# Do you have longitudinal, multilevel, or repeated measures data? Take advantage of mixed effects models

3 mins

Mixed effects models are statistical tools designed to handle complex data structures commonly encountered in biomedical research. They’re like your Swiss Army knife for analyzing data with repeated measurements or nested data, such as longitudinal studies or experiments involving multiple subjects or centers.

At their core, mixed effects models can simultaneously capture both fixed effects (like treatment effects or covariates) and random effects (variations between subjects, time points, or any other grouping factor). This makes them incredibly versatile and powerful.

## Types of Mixed Effects Models

Let’s take a look at some of the most popular mixed effects models used in biomedical research.

### Linear Mixed Effects Model

A linear mixed effects model combines elements of both linear regression (fixed effects) and mixed effects models (random effects). Fixed effects represent population-level parameters and capture the average relationships between predictor variables and the response variable. Random effects account for subject-specific variations or hierarchical structure in the data. Random effects allow for the modeling of correlations within groups, such as repeated measurements on the same subjects. Take a look at how Murphy et al. (2022) used linear mixed effects models to analyze longitudinal data on growth trajectories in mice.

### Nonlinear Mixed-Effects Model (NLMEM)

This model allows for non-linear relationships between predictors and responses. It’s used when the relationship between variables isn’t linear. NLMEM includes both fixed effects (population-level parameters) and random effects (subject-specific variations). It’s commonly used for modeling longitudinal data with non-linear trends. For example, see how Bilgel et al. (2016) used NLMEM to analyze longitudinal neuroimaging data.

### Generalized Linear Mixed Model (GLMM)

A GLMM is a flexible modeling approach used when the response variable is not normally distributed or when there are non-constant variances. GLMMs are useful for analyzing data with hierarchical or nested structures, count data, binary data, or other non-Gaussian response types while accounting for random variability. Take a look at how Wang et al. (2017) used GLMM to investigate urban-rural differences in factors affecting colorectal cancer screening.

These three models cater to different types of data and research questions, providing researchers with a toolbox of options to choose from when analyzing and interpreting their data.

## Assumptions Underlying Mixed Effects Models

Despite being very versatile, mixed effects models need certain conditions to be fulfilled if you want robust and reliable results. Here are some crucial assumptions you need to check for:

1. Independence of Observations: The observations within each group (defined by random effects, such as subjects or clusters) should be independent of each other. Violating this assumption can lead to biased parameter estimates and incorrect inferences.

2. Homoscedasticity: This assumption implies that the variance of the errors (residuals) is constant across all levels of the random effects. Heteroscedasticity[MR1]  (varying variance) can impact the accuracy of parameter estimates, so it’s important to check for this.
3. Independence of Fixed and Random Effects: The fixed effects (population-level parameters) and random effects (subject-specific variations) should be independent of each other. This assumption ensures that random effects capture unique variations beyond the fixed effects.
4. Absence of Multicollinearity: Just like in traditional linear models, multicollinearity (high correlation between predictor variables) can be problematic. It can make it challenging to estimate the individual effects of predictors accurately.
5. Non-informative Missing Data: If data are missing, it’s assumed to be missing at random, meaning that the probability of missingness is unrelated to the unobserved values themselves. Biased missing data can affect model estimates.

Keep in mind that while these assumptions are important to consider, mixed effects models are relatively robust and flexible, allowing for some deviations from these assumptions. But it’s good practice to assess and report on the extent to which these assumptions hold in your specific dataset, as violations can impact the reliability of your results and interpretations.

## Advantages of Mixed Effects Models

What makes mixed effects models so appealing to biomedical researchers? Take a look at some of their advantages:

• Handling Hierarchical Data: Biomedical data often have a hierarchical structure, with measurements nested within subjects or groups. Mixed effects models can model this hierarchy, accounting for correlations within and between groups.

• Efficient Use of Data: They make efficient use of all available data, even when some observations are missing or irregularly spaced. This is crucial in longitudinal studies where subjects may drop out or have varying follow-up times.
• Reduced Bias: By accounting for random effects, mixed effects models can reduce bias in parameter estimates, leading to more accurate results compared to traditional linear models.
• Increased Power: These models can improve statistical power by reducing variability due to individual differences, making it easier to detect true effects, especially in small sample sizes.
• Flexibility: Mixed effects models can handle various types of response variables, including continuous, binary, or count data, making them adaptable to a wide range of biomedical research scenarios.

## Disadvantages of Mixed Effects Models

• Complexity: They can be challenging to set up and interpret, especially for researchers new to the technique. Proper training and software are essential.

• Computational Resources: Running mixed effects models can be computationally intensive, especially for large datasets. This may require access to powerful computers or clusters.

• Assumptions: Like any statistical model, mixed effects models rely on certain assumptions, as described earlier. Violating these assumptions can lead to incorrect inferences, so it’s essential to check them carefully.
• Data Requirements: They work best with a sufficient number of observations per group or subject. In cases with very few data points per group, results may be unreliable.

## Applications of Mixed Effects Models in Biomedical Research

Mixed effects models are versatile and have found numerous applications in our field:

• Clinical Trials: They are widely used to analyze data from clinical trials, accounting for patient-specific variability and repeated measurements over time.

• Longitudinal Studies: Whether it’s tracking changes in biomarkers over time or monitoring disease progression, mixed effects models are invaluable for analyzing longitudinal data.
• Pharmacokinetics: In drug development, they help model the concentration-time profiles of drugs in the body, aiding in dose optimization and safety assessments.
• Genetics: Analyzing genetic data can involve modeling the effects of multiple genes, family relationships, or repeated measurements within individuals, all of which mixed effects models can handle.
• Neuroimaging: In brain research, these models are used to analyze fMRI or EEG data, considering both subject-specific and spatial variability.

## Wrapping Up

In conclusion, mixed effects models are potent tools in biomedical research, enabling us to handle complex data structures, reduce bias, and increase statistical power. While they have their challenges, the benefits they bring to the table are well worth the effort. So, don’t hesitate to explore this fascinating statistical approach and unlock new insights in your research journey.

Ready to leverage the power of mixed effects models in your research project? Get the help of an expert biostatistician under Editage’s Statistical Analysis & Review Services.

### Marisha Fonseca

An editor at heart and perfectionist by disposition, providing solutions for journals, publishers, and universities in areas like alt-text writing and publication consultancy.

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