Bayesian mixture modelling with ranked set samples.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

Efficient estimators with categorical ranked set samples: estimation procedures for osteoporosis.

Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtained easily through inexpensive and easy to measure characteristics at little or no cost. In this paper, we study RSS data for analysis of an ordinal population. First, we compare the problem of non-representative extreme samples under RSS and commonly-used simple random sampling. Using RSS data with tie information, we propose non-parametric and maximum likelihood estimators for population parameters. Through extensive numerical studies, we investigate the effect of various factors including ranking ability, tie generating mechanisms, the number of categories and population setting on the performance of the estimators. Finally, we apply the proposed methods to the bone disorder data to estimate the proportions of patients with osteopenia and osteoporosis status.

Wnt Site Signaling Inhibitor Secreted Frizzled-Related Protein 3 Protects Mitral Valve Endothelium From Myocardial Infarction-Induced Endothelial-to-Mesenchymal Transition.

Background The onset and mechanisms of endothelial-to-mesenchymal transition (EndMT) in mitral valve (MV) leaflets following myocardial infarction (MI) are unknown, yet these events are closely linked to stiffening of leaflets and development of ischemic mitral regurgitation. We investigated whether circulating molecules present in plasma within days after MI incite EndMT in MV leaflets. Methods and Results We examined the onset of EndMT in MV leaflets from 9 sheep with inferior MI, 8 with sham surgery, and 6 naïve controls. Ovine MVs 8 to 10 days after inferior MI displayed EndMT, shown by increased vascular endothelial cadherin/α-smooth muscle actin-positive cells. The effect of plasma on EndMT in MV endothelial cells (VECs) was assessed by quantitative polymerase chain reaction, migration assays, and immunofluorescence. In vitro, post-MI plasma induced EndMT marker expression and enhanced migration of mitral VECs; sham plasma did not. Analysis of sham versus post-MI plasma revealed a significant drop in the Wnt signaling antagonist sFRP3 (secreted frizzled-related protein 3) in post-MI plasma. Addition of recombinant sFRP3 to post-MI plasma reversed its EndMT-inducing effect on mitral VECs. RNA-sequencing analysis of mitral VECs exposed to post-MI plasma showed upregulated FOXM1 (forkhead box M1). Blocking FOXM1 reduced EndMT transcripts in mitral VECs treated with post-MI plasma. Finally, FOXM1 induced by post-MI plasma was downregulated by sFRP3. Conclusions Reduced sFRP3 in post-MI plasma facilitates EndMT in mitral VECs by increasing the transcription factor FOXM1. Restoring sFRP3 levels or inhibiting FOXM1 soon after MI may provide a novel strategy to modulate EndMT in the MV to prevent ischemic mitral regurgitation and heart failure.

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

In many surveys, we often deal with situations where measuring the study variable is expensive; however, there are easy-to-measure characteristics which can be used as ranking information to obtain more representative samples from the population. Ranked set sampling is successfully employed in these cases as an alternative to commonly used simple random sampling. When the data is ordinal categorical, it is common to apply the ordinal logistic regression approach to ranked set sampling data for the estimation of parameters. This technique first depends on the information of training data. Besides, one is not capable of using the ranking information in the estimation process. In this paper, we propose a ranked set sampling scheme in which ranking information from multiple sources can be combined and incorporated efficiently into both data collection and estimation. The ranked set sampling data is used for non-parametric and maximum likelihood estimation of ordinal categorical population. Through extensive simulation studies, the performance of estimators is evaluated. The methods are finally applied to analyze bone disorder data and obesity data.