Estimation of the area under a curve via several B-spline-based regression methods and applications

Estimating the area under a curve (AUC) is an important subject in many fields of medicine and science. The regression model using B-spline functions provides flexibility in curve fitting, making it suitable for AUC estimation with various types of nonlinear trends. Despite the versatility of the B-spline approach, comprehensive discussions regarding relevant AUC estimation techniques using B-spline functions and their comparison with existing methods cannot be found in extant literature. In this paper, we investigate AUC estimation using B-spline regression and B-spline regression with several penalties, as well as discuss corresponding inferences. We carry out an extensive Monte Carlo study to evaluate the performance of the proposed methods in various realistic pharmacokinetics and analytical chemistry data settings. We show that the proposed methods provide robust and reliable AUC estimation regardless of different types of nonlinear models from scientific and medical research areas. Our proposed method is appropriate for general AUC estimation since it does not require nonlinear model specifications and inference techniques corresponding to the specified model.