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

In this paper, we use partially rank-ordered set (PROS) sampling design with multiple concomitants in a breast cancer study and propose a method to estimate the proportion of patients with malignant (cancerous) breast tumours in a given population. Through extensive numerical studies, the performance of the estimator is evaluated under various concomitants with different ranking potentials (i.e., good, intermediate and bad) and tie-structures. We show that the PROS estimator with multiple concomitants based on the ranking information provided through some easy to obtain cytological characteristics that are associated with the malignancy of breast tumours performs better than its counterparts under simple random sampling (SRS) and ranked set sampling (RSS) designs with logistic regression models. As opposed to available RSS based methods in the literature, our proposed methodology allows to declare ties among the ranks and does not rely on the existence of any specific regression model assumptions.

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