Post-test diagnostic accuracy measures under tree ordering of disease classes.

The medical field commonly employs post-test measures such as predictive values and likelihood ratios to assess diagnostic accuracy. Predictive values, including positive and negative values (PPV and NPV), indicate the probability that individuals have a target health condition based on test results. On the other hand, likelihood ratios, including positive and negative ratios (LR+ and LR- respectively), compare the probability of a particular test result between the diseased and non-diseased groups. While predictive values are useful in evaluating diagnostic test accuracy in populations with varying disease prevalence, likelihood ratios provide a direct link between pre-test and post-test probabilities in specific patients. In this study, we introduce and analyze a new approach called generalized predictive values and likelihood ratios, using a tree ordering of disease classes. We evaluate the effectiveness of these methods through simulation studies and illustrate their use with real data on lung cancer.

Testing against umbrella or tree orderings for binomial proportions with an adaptation of an insect resistance case.

Alternative hypotheses for order restrictions, such as umbrella or inverse umbrella (a.k.a tree) orderings, have been studied extensively in the literature, although less so when the studied response for each individual is the presence or absence of the event of interest. Two families of test statistics for solving the problem of testing against an umbrella or a tree ordering when the responses are binomial proportions are studied in this work and their asymptotic distributions are derived. A simulation study is conducted to compare the empirical power of some members of the derived families of test statistics with competing approaches. The methodology developed here was driven by an applied problem arising in stored products research where despite universal mortality in the case of doses of 1000 ppm of the insecticide phosphine, unexpected survival was noted at higher doses.

Receiver operating characteristic analysis under tree orderings of disease classes.

Receiver operating characteristic (ROC) curve and its summary statistics (e.g., the area under curve (AUC)) are commonly used to evaluate the diagnostic accuracy for disease processes with binary classification. The ROC curve has been extended to ROC surface for scenarios with three ordinal classes or to hyper-surface for scenarios with more than three classes. For classifier under tree or umbrella ordering in which the marker measurement for one class is lower or higher than those for the other classes, the commonly adopted diagnostic measures are the naive AUC (NAUC) based on a pooled class of all the unordered classes and the umbrella volume (UV) based on the concept of volume under surface. However, both NAUC and UV have some limitations. For example, NAUC depends on the sampling weights for all the classes in population, and UV has only been introduced for three-class settings. In this article, we initiate the idea of a new ROC framework for tree or umbrella ordering (denoted as TROC) and propose the area under TROC curve (denoted as TAUC) as an appropriate diagnostic measure. The proposed TROC and TAUC share many nice features with the traditional ROC and AUC. Both parametric and nonparametric approaches are explored to construct the confidence interval estimation of TAUC. The performances of these methods are compared in simulation studies under a variety settings. At the end, the proposed methods are applied to a published microarray data set.

Measuring diagnostic accuracy for biomarkers under tree-ordering.

In the field of diagnostic studies for tree or umbrella ordering, under which the marker measurement for one class is lower or higher than those for the rest unordered classes, there exist a few diagnostic measures such as the naive AUC ( NAUC), the umbrella volume ( UV), and the recently proposed TAUC, i.e. area under a ROC curve for tree or umbrella ordering (TROC). However, an important characteristic about tree or umbrella ordering has been neglected. This paper mainly focuses on promoting the use of the integrated false negative rate under tree ordering ( ITFNR) as an additional diagnostic measure besides TAUC, and proposing the idea of using ( TAUC, ITFNR) instead of TAUC to evaluate the diagnostic accuracy of a biomarker under tree or umbrella ordering. Parametric and non-parametric approaches for constructing joint confidence region of ( TAUC, ITFNR) are proposed. Simulation studies under a variety of settings are carried out to assess and compare the performance of these methods. In the end, a published microarray data set is analyzed.