In biomedical research, the outcome of longitudinal studies has been traditionally analyzed using the repeated measures analysis of variance (rm-ANOVA) or more recently, linear mixed models (LMEMs). Although LMEMs are less restrictive than rm-ANOVA as they can work with unbalanced data and non-constant correlation between observations, both methodologies assume a linear trend in the measured response. It is common in biomedical research that the true trend response is nonlinear and in these cases the linearity assumption of rm-ANOVA and LMEMs can lead to biased estimates and unreliable inference. In contrast, GAMs relax the linearity assumption of rm-ANOVA and LMEMs and allow the data to determine the fit of the model while also permitting incomplete observations and different correlation structures. Therefore, GAMs present an excellent choice to analyze longitudinal data with non-linear trends in the context of biomedical research. This paper summarizes the limitations of rm-ANOVA and LMEMs and uses simulated data to visually show how both methods produce biased estimates when used on data with non-linear trends. We present the basic theory of GAMs and using reported trends of oxygen saturation in tumors, we simulate example longitudinal data (2 treatment groups, 10 subjects per group, 5 repeated measures for each group) to demonstrate their implementation in R. We also show that GAMs are able to produce estimates with non-linear trends even when incomplete observations exist (with 40% of the simulated observations missing). To make this work reproducible, the code and data used in this paper are available at: https://github.com/aimundo/GAMs-biomedical-research.

中文翻译：

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使用 R 分析生物医学纵向数据的非线性趋势的广义相加模型：超越重复测量方差分析和线性混合模型

在生物医学研究中，纵向研究的结果传统上是使用重复测量方差分析(rm-ANOVA) 或最近的线性混合模型(LMEM) 进行分析。尽管 LMEM 比 rm-ANOVA 限制较少，因为它们可以处理不平衡数据和观测值之间的非恒定相关性，但这两种方法都假设测量响应呈线性趋势。在生物医学研究中，真实的趋势响应是非线性的，这种情况很常见，在这些情况下，rm-ANOVA 和 LMEM 的线性假设可能会导致有偏差的估计和不可靠的推断。相比之下，GAM 放宽了 rm-ANOVA 和 LMEM 的线性假设，允许数据确定模型的拟合度，同时还允许不完整的观察和不同的相关结构。因此，GAM 是在生物医学研究背景下分析具有非线性趋势的纵向数据的绝佳选择。本文总结了 rm-ANOVA 和 LMEM 的局限性，并使用模拟数据直观地展示了这两种方法在用于具有非线性趋势的数据时如何产生有偏差的估计。我们介绍了 GAM 的基本理论，并使用报告的肿瘤氧饱和度趋势，模拟示例纵向数据（2 个治疗组，每组 10 名受试者，每组 5 次重复测量）以证明其在 R 中的实施。我们还表明即使存在不完整的观测值（缺少 40% 的模拟观测值），GAM 也能够生成具有非线性趋势的估计值。为了使这项工作具有可重复性，本文中使用的代码和数据可从以下网址获取：https://github.com/aimundo/GAMs-biomedical-research。