Roc software age war

The lower i. The larger value of LR - has lower information values. The Bayesian analysis combines the data of the likelihood ratio of test and prior odds of disease in order to obtain the posterior odds of disease among positive and negative test results Conventional analyses consider the sensitivity and the specificity of a diagnostic test as the primary indices of accuracy since these indices are considered to be independent of the prior probability of disease.

However, using a single sensitivity and a single specificity as measures of accuracy is problematic since these measures depend on a diagnostic criterion i. For example, one observer may choose a lenient decision criterion and the other may choose a stringent decision criterion for positivity. ROC analysis circumvents this arbitrariness. ROC analysis originated in the early 's with electronic signal detection theory One of the first applications was in radar, to separate observer variability from the innate delectability of signal.

Psychologists also adapted ROC methodology into psychology in the early 's in order to determine the relationship between properties of physical stimuli and the attributes of psychological experience sensory or perceptual The task of observers is to detect a weak signal in the presence of noise; e.

The applications of ROC methodology in diagnostic radiology and radionuclide imaging date back to the early 's. The first ROC curve in diagnostic radiology was calculated by Lusted who re-analyzed the previously published data on the detection of pulmonary tuberculosis and showed the reciprocal relationship between the percentage of false positive and of false negative results from the different studies of chest film interpretations Since then, several authors have used ROC methodology to diagnostic imaging systems.

The work of Dorfman and Alf was a pioneering step toward objective curve fitting and the use of computerized software in ROC analysis An automated program of maximum likelihood approach under binormal assumption was developed in They are available in the public domain During the past four decades, ROC analysis has become a popular method for evaluating the accuracy of medical diagnostic systems.

The most desirable property of ROC analysis is that the accuracy indices derived from this technique are not distorted by fluctuations caused by the use of arbitrarily chosen decision criteria or cut-offs.

In other words, the indices of accuracy are not influenced by the decision criterion i. The derived summary measure of accuracy, such as the area under the curve AUC determines the inherent ability of the test to discriminate between the diseased and healthy populations Using this as a measure of a diagnostic performance, one can compare individual tests or judge whether the various combination of tests e. ROC analysis is used in clinical epidemiology to quantify how accurately medical diagnostic tests or systems can discriminate between two patient states, typically referred to as "diseased" and "nondiseased" 16 , 17 , 21 , An ROC curve is based on the notion of a "separator" scale, on which results for the diseased and nondiseased form a pair of overlapping distributions 1.

The complete separation of the two underlying distributions implies a perfectly discriminating test while complete overlap implies no discrimination. Figure 1 show the two overlapping distributions with four thresholds used and figure 2 is the corresponding ROC curve and the arrows on the curve show ROC operating points.

Derived indices, such as the area under the entire curve AUC , the TPF at a specific FPF, or the partial area corresponding to a clinically relevant range of FPF 5 , 23 - 25 , are the most commonly used to measure diagnostic accuracy.

Here, we briefly discuss the concept of ROC curve and the meaning of area under the curve. The two overlapping distributions binormal model: probability density function-PDF for diseased right site and nondiseased left side and four different decision threshold.

The concept of an ROC curve is based on the notion of a "separator" or decision variable. The frequencies of positive and negative results of the diagnostic test will vary if one changes the "criterion" or "cut-off" for positivity on the decision axis. Where the results of a diagnostic system are assessed based on subjective judgement, the decision scale is only "implicit". Such a decision variable is often called a "latent" or unobservable variable.

ROC curve corresponding to progressively greater discriminant capacity of diagnostic tests are located progressively closer to the upper lefthand corner in "ROC space" figure 3 shows test B has a greater discriminate capacity than test A. An ROC curve lying on the diagonal line reflects the performance of a diagnostic test that is no better than chance level, i.

The slope of an ROC curve at any point is equal to the ratio of the two density functions describing, respectively, the distribution of the separator variable in the diseased and nondiseased populations, i.

A monotonically increasing likelihood ratio corresponds to a concave ROC curve 16 , The area under the curve AUC summarizes the entire location of the ROC curve rather than depending on a specific operating point 1 , 5.

