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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.

An innovative sampling strategy is proposed, which applies to large-scale population-based surveys targeting a rare trait that is unevenly spread over a geographical 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 to both intensify detection of positive cases, upon exploiting the spatial clusterisation, and provide a flexible framework for managing logistical and budget constraints. To account for the selection bias, a ready-to-implement weighting system is provided to release unbiased and accurate estimates. Empirical evidence is illustrated from tuberculosis prevalence surveys, which are recommended in many countries and supported by the WHO as an emblematic example of the need for an improved sampling design. Simulation results are also given to illustrate strengths and weaknesses of the proposed sampling strategy with respect to traditional cross-sectional sampling., 21 pages, 1 tenable, 3 figures - Submitted

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.

Multiple-frame surveys are commonly used to deal with under-coverage bias. The use of more than one frame introduces the possibility that frames overlap leading to increased inclusion probabilities of units that appear in multiple lists. Following the guide example of a dual frame set-up (DF) in telephone surveys, this contribution presents an extensive simulation study where different types of screenings to deal with the overlap issue are compared with the proper DF approach. We empirically show that the efforts of screening do not guarantee estimators more efficient than the DF estimators that do not need screening. Moreover simulation results show that screening at sample level does not correct for the increased inclusion probability of units in both frames produced by the DF set-up nor improve efficiency. The different estimation options will be compared with regards to survey costs, amount of information required and statistical properties of the final estimates