Confidence interval estimation of the difference between two sensitivities to the early disease stage

The generalized order statistics arising from three populations with the lower truncated proportional hazard rate models and its application to the sensitivity to the early disease stage

In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods.

Empirical likelihood confidence interval for sensitivity to the early disease stage

Disease status can naturally be classified into three or more ordinal stages rather than just being binary stages. Many works have been done for the estimation and inference procedure regarding three ordinal disease stages, which are non-disease, early disease, and full disease stages. The early disease stage can be very important for therapeutic intervention and prevention potentiality. As a diagnostic measure, sensitivity to the early disease stage is often used. In this article, we propose confidence intervals for the sensitivity to early disease stage based on given target specificity for non-disease stage and target sensitivity to full disease stage using both empirical likelihood (EL) and adjusted EL procedures. We compare the performance of the proposed EL confidence intervals with other procedures in our simulation study. The proposed procedures are further applied to Alzheimer's Disease Neuroimaging Initiative data set.

Confidence interval estimation for sensitivity and difference between two sensitivities at a given specificity under tree ordering

This article considers a setting in diagnostic studies (or biomarker study) which involves a healthy class and a diseased class and the latter consists of several subclasses. The problem of interest is to evaluate the accuracy of a biomarker (or a diagnostic test) measured on a continuous scale correctly identifying healthy subjects from diseased subjects without requiring specification of an ordering in terms of marker values for subclasses relative to each other within the diseased class. Such setting is quite common in practice and it falls in the framework of tree ordering or umbrella ordering. This article explores several parametric and nonparametric approaches for estimating confidence intervals of sensitivity of single biomarker and difference between sensitivities of two correlated biomarkers under tree ordering at a given specificity. The performances of all the methods are evaluated and compared by a comprehensive simulation study. A published microarray data set is analyzed using the proposed methods.

Confidence Interval Estimation for Sensitivity to the Early Diseased Stage Based on Empirical Likelihood

Many disease processes can be divided into three stages: the non-diseased stage: the early diseased stage, and the fully diseased stage. To assess the accuracy of diagnostic tests for such diseases, various summary indexes have been proposed, such as volume under the surface (VUS), partial volume under the surface (PVUS), and the sensitivity to the early diseased stage given specificity and the sensitivity to the fully diseased stage (P2). This paper focuses on confidence interval estimation for P2 based on empirical likelihood. Simulation studies are carried out to assess the performance of the new methods compared to the existing parametric and nonparametric ones. A real dataset from Alzheimer's Disease Neuroimaging Initiative (ADNI) is analyzed.