The diagnostic accuracy of multiple biomarkers in medical research is crucial for detecting diseases and predicting patient outcomes. An optimal method for combining these biomarkers is essential to maximize the Area Under the Receiver Operating Characteristic (ROC) Curve (AUC). Although the optimality of the likelihood ratio has been proven by Neyman and Pearson, challenges persist in estimating the likelihood ratio, primarily due to the estimation of multivariate density functions. In this study, we propose a non-parametric approach for estimating multivariate density functions by utilizing Smoothing Spline density estimation to approximate the full likelihood function for both diseased and non-diseased groups, which compose the likelihood ratio. Simulation results demonstrate the efficiency of our method compared to other biomarker combination techniques under various settings for generated biomarker values. Additionally, we apply the proposed method to a real-world study aimed at detecting childhood autism spectrum disorder (ASD), showcasing its practical relevance and potential for future applications in medical research.