Sequential adaptive strategies for sampling rare clustered populations

Abstract

A new class of sampling strategies is proposed that can be applied to population-based surveys targeting a rare trait that is unevenly spread over an area of interest. Our proposal is characterised by the ability to tailor the data collection to specific features and challenges of the survey at hand. It is based on integrating an adaptive component into a sequential selection, which aims both to intensify the detection of positive cases, upon exploiting the spatial clustering, and to provide a flexible framework to manage logistics and budget constraints. A class of estimators is also proposed to account for the selection bias, that are proved unbiased for the population mean (prevalence) as well as consistent and asymptotically Normal distributed. Unbiased variance estimation is also provided. A ready-to-implement weighting system is developed for estimation purposes. Two special strategies included in the proposed class are presented, that are based on the Poisson sampling and proved more efficient. The selection of primary sampling units is also illustrated for tuberculosis prevalence surveys, which are recommended in many countries and supported by the World Health Organisation as an emblematic example of the need for an improved sampling design. Simulation results are given in the tuberculosis application to illustrate the strengths and weaknesses of the proposed sequential adaptive sampling strategies with respect to traditional cross-sectional non-informative sampling as currently suggested by World Health Organisation guidelines.

Keywords: Asymptotics; Budget and logistic constraints; Informative designs; Intra-cluster variation; Over-sampling; Poisson sampling; Pseudo Horvitz-Thompson estimator.

Fig. 1

Six simulated scenarios: dots depict positive cases gathered in 3 clusters

Fig. 2

CPoSA versus PoSA for increasing values of $n_{\mathit{min}}$: boxplots of the MC distribution of final sample size (upper panels) and number of positive cases detected (lower panel) (98% values represented)

Fig. 3

CPoSA versus traditional WHO design: over-sampling of positive cases and accuracy of the final estimate, for increasing level of k. Ratio over the traditional design (dashed line means equal performance)

Fig. 4

CPoSA versus traditional WHO design: final sample size and cost per case detected, for increasing level of k. Ratio over the traditional design (dashed line means equal performance)