Proportion estimation in multistage pair ranked set sampling

Abstract Estimating the proportion of individuals having a disease in a given population is a common problem in medicine. This is simply done by drawing a random sample from the target population, and computing the proportion of positive results based on a suitable diagnostic test. In some situations, the number of quantified units is limited because measuring the variable of interest is difficult or expensive. In this setting, one can utilize alternative designs that allow achieving the desired precision level with a smaller sample size. Multistage pair ranked set sampling (MSPRSS) is such a design that can be used instead of simple random sampling. It is a rank-based sampling method that incorporates auxiliary information in order to collect an informative sample. This article deals with the proportion estimation in MSPRSS. Some results about the proposed estimator are proved. A simulation experiment and a real data set in the context of breast cancer are used to demonstrate the finite sample properties of the new estimator.