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In this paper, we use partially rank-ordered set (PROS) sampling design withmultiple concomitants in a breast cancer study and propose a method to estimatethe proportion of patients with malignant (cancerous) breast tumours in a givenpopulation. Through extensive numerical studies, the performance of theestimator is evaluated under various concomitants with different rankingpotentials (i.e., good, intermediate and bad) and tie-structures. We show thatthe PROS estimator with multiple concomitants based on the ranking informationprovided through some easy to obtain cytological characteristics that areassociated with the malignancy of breast tumours performs better than itscounterparts under simple random sampling (SRS) and ranked set sampling (RSS)designs with logistic regression models. As opposed to available RSS basedmethods in the literature, our proposed methodology allows to declare tiesamong the ranks and does not rely on the existence of any specific regressionmodel assumptions.

Proportion estimation based on a partially rank ordered set sample with multiple concomitants in a breast cancer study