An improved procedure for estimation of malignant breast cancer prevalence using partially rank ordered set samples with multiple concomitants

Abstract

Rank-based sampling designs are widely used in situations where measuring the variable of interest is costly but a small number of sampling units (set) can be easily ranked prior to taking the final measurements on them and this can be done at little cost. When the variable of interest is binary, a common approach for ranking the sampling units is to estimate the probabilities of success through a logistic regression model. However, this requires training samples for model fitting. Also, in this approach once a sampling unit has been measured, the extra rank information obtained in the ranking process is not used further in the estimation process. To address these issues, in this paper, we propose to use the partially rank-ordered set sampling design with multiple concomitants. In this approach, instead of fitting a logistic regression model, a soft ranking technique is employed to obtain a vector of weights for each measured unit that represents the probability or the degree of belief associated with its rank among a small set of sampling units. We construct an estimator which combines the rank information and the observed partially rank-ordered set measurements themselves. The proposed methodology is applied to a breast cancer study 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 among the ranks. We show that the precision of the partially rank-ordered set estimator is better than its counterparts under simple random sampling and ranked set sampling designs and, hence, the sample size required to achieve a desired precision is reduced.

Bayesian mixture modelling with ranked set samples

“…Unlike simple random sampling (SRS), RSS design creates artificial ranking strata over the population and allows to draw samples from all aspects of the population. RSS has found applications in various research areas such as nonparametric statistics, [15][16][17] clustered randomized designs, 18,19 breast cancer, 20 behavioural science 21 and fishery 22 to name a few. For more detail about the theory and applications, readers are referred to Chen et al 23 Finite mixture models (FMMs), as a powerful and flexible tool, play a crucial role in classifying and analyzing heterogeneous populations.…”

A review of ranked set sampling and modified methods in designing control charts

“…The RSS can be implemented to obtain more efficient estimators of population parameters compared to SRS using the same number of quantitative observations. The RSS scheme has many applications in different fields, including environmental and ecological studies, 10 fisheries, 11 and medical studies, 12,13 among others. 14,15 Takahasi and Wakimoto 6 were the first researchers to discuss the statistical theory of RSS.…”

Estimation of ordinal population with multi-observer ranked set samples using ties information

“…The RSS has found a wide range of applications. To say a few of these applications, we indicate breast cancer, 10 lung cancer, 11 trauma, 12 osteoporosis, 13–14 education, 15 zoological research, 16 agricultural studies, 17–18 and fishery surveys. 19…”

“…The RSS has found a wide range of applications. To say a few of these applications, we indicate breast cancer, 10 lung cancer, 11 trauma, 12 osteoporosis, [13][14] education, 15 zoological research, 16 agricultural studies, [17][18] and fishery surveys. 19 A significant amount of literature has developed different non-parametric and maximum likelihood (ML) estimators based on RSS data for binary populations.…”

“…19 A significant amount of literature has developed different non-parametric and maximum likelihood (ML) estimators based on RSS data for binary populations. 10,[20][21][22] Despite this rich literature in binary population, there are very few research works regarding the categorical population. Although a number of RSS-based estimation procedures was developed for the problem of the ordinal categorical population, 23,24 the proposed methods are not capable of using ranking information of multiple concomitant variables.…”