Using generalized additive models to analyze biomedical non-linear longitudinal data

Abstract

1AbstractIn 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 in terms of correlation and missing observations, both methodologies share an assumption of linearity in the measured response, which results in biased estimates and unreliable inference when they are used to analyze data where the trends are non-linear, which is a common occurrence in biomedical research.In contrast, generalized additive models (GAMs) relax the linearity assumption, and allow the data to determine the fit of the model while permitting missing observations and different correlation structures. Therefore, GAMs present an excellent choice to analyze non-linear longitudinal data 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 non-linear data. We also present the basic theory of GAMs, and using trends of oxygen saturation in tumors reported in the biomedical literature, we simulate example longitudinal data (2 treatment groups, 10 subjects per group, 6 repeated measures for each group) to demonstrate how these models can be computationally implemented. We show that GAMs are able to produce estimates that are consistent with the trends of biomedical non-linear data even in the case when missing observations exist (with 40% of the observations missing), allowing reliable inference from the data. To make this work reproducible, the code and data used in this paper are available at: https://github.com/aimundo/GAMs-biomedical-research.