Analyzing Clustered Data: Why and How to Account for Multiple Observations Nested within a Study Participant?

Abstract

A conventional study design among medical and biological experimentalists involves collecting multiple measurements from a study subject. For example, experiments utilizing mouse models in neuroscience often involve collecting multiple neuron measurements per mouse to increase the number of observations without requiring a large number of mice. This leads to a form of statistical dependence referred to as clustering. Inappropriate analyses of clustered data have resulted in several recent critiques of neuroscience research that suggest the bar for statistical analyses within the field is set too low. We compare naïve analytical approaches to marginal, fixed-effect, and mixed-effect models and provide guidelines for when each of these models is most appropriate based on study design. We demonstrate the influence of clustering on a between-mouse treatment effect, a within-mouse treatment effect, and an interaction effect between the two. Our analyses demonstrate that these statistical approaches can give substantially different results, primarily when the analyses include a between-mouse treatment effect. In a novel analysis from a neuroscience perspective, we also refine the mixed-effect approach through the inclusion of an aggregate mouse-level counterpart to a within-mouse (neuron level) treatment as an additional predictor by adapting an advanced modeling technique that has been used in social science research and show that this yields more informative results. Based on these findings, we emphasize the importance of appropriate analyses of clustered data, and we aim for this work to serve as a resource for when one is deciding which approach will work best for a given study.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Fig 1. Experimental design underlying the neuroscience dataset.

The mouse-level treatment was fatty acid delivery, vehicle control, or no treatment. The neuron-level treatment was Pten or control shRNA. The two levels of treatment resulted in a hierarchical study design with a between-mouse and within-mouse treatment factor.

Fig 2. Visualization of clustered data.

(A) Visualization of a between-mouse factor. Each point represents the mean soma size of a mouse ± standard error (SE). [SE = standard deviation (mean soma size)]. (B) Visualization of a within-mouse factor. Each point represents the soma size of an individual neuron within a mouse. The colors correspond to the mouse to which the neurons belonged. Each mouse has neurons with control and Pten shRNA. (C) Visualization of an interaction effect between the within-mouse and between-mouse factor. The red dotted line represents the vehicle control mice and the blue solid line represents the fatty acid delivery mice. Pten knockdown status 0 = control shRNA and 1 = Pten shRNA. The black dotted line depicts the expected result if there were no interaction effect, and the space between the black dotted line and the blue line, denoted by the curly bracket, represents the size of the interaction effect.

Fig 3. Main decision points for statistical analysis of clustered data.

The flow chart outlines the primary questions researchers should address when weighing options of statistical research design of a study with clustered data. *Readers should refer to Table 2 for subtler differences between the marginal and mixed-effect model.