In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional) polynomials and spline-based approaches, are available. Such methods can be systematically compared in simulation studies, which require suitable performance measures to evaluate the accuracy of the estimated curves against the true data-generating functions. Although various measures have been proposed in the literature, no systematic overview exists so far. To fill this gap, we introduce a categorization of performance measures for evaluating estimated non-linear associations between an outcome and continuous predictors. This categorization includes many commonly used measures. The measures can not only be used in simulation studies, but also in application studies to compare different estimates to each other. We further illustrate and compare the behavior of different performance measures through some examples and a Shiny app.

翻译：在回归分析中，连续预测变量与结局之间的关联常被假定为线性。然而，将关联建模为非线性可以改进模型拟合。目前已有许多灵活的建模技术可用，如（分数）多项式及基于样条的方法。此类方法可通过模拟研究进行系统比较，这需要合适的性能度量来评估估计曲线相对于真实数据生成函数的准确性。尽管文献中已提出多种度量指标，但迄今尚无系统的综述。为填补这一空白，本文提出了用于评估结局与连续预测变量间非线性关联估计的性能度量分类体系。该分类涵盖了许多常用度量指标。这些度量不仅可用于模拟研究，亦可在应用研究中用于比较不同估计结果。我们进一步通过若干示例及一个Shiny应用程序演示并比较了不同性能度量的表现特性。