Conventional sampling theory is widely used in environmental and health hazard assessment. However, spatial sampling techniques are among the most efficient methods when sampling units are spatially correlated. Spatial sampling has been introduced and used for population mean estimation. In addition, few works have also been focused for the population proportion estimation. However, in many health-related data applications, we are interested to also know the proportion of non-rare specific health condition (e.g. asthma) or rate of rare specific health condition (e.g. cancer) in each small area rather than overall population to inform public and policy-makers to focus on areas which are most in need. In this paper, we develop design-based and model-based approaches for overall and area-specific proportion and rate estimation. In particular, we expand dependent unit sequential technique method on model-assisted (ranked set sampling) and model-based (small area estimation) approaches which are more efficient than the sampling methods originated from simple random sampling. We evaluate the performance of proposed approaches using stimulation studies and also by a real data application on teen birth rate in Georgia, USA.
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