  It is highly important for governments and health organizations to monitor
the prevalence of breast cancer as a leading source of cancer-related death
among women. However, the accurate diagnosis of this disease is expensive,
especially in developing countries. This article concerns a cost-efficient
method for estimating prevalence of breast cancer, when diagnosis is based on a
comprehensive biopsy procedure. Multistage ranked set sampling (MSRSS) is
utilized to develop a proportion estimator. This design employs some visually
assessed cytological covariates, which are pertinent to determination of breast
cancer, so as to provide the experimenter with a more informative sample.
Theoretical properties of the proposed estimator are explored. Evidence from
numerical studies is reported. The developed procedure can be substantially
more efficient than its competitor in simple random sampling (SRS). In some
situations, the proportion estimation in MSRSS needs around 76% fewer
observations than that in SRS, given a precision level. Thus, using MSRSS may
lead to a considerable reduction in cost with respect to SRS. In many medical
studies, e.g. diagnosing breast cancer based on a full biopsy procedure, exact
quantification is difficult (costly and/or time-consuming), but the potential
sample units can be ranked fairly accurately without actual measurements. In
this setup, multistage ranked set sampling is an appropriate design for
developing cost-efficient statistical methods.
