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Distribution-free confidence bounds for ROC curves.

ROC curves are widely used for the evaluation of diagnostic tests to decide between "healthy" and "diseased" individuals when the measurements are on a continuous scale. These curves are graphical displays of the interdependence between specificity and sensitivity of the test varying with the cut-off point chosen for the decision. Up to now only point estimators derived from the empirical distribution functions are used which may be misleading if they are based on rather small samples. In this paper we propose reasonable confidence bounds for ROC curves and a corresponding point estimator. Our bounds are strongly related to two-sided distribution-free tolerance regions because they are constructed from minimum and maximum coverages which at a given value chi can be guaranteed with a confidence (2 pi*-1). The interpretation of the bounds is that if a cut-off-point is chosen on the basis of the ROC curve then with a nominal confidence of at least (2 pi*-1)2 the real sensitivity and specificity will be within a rectangle.

Algorithms

Evaluation of diagnostic tests using relative operating characteristic (ROC) curves and the differential positive rate. An example using the total serum bile acid concentration and the alanine aminotransferase activity in the diagnosis of canine hepatobiliary diseases.

The value of a diagnostic test depends on most cases on its ability to discriminate between patients with and without a certain disease. One way of evaluating a diagnostic test is to use the relative operating characteristic curve (ROC curve) and the differential positive rate (DPR). The ROC curve displays the relationship between the true positive ratio and the false positive ratio for a range of cutoff values and it can be used to compare various diagnostic tests under equivalent conditions (equal true positive ratios or false positive ratios) and over the entire range of cutoff values. The DPR is the difference between the true positive ratio and the false positive ratio at various cutoff values and it can be used to obtain the cutoff value associated with the highest sensitivity and specificity. The purpose of this study was to describe the evaluation and comparison of diagnostic tests using ROC curves and DPR. Eventually, the positive and negative predictive values were used to assess the differences between the sensitivity and specificity obtained when the upper limit of the reference interval, or the optimal cutoff value indicated by the DPR, was used as cutoff value. To illustrate the methods, the 2 h post-prandial total serum bile acid concentration (PSBA) and the alanine aminotransferase activity (ALAT) in the diagnosis of primary or secondary hepatobiliary diseases in dogs were used. The ROC curves showed, as expected from previous studies, that PSBA was superior to ALAT in diagnosing dogs with hepatobiliary diseases. Using DPR, the optimal cutoff value for PSBA was suggested to be 15.48 mumol/l. Compared to the traditionally used cutoff value of 22.24 mumol/l, no decisive difference in the positive predictive values were observed. However, the cutoff value of 15.48 mumol/l appeared to produce higher negative predictive values compared to a cutoff value of 22.24 mumol/l. Seemingly, ROC curves and DPR are simple methods useful to the evaluation of diagnostic tests and due to the simplicity, there seems to be a great potential for these methods in the evaluation of diagnostic tests in veterinary medicine.

Alanine Transaminase

Variation in restorative treatment decisions: application of Receiver Operating Characteristic curve (ROC) analysis.

It has been evident for many years that dentists, when planning treatment for patients, do not act in a standard manner, and previous research has shown there to be wide variations in treatment planning amongst groups of dentists. Signal detection theory and Receiver Operating Characteristic (ROC) analysis allows measurement of an observer's ability to detect a lesion, while at the same time allowing examination of how a lesion, once perceived, is judged to be in need of treatment. An ROC curve is constructed by plotting the sensitivity (or true positive rate) of decisions made, against the false positive rate (equivalent to 1-specificity) when various decision attitudes, from interventionist to non-interventionist, are held. Fifteen pairs of simulated bitewing radiographs were shown to 20 dentists, who were asked to specify, for each approximal lesion, whether or not they would place a conventional restoration. The 7200 decisions made by the dentists were validated by sectioning and microscopically examining the teeth. The mean sensitivity of the dentists' decisions, when the strictest operating thresholds were held and caries into dentine was the validating criterion, was 0.26 and the mean specificity was 0.96. ROC analysis shows that when operating at the strictest threshold, the dentists were implying that specificity was weighted as being 2.7 times more important than sensitivity. ROC analysis leads to insight into how dentists differentially weight the true and false, positive and negative, outcomes of their decisions and thus allows explanation of why two dentists would rarely make exactly the same treatment plan for one patient, and also why different treatments might be offered to two patients exhibiting the same levels of disease.

Decision Support Techniques

Signal detectability: the use of ROC curves and their analyses.

Issues related to ROC curves are addressed. The original article on the subject by Lee Lusted, describing the "state of the art" 20 years ago, is reviewed. The concepts that Lusted addressed are then expanded, suggesting the current state of the art. New issues that have arisen with regard to ROC curves and their use in medicine are addressed. Finally, potential areas for future investigation are suggested.

Diagnosis, Computer-Assisted

[ROC-curve analysis. A statistical method for the evaluation of diagnostic tests].

Receiver operating characteristic (ROC)-curves are a statistical method which may be employed inter alii for assessing a diagnostic test. These have been employed particularly in radiology but have also been employed for assessing laboratory tests and obstetric estiamation scales. The method is based on an analysis of nosological probabilities for varying limits of decision thresholds. ROC-curves may be employed for data on ratio/interval scales and data on rank scales. Parametric and non-parametric methods are available for obtaining a single quantitative measurement for the entire ROC-curve and to carry out significance tests between several ROC-curves.