The AUC is an effective and combined measure of sensitivity and specificity that describes the inherent validity of diagnostic tests 7. As an example of real data of breast cancer study that was reported recently by Hajian-Tilaki et al. This curve and the corresponding AUC show that BMI as a biomarker has predictive ability to discriminate breast cancer from normal subjects. An example of real data showing sensitivity and specificity at various cut- off points of BMI for detection of breast cancer.

Several indices of accuracy have been proposed to summarize ROC curves 1 , 5 , Based on these indices, statistical tests have been developed to compare the accuracy of two or more different diagnostic systems. These indices can be estimated both parametrically and nonparametrically. The area under the curve AUC , as a one-dimensional uni-dimensional index, summarizes the "overall" location of the entire ROC curve.

It is of great interest, since it has a meaningful interpretation. The AUC can be interpreted as the probability that a randomly chosen diseased subject is rated or ranked as more likely to be diseased than a randomly chosen nondiseased subject 5. The other interpretation is the average value of sensitivity for all the possible values of specificity.

Such an index is especially useful in a comparative study of two diagnostic tests or systems. If two tests are to be compared, it is desirable to compare the entire ROC curve rather than at a particular point 1. This happens when the distribution of test results for the diseased and nondiseased do not overlap.

The minimum AUC should be considered a chance level i. Partial Area Index: Despite the meaningful interpretation and statistical properties of AUC, it may still be argued that a large part of the area arises from the right side of the unit square where the high false positive fraction is of no clinical relevance.

Thus, one may be adding noise when using the area index to compare the two different diagnostic systems. In this situation, a partial area under the curve corresponding to a clinical relevant FPF is recommended as an index of choice 25 , 28 - One may be interested in comparing the performance of two tests at a given FPF for clinical reasons, especially in a case where two ROC curves cross.

The areas under the curves may be equal but in a clinical range of interest the FPF for one test may be superior to that of the other. If so, the two TPF from the different investigators of the same test may not be comparable. ROC curve analysis has several advantages 31 - First, in contrast to single measures of sensitivity and specificity, the diagnostic accuracy, such as AUC driven from this analysis is not affected by decision criterion and it is also independent of prevalence of disease since it is based on sensitivity and specificity.

Second, several diagnostic tasks on the same subjects can be compared simultaneously in a ROC space and the methods also developed to consider the covariance between two correlated ROC curve 6 , Third, one can easily obtain the sensitivity at specific FPF by visualizing the curve. Forth, the optimal cut- off value can be determined using ROC curve analysis In determining optimal cut off values, at least three methods have been proposed 7 , 26 , 32 , 33 , The two methods give equal weight to sensitivity and specificity with no ethical, cost and prevalence constraints 7.

The first method uses the square of distance between the point 0, 1 on the upper left hand corner of ROC space and any point on ROC curve ie. In order to obtain the optimal cut off points, the square of this distance is minimized.

In other words, one can calculate this distance for each cut off point in order to find the optimal cut- off value. The second method called Youden index uses the maximum of vertical distance of ROC curve from the point x, y on diagonal line chance line. The third method incorporates the financial costs for correct and false diagnosis and the costs of further work up for diagnosis. In fact, the consequence of each possible test outcome is ascertained to their costs and combining ROC analysis with utility-based decision theory can be used to determine the optimal cut point For example, given a disease with low prevalence and high cost of false positive diagnosis, the cut-point may be chosen at higher value to maximize specificity while for a disease occurring at high prevalence and missing diagnosis has a serious fatal consequences, a lower cut-point value would be selected to maximize sensitivity.

Suppose clinical researcher may wish to test the accuracy AUC of a single diagnostic test as unknown parameter with a pre-specified value of AUC 0. Delong et al. In comparative diagnostic studies in the context of ROC analysis, as an example, an investigator has a plan to compare the accuracy of MRI and CT in detecting abnormality. The accuracy of these two diagnostic tests are usually calculated on the same subjects i. However, the advantage of Delong method is that the covariance between two correlated AUC can be estimated from its components of variance covariance matrix as well The defects in designing of diagnostic studies concern spectrum and bias.

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