive. A range of issues and strategies for sampling rare subpopulations is reviewed. The most common approaches in practice are the use of a large screening sample, and disproportionate sampling by strata. Optimal sample designs have been derived for the case of one-stage sampling, but most household interview surveys use two or more stages of selection. This paper develops optimal designs for two-stage sampling, where there is auxiliary information on subpopulation numbers for each primary sampling unit. Various alternative designs are evaluated using a simulated population derived from the New Zealand Census.