We can calculate the estimated sensitivity and specificity for different cutoffs. But how should we judge a patient with a score of 2, 3, or 4? What we set our cutoff for judging a patients as abnormal or normal to determines the sensitivity and specificity of the resulting test. We see that when the predictor is 1, ‘Definitely normal’, the patient is usually normal (true for 33 of the 36 patients), and when it is 5, ‘Definitely abnormal’ the patients is usually abnormal (true for 33 of the 35 patients), so the predictor makes sense.
So there are in total 58 ‘normal’ patients and ‘51’ abnormal ones. The first number on the right is the number of patients with true disease status ‘normal’ and the second number is the number of patients with true disease status ‘abnormal’: They have the following table of disease status and test result (corresponding to, for example, the estimated risk from a logistic model). I would recommend Hanley’s & McNeil’s 1982 paper ‘ The meaning and use of the area under a receiver operating characteristic (ROC) curve’.
I am aware of TP, FP, FN, TN, but not aware of how to calculate the c-statistic given this information. Additionally, if the true retention status of an observation = 0 and the predicted retention status is 0.5. By "correct", if the true retention status of an observation = 1 and the predicted retention status is > 0.5 then that is a "correct" classification.
My initial thoughts were to identify the "correct" number of model classifications and simply divide the number of "correct" observations by the number of total observations to calculate the c-statistic. I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model.įor example, in the validation dataset, I have the true value for the dependent variable, retention (1 = retained 0 = not retained), as well as a predicted retention status for each observation generated by my regression analysis using a model that was built using the training set (this will range from 0 to 1).
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