New Perspectives on Sampling Rare and Clustered

A new sampling design is derived for sampling a rare and clustered population under both cost and logistic constraints. It is motivated based on the example of national TB prevalence surveys, sponsored by WHO for high TB-burden countries and usually located in the poorest parts of the world. A Poisson-type sampling design named Poisson Sequential Adaptive (PoSA) is proposed with a twofold purpose: (i) to increase the detection rate of positive cases; and (ii) to reduce survey costs by accounting for logistic constraints at the design level of the survey. PoSA is derived by integrating both an adaptive component able to enhace detectability and a sequential component for dealing with costs and logistic constraints. An unbiased HT-type estimator for the population prevalence (mean) is derived by adjusting for both the over-selection bias and for the conditional structure induced by the sequential selection. Unbiased variance estimation in a closed form is also provided. Simulation results are presented and show a significant pontential of PoSA in improving the sampling methodology currently suggested by WHO guidelines.