Mixed Effects Models: a powerful modelling approach

Longitudinal studies are essential for understanding how treatments impact individuals over time. These studies track changes, observe trends, and enable researchers to make informed decisions about the effectiveness of interventions. However, the challenge in analysing data from these studies arises from the repeated measurements often taken from the same subjects, which introduces complex correlations.

Mixed Effects Models (MEMs) provide a sophisticated and practical solution for exploring these complexities and drawing meaningful conclusions about treatment effects [Gibbons2010].

What Are Mixed Effects Models?

Fundamentally, MEMs are statistical models that have been designed to describe data with non-independent observations better than less sophisticated (and more standard) approaches. In describing the effect of different elements on an outcome variable of interest (blood pressure, for example), MEMs account for both fixed effects, those that are expected to be consistent across all subjects (e.g., treatment type), and random effects, which are subject-dependent (e.g., baseline blood pressure levels). This dual approach grants MEMs significant power.

In longitudinal studies, information is collected at multiple time points, creating dependencies in the data, given that measurements from the same individual over time are likely to be correlated. Traditional statistical models often fail to account for these correlations, potentially leading to biased results. MEMs, however, are explicitly designed to handle such data structures [Brown2021].

Advantages and Limitations of Mixed Effects Models

The beauty of MEMs lies in their flexibility and robustness [Schielzeth2020]. They can manage unbalanced data, where not all subjects have the same number of observations due to missed visits or dropouts, which are common issues in longitudinal studies. MEMs also allow for complex covariance structures, providing a more accurate representation of the underlying data. Moreover, MEMs enable the inclusion of covariates that might explain some of the variability between subjects, such as age, sex, or lifestyle factors. This leads to more precise estimates of treatment effects, ensuring that the conclusions drawn from the study are as accurate as possible.

However, choosing the appropriate random effects structure is critical. Overly simplistic models may not capture the necessary variability among subjects, while overly complex models can lead to overfitting. Additionally, like any statistical model, MEMs rely on certain assumptions. Violations of these assumptions can lead to biased estimates and incorrect inferences. The interpretation of MEMs, particularly understanding the implications of random effects, can be challenging and may lead to misunderstandings [Silk2020].

Current Developments

Recent advancements in statistical methodologies and computational capabilities continue to enhance the utility and efficiency of MEMs: their integration with machine learning algorithms is improving model selection and error estimation [Ngufor2019], and the development of more user-friendly software has made MEMs more accessible [Bates2015, Brooks2017]. The choice of a particular modelling framework is a delicate aspect that scientists should carefully consider depending on the particular research question being asked, and MEMs might not always be the best approach. However, having the ability to employ MEMs for statistical modelling can be a very powerful tool, especially when intricate dependencies in the data are well-established (e.g., due to repeated measurements or the longitudinal nature of a study). 

References

[Gibbons2010] Gibbons RD, Hedeker D, and DuToit S (2010). Advances in Analysis of Longitudinal Data. Annual Review of Clinical Psychology, 6:79-107.

[Brown2021] Brown VA (2021). An introduction to Linear Mixed-Effects Modeling in R. Advances in Methods and Practices in Psychological Science, 4(1).

[Schielzeth2020] Schielzeth H et al (2020). Robustness of linear mixed-effects models to violations of distributional assumptions. Methods in Ecology and Evolution, 11(9), 1141-1152.

[Silk2020] Silk MJ, Harrison XA, Hodgson DJ (2020). Perils and pitfalls of mixed-effects regression models in biology. PeerJ, 8:e9522.

[Ngufor2019] Ngufor C et al (2019). Mixed effect machine learning: A framework for predicting longitudinal change in hemoglobin A1c. Journal of Biomedical Informatics, 89, 56-67.

[Bates2015] Bates D et al (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1-48.

[Brooks2017] Brooks ME et al (2017). glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. The R journal, 9(2), 378-400.