Diagnosis

ROC curves for the initial assessment of new diagnostic tests.

New diagnostic tests are mainly evaluated by determining the sensitivity and specificity of the test. These test characteristics were originally meant to be used in making diagnoses. For evaluative purposes their usefulness is weakened by their susceptibility to selection and their dependence on the cut-off points that are used for test positivity. The plotting of a receiver operating characteristic (ROC) curve might be a solution to these problems. Furthermore, the ROC curve yields a measure for the diagnostic power of the test expressed in one number instead of two, namely the area under the curve (AUC). Finally, the ROC curve and its AUC permit easy comparison of different tests and the performance of different interpreters of one test. The construction and use of ROC curves are described and illustrated with data of a case-referent investigation into the relationship between iron status parameters and the presence of acute myocardial infarction. The AUCs of ferritin and serum iron, 0.61 and 0.68 respectively, are too low to suggest meaningful usefulness in clinical practice.

Humans

[Clinical decision analysis and ROC curve].

This workshop was planned to teach the importance of clinical decision analysis and the ROC curve in clinical medicine. A pre-workshop test and post-workshop test were given before and after the workshop. In the clinical decision analysis a heart disease case was shown, a decision tree was made, and the chance node and expected value were calculated. The ROC curve was prepared from the results of urine analysis of patients with renal and urinary tract infections, and the cut-off points were changed variously. There were 27 participants. Twelve of them took both the pre-workshop test and post-workshop test, and about half of them answered that they understood how to perform the analysis. There tended to be more participants who understood how to make the clinical decision analysis than the ROC curve.

Decision Support Techniques

The area under the ROC curve and its competitors.

The area under the receiver operating characteristic (ROC) curve is a popular measure of the power of a (two-disease) diagnostic test, but it is shown here to be an inconsistent criterion: tests of indistinguishable clinical impacts may have different areas. A class of diagnosticity measures (DMs) of proven optimality is proposed instead. Once a regret(-like) measure of diagnostic uncertainty is agreed upon, the associated DM is uniquely defined and, indeed, calculable from the ROC curve configuration. Two scaled variants of the ROC are introduced and used to advantage in the analysis. They may also be helpful to students of medical decision making.

Decision Theory

ROC curve analysis: an example showing the relationships among serum lipid and apolipoprotein concentrations in identifying patients with coronary artery disease.

Clinical accuracy, defined as the ability to discriminate between states of health, is the fundamental property of any diagnostic test or system. It is readily expressed as clinical sensitivity and specificity, and elegantly represented by the receiver operating characteristic (ROC) curve. To demonstrate the use of ROC curves, we reexamine a study of the ability of serum lipid and apolipoprotein measures to discriminate among degrees of coronary artery disease in patients undergoing coronary angiography. ROC curve analysis reveals that none of these indexes is highly accurate, but demonstrates a modest increase in the accuracy of apolipoprotein over lipid indexes.

Apolipoproteins

ROC curves and the binormal assumption.

Previous articles in this series have described how receiver operating characteristic (ROC) graphs provide comprehensive graphic representations of the diagnostic performance of non-binary tests and have explained how one constructs "trapezoidal" ROC graphs in which discrete cutoff points are plotted and connected with line segments. In this article, we describe a set of mathematical assumptions that permit the generation of a continuous, smooth ROC curve for a given diagnostic test. These assumptions permit us to characterize a test's performance using a small number of parameters and also to explore properties of diagnostic tests. In this article, we describe a set of mathematical assumptions that can be used to link receiver operating characteristic (ROC) curves to the underlying distribution of values of the diagnostic variable being measured. We will illustrate these assumptions using a diagnostic test that distinguishes alcohol abusers from normal consumers of alcohol and abstainers.

Alcoholism

A receiver operating characteristic (ROC) curve analysis of a model of mental health services use by Puerto Rican poor.

In this study, the contribution of four distinct domains of the Help Seeking-Decision Making model to predicting the use of mental health services is examined. Using a proposed methodology the authors assess the relevance of this model and its domains to mental services planning. The methodology combines logistic regression analysis and receiver operating characteristic (ROC) curves. Logistic regression analysis allows us to examine the individual variables of the model and generate predictions about use. ROC curves allow us to compare and interpret the relative contribution of a predisposing domain, a physical and mental health domain, an enabling-restrictive domain, and an organizational domain in correctly classifying users and nonusers of mental health services. The physical and mental health domain yielded a Somer's D-statistic of 0.7, which corresponds to an 85% correct classification of randomly selected pairs of users and nonusers. The study findings suggest that comparing ROC curves helps to describe and interpret the domains of the model that are relevant for making predictions about who will or will not use mental health services during a 1-year period.

Adolescent

[Comparison of the quality of diagnostic approaches using the characteristic (ROC) curve test].

The method is described to compare the quality of two diagnostic approaches as based on comparing surfaces under the ROC test curve. Apart from small deviations, this method may be applied on independent samples and paired observations carried on identical individuals. Experimental data are issued from comparing two methods of prediction of the survival in dogs on the radiobiologic experiment.

Animals

ROC curves, test accuracy, and the description of diagnostic tests.

Clinicians can gain an enhanced understanding of the role of diagnostic tests once they are familiar and comfortable with the descriptions of test performance provided by receiver operating characteristic (ROC) analysis. This article explores the ways that ROC methods quantify test accuracy and describes how ROC methods characterize the distributions of test outcomes in study populations.

Humans