Efficient estimation of a disease prevalence using auxiliary ranks information

It is a common challenge in medical field to obtain the prevalence of a specific disease within a given population. To tackle this problem, researchers usually draw a random sample from the target population to obtain an accurate estimate of the proportion of diseased people. However, some limitations may occur in practice due to constraints, such as complexity or cost. In these situations, some alternative sampling techniques are needed to achieve precision with smaller sample sizes. One such approach is Neoteric Ranked Set Sampling (NRSS), which is a variation of Ranked Set Sampling (RSS) design. NRSS scheme involves selecting sample units using a rank-based method that incorporates auxiliary information to obtain a more informative sample. In this article, we focus on the problem of estimating the population proportion using NRSS. We develop an estimator for the population proportion using the NRSS design and establish some of its properties. We employ Monte Carlo simulations to compare the proposed estimator with competitors in Simple Random Sampling (SRS) and RSS designs. Our results demonstrate that statistical inference based on the introduced estimator can be significantly more efficient than its competitors in RSS and SRS designs. Finally, to demonstrate the effectiveness of the proposed procedure in estimating breast cancer prevalence within the target population, we apply it to analyze Wisconsin Breast Cancer data.