# How to perform a meta-analysis of regression coefficients?

I want to perform a meta-analysis but the included studies use different models to analyze the data. There are Pearson correlation (3 studies), Spearman correlation (1 study) and several studies (~7-10) with regression coefficients (linear regression, weighted least squares regression, multivariate regression, and so on).

What would be preferable (and possible): a) to use the correlation coefficients. In this case should I ask for data to authors of the remaining articles that didn't use correlation and calculate it, or is there any way of extracting it from the beta coefficient? b) perform a meta-analysis of beta coefficients. Is this possible? How can I analyze such different models?

What can you suggest me?

## 2 Answers

It is perfectly possible to analyse the regression coefficients as long as you have their standard errors. If the authors of the primary studies have given a confidence interval you can use it to back-calculate the standard error. You then need to feed these to your favourite software which will probably ask you for effect size (the coefficient) and either the standard error or the sampling variance (the square of the standard error). The problem now is what to do with the correlations. You could ask the authors if they did regression. If they are really kind they may run it for you specially (yes, there are some nice people out there). Without quite a lot of extra information you would not be able to do this yourself. Converting the Spearman is not going to be possible, you need them to provide the regression. If you cannot get the information you will have to report that fact and leave them out of the meta-analysis.

Regarding the regression coefficients: In this kind of meta analysis I find a simple histrogramm showing the distribution of the coefficients in the different studies to be very informative and easy to do. One gets a clear pictures regarding the different magnitudes of coefficients found. