A sequential adaptive approach for surveying rare and clustered populations

In this thesis, 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 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 enhance 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. The PoSA design is characterised by a random sample size that may lead to very small samples, hence as a first proposal we considered a sampling design with a fixed a minimum sample size. An extensive simulation study shows the potentials of the proposed strategies. In particular, the proposed designs improve the sampling methodology currently suggested by WHO guidelines when the trait of interest appears clustered, as the proposed procedures are able to deal with logistic constraints and increase the number of cases found with the same budget, without losses in efficiency.