# How to choose between fixed-effects and random-effects model in meta-analysis?

In meta-analysis packages, both fixed effects and random effects models are available. How do one choose between these two models? Since one is assessing different studies, should one not choose random effects model all the time?

## 1 Answer

You use a fixed-effects model if you want to make a conditional inference about the average outcome of the $k$ studies included in your analysis. So, any statements you make about the average outcome only pertain to those $k$ studies and you cannot automatically generalize to other studies.

You use a random-effects model if you want to make an unconditional inference about the average outcome in a (typically hypothetical) population of studies from which the $k$ studies included in your analysis are assumed to have come. So, any statements you make about the average outcome in principle pertain to the that entire population of studies (assuming that the $k$ studies included in your meta-analysis are a random sample of the studies in the population or can in some sense be considered to be representative of all of those studies).

A very common misconception is that the fixed-effects model is only appropriate when the true outcomes are homogeneous and that the random-effects model should be used when they are heterogeneous. However, both models are perfectly fine even under heterogeneity -- the crucial distinction is the type of inference you can make (conditional versus unconditional).

In fact, it is also perfectly fine to fit both models: Once to make a statement about the average outcome of those $k$ studies and once to try the more difficult task of making a statement about the average effect 'in general'.

• Thanks for a clear answer. I believe power of any meta-analysis will be less for random-effects model. On the other hand, usually the idea is to find what is happening in the population rather than just in those studies. So I presume that random-effects model needs to be used most of the time. Are there any circumstances when fixed effects model is appropriate and random-effects model is not? – rnso Jun 12 '15 at 10:13
• "When you want to make a conditional inference about the average outcome of the $k$ studies included in your analysis." Yes, I am repeating my answer, but that's a circumstance when a fixed-effects model is appropriate and a random-effects model is not. – Wolfgang Jun 13 '15 at 12:29
• Might you be able to cite a good paper or link which gives an example of the two types of inferences at a step-by-step level? – cerd Mar 3 '16 at 13:51