Time‐Dependent <scp>ROC</scp> Curve for Multiple Longitudinal Biomarkers and Its Application in Diagnosing Cardiovascular Events

Since they can help people detect the early signs of diseases, accurate diagnostic techniques based on biomarkers are crucial in biomedical research. This article proposes a novel bivariate time-varying coefficients logistic regression model for addressing the combined longitudinal biomarkers. Using the B-splines method to estimate the proposed model, we can effectively combine multiple longitudinal biomarkers and improve diagnostic accuracy. We show that the proposed method is theoretically consistent. And it exhibits superior performance compared to the existing method, as presented through numerical results. The proposed method is verified in a study on predicting the probability of onset of future cardiovascular events for type 2 diabetic patients. The longitudinal biomarkers, HbA1c and LDL-C, are considered in this study. We demonstrate that the combined longitudinal biomarkers significantly improved disease diagnostic accuracy over only a combination of the latest measured biomarkers in most cases.