Another look at regression analysis using ranked set samples with application to an osteoporosis study

Abstract

Statistical learning with ranked set samples has shown promising results in estimating various population parameters. Despite the vast literature on rank‐based statistical learning methodologies, very little effort has been devoted to studying regression analysis with such samples. A pressing issue is how to incorporate the rank information of ranked set samples into the analysis. We propose two methodologies based on a weighted least squares approach and multilevel modeling to better incorporate the rank information of such samples into the estimation and prediction processes of regression‐type models. Our approaches reveal significant improvements in both estimation and prediction problems over already existing methods in the literature and the corresponding ones with simple random samples. We study the robustness of our methods with respect to the misspecification of the distribution of the error terms. Also, we show that rank‐based regression models can effectively predict simple random test data by assigning ranks to them a posteriori using judgment poststratification. Theoretical results are augmented with simulations and an osteoporosis study based on a real data set from the Bone Mineral Density (BMD) program of Manitoba to estimate the BMD level of patients using easy to obtain covariates.

Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples

“…Various topics have been studied on RSS such as distribution functions, 11 nonparametric two-sample tests, 12,13 and rank regression. 14 In the past decade, RSS has been applied to diverse areas including agriculture, 15,16,17,18,19 education, 20 engineering, 21 environment, 22,23 public health, 24,25,26,27,28 and medicine. 29,27 The main theme of this paper is the inference on the AUC based on EL when data are obtained from RSS.…”

“…14 In the past decade, RSS has been applied to diverse areas including agriculture, 15,16,17,18,19 education, 20 engineering, 21 environment, 22,23 public health, 24,25,26,27,28 and medicine. 29,27 The main theme of this paper is the inference on the AUC based on EL when data are obtained from RSS. In RSS, the estimation and testing of the AUC have been of great interest.…”