Detecting diagnostic accuracy of two biomarkers through a bivariate log-normal ROC curve

In biomedical research, two or more biomarkers may be available for diagnosis of a particular disease. Selecting one single biomarker which ideally discriminate a diseased group from a healthy group is confront in a diagnostic process. Frequently, most of the people use the accuracy measure, area under the receiver operating characteristic (ROC) curve to choose the best diagnostic marker among the available markers for diagnosis. Some authors have tried to combine the multiple markers by an optimal linear combination to increase the discriminatory power. In this paper, we propose an alternative method that combines two continuous biomarkers by direct bivariate modeling of the ROC curve under log-normality assumption. The proposed method is applied to simulated data set and prostate cancer diagnostic biomarker data set.     

Sample Size and Power Calculation in Comparing Diagnostic Accuracy of Biomarkers with Pooled Assessments

When testing of a biomarker is costly, pooling of samples becomes a useful and efficient alternative (Faraggi et al., 2003). In this paper, we develop procedures for sample size and power calculations for planning a study comparing the accuracy of biomarkers in diagnosis of diseases with pooled samples. Explicit formulas are derived for several important pooling strategies. The effects of pooling samples on sample size and power of the test are also discussed.     

Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non-parametric approaches

Summary.  The evaluation of the performance of a continuous diagnostic measure is a commonly encountered task in medical research. We develop Bayesian non-parametric models that use Dirichlet process mixtures and mixtures of Polya trees for the analysis of continuous serologic data. The modelling approach differs from traditional approaches to the analysis of receiver operating characteristic curve data in that it incorporates a stochastic ordering constraint for the distributions of serologic values for the infected and non-infected populations. Biologically such a constraint is virtually always feasible because serologic values from infected individuals tend to be higher than those for non-infected individuals. The models proposed provide data-driven inferences for the infected and non-infected population distributions, and for the receiver operating characteristic curve and corresponding area under the curve. We illustrate and compare the predictive performance of the Dirichlet process mixture and mixture of Polya trees approaches by using serologic data for Johne's disease in dairy cattle.     

An application of ranked set sampling when observations from several distributions are to be included in the sample

ABSTRACT

In this article, we propose a method to estimate the common location and common scale parameters of several distributions using suitably defined ranked set sampling. Efficiency comparison of the obtained estimators with some of the standard estimators is made. Illustration of the results to real life data sets is also described.