# Mixed Variable Logistic Regression Model for Assessing Diagnostic Markers in Prostate Cancer

## Keywords:

Diognostic Marker; Logistic Regression; Prostate Cancer; Receiver Operating Characteristic Curve; Youden## Abstract

**Communication in Physical Sciences 1(1):77-85**

**Author: Fidelis .I. Ugwuowo**

When a diagnostic test is based on so,^{t}ne observed variable, an assessntent of the overall value of the test can be made through the use of receiver operating characteristic (ROC) curve. We present the methodology for assessing some dichotomous and continuous variable in a diagnostic process. The approach uses logistic regression (LR) model to obtain the best linear combination of Inarkers. The area under the ROC cun•e of this contbination is maxinüsed among all possible linear conibinations. We further dentonstrate using confusion nuztrix and Youden Index (YI) that the discrintinating power of this nudtiple jnarker combination is higher than for all other contbinations. The corresponding optinuun critical threshold value to the Youden Index is derived for all possible combinations. Finally, an illustration of this methodology is given using prostate cancer diagnostic data fronl University of Nigeria Teaching Hospital (UNTH) Enugu.

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