Youden's J statistic(also calledYouden's index) is a single statistic that captures the performance of adichotomousdiagnostic test.Informednessis its generalization to the multiclass case and estimates the probability of an informed decision.

約登指數可與ROC曲線一起使用，使Youden's index最大化的點可作為最佳截斷閾值。

The index gives equal weight to false positive and false negative values, so all tests with the same value of the index give the same proportion of total misclassified results. While it is technically possible to obtain a value of less than zero from this equation, e.g. Classification yields only False Positives and False Negatives, a value of less than zero just indicates that the positive and negative labels have been switched. After correcting the labels the result will then be in the 0 through 1 range.

該指標給予假陽性和假陰性值相同的權重，因此所有具有該指標相同值的測試在總誤分類結果中所佔的比例相同。雖然從這個等式中得到一個小於零的值在技術上是可能的，例如，分類只會產生假陽性和假陰性，但小於零的值只是表明正標籤和負標籤被切換了。在糾正標籤之後，結果將在0到1的範圍內。

Youden's index is often used in conjunction withreceiver operating characteristic(ROC) analysis.^[2]The index is defined for all points of an ROC curve, and the maximum value of the index may be used as a criterion for selecting the optimum cut-off point when a diagnostic test gives a numeric rather than a dichotomous result. The index is represented graphically as the height above the chance line, and it is also equivalent to the area under the curve subtended by a single operating point.

該指數圖形上表示為ROC機會線之上的高度。

Youden's index is the probability of an informed decision (as opposed to a random guess) and takes into account all predictions.

約登指數是一個有根據的決策(而不是隨機猜測)的概率，它考慮了所有的預測。

An unrelated but commonly used combination of basic statistics frominformation retrievalis theF-score, being a (possibly weighted) harmonic mean of

recall and precisionwhererecall=sensitivity= true positive rate, butspecificityandprecisionare totally different measures. F-score, like recall and precision, only considers the so-called positive predictions, with recall being the probability of predicting just the positive class, precision being the probability of a positive prediction being correct, and F-score equating these probabilities under the effective assumption that the positive labels and the positive predictions should have the same distribution andprevalence,^[3]similar to the assumption underlying ofFleiss' kappa. Youden's J, Informedness, Recall, Precision and F-score are intrinsically undirectional, aiming to assess thedeductiveeffectiveness of predictions in the direction proposed by a rule, theory or classifier. Markedness (deltaP) is Youden's J used to assess the reverse orabductivedirection,^[3][6]and matches well human learning ofassociations; rules and,superstitionsas we model possiblecausation;^[4]while correlation and kappa evaluate bidirectionally.

Matthews correlation coefficientis thegeometric meanof theregression coefficientof the problem and itsdual, where the component regression coefficients of the Matthews correlation coefficient areMarkedness(inverse of Youden's J or deltaP) and informedness (Youden's J or deltaP'). Kappa statistics such asFleiss' kappaandCohen's kappaare methods for calculatinginter-rater reliabilitybased on different assumptions about the marginal or prior distributions, and are increasingly used aschance correctedalternatives toaccuracyin other contexts.Fleiss' kappa, like F-score, assumes that both variables are drawn from the same distribution and thus have the same expected prevalence, whileCohen's kappaassumes that the variables are drawn from distinct distributions and referenced to a model ofexpectationthat assumesprevalencesare independent.^[6]

When the trueprevalencesfor the two positive variables are equal as assumed in Fleiss kappa and F-score, that is the number of positive predictions matches the number of positive classes in the dichotomous (two class) case, the different kappa and correlation measure collapse to identity with Youden's J, and recall, precision and F-score are similarly identical withaccuracy.^[3][6]

來自：https://en.wikipedia.ahau.cf/wiki/Youden%27s_J_statistic

快去成為你想要的樣子！