What is so special about random effects?


Apologies for the rather glib answer, but this blog is not aimed at my fellow statisticians for whom issues around power, parsimony, computational efficiency, and distributional assumptions keep them awake at night. Nor should these issues be ignored when we are thinking about the design of a study or the analysis methods to use. However, if you are trying to understand what a random effect is doing when it has been applied to a set of data then this blog is for you, and the answer is nothing special.

In health services research our data are often structured by the very health service that we are trying to understand. A prime example is the work we do with the General Practice Patient Survey where the data are structured as patient responses within general practices. This structure is something we often model using a random effect for general practice, but what does the random effect do?

One of the main assumptions in nearly every statistical test is the assumption of conditional independence, i.e. conditional on the things you account for in the model your observations are independent of one another. In the example of the General Practice Patient Survey individuals at the same practice are more likely to give similar answers to each other than individuals at different practices and so without accounting for practice the observations will not be conditionally independent. A random effect is one way of accounting for this, but there are other ways (such as using as scaling standard errors or using General Estimating Equations). What these other methods don’t do but a random effect does is to adjust your model for practice so that differences estimated are within cluster (in this case practice) differences. This is often discussed under the umbrella term of adjusting for clustering, but is essentially adjusting for confounding by cluster (arguments about causal pathways notwithstanding). In the same way as adjusting for gender (with a fixed effect) will allow you to see the effect of another variable whilst gender is held constant, adjusting for practice allows you to see the effect of another variable when practice is held constant. In other words you will be looking at differences for patients at the same practice.

An example can be found in this paper by Yoryos Lyratzopoulos using the General Practice Patient Survey to estimate socio-demographic differences in patient experience of primary care. As part of this they wanted to see whether or not patients from ethnic minorities systematically report worse experiences than white British patients. Without adjusting for practice they found this to be true. However, it may be the case that this is only true because patients from ethnic minority backgrounds are more likely to attend (or are clustered within) poorly performing practices. Indeed, when adjustment was made for practice, using a random effect, the differences between ethnic minority and white British patients was substantially attenuated. In the case of black African patients this attenuation was 94%. In other words the difference in reported patient experience scores between black African and white British patients was confounded by practice such that it almost disappeared when adjustment for practice was made.

Please don’t read this and go away with the thought that random effects are a waste of time; they are very powerful tools. However, if you are simply trying to understand what they do, thinking of them as any other adjuster will get you a long way.

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