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.

估计曲线下面积 (AUC) 是许多医学和科学领域的重要课题。使用 B 样条函数的回归模型提供了曲线拟合的灵活性，使其适用于具有各种非线性趋势的 AUC 估计。尽管 B 样条方法具有多功能性，但在现有文献中找不到关于使用 B 样条函数的相关 AUC 估计技术及其与现有方法的比较的综合讨论。在本文中，我们使用 B 样条回归和 B 样条回归研究了 AUC 估计，并讨论了相应的推论。我们进行了广泛的蒙特卡罗研究，以评估所提出方法在各种现实药代动力学和分析化学数据设置中的性能。我们表明，无论来自科学和医学研究领域的不同类型的非线性模型如何，所提出的方法都提供了稳健可靠的 AUC 估计。我们提出的方法适用于一般 AUC 估计，因为它不需要与指定模型相对应的非线性模型规范和推理技术。