The optimal linear combination of multiple predictors under the generalized linear models

Multiple alternative diagnostic tests for one disease are commonly available to clinicians. It is important to use all the good diagnostic predictors simultaneously to establish a new predictor with higher statistical utility. Under the generalized linear model for binary outcomes, the linear combination of multiple predictors in the link function is proved optimal in the sense that the area under the receiver operating characteristic (ROC) curve of this combination is the largest among all possible linear combinations. The result was applied to analysis of the data from the Study of Osteoporotic Fractures (SOF) in comparison with Su and Liu's approach.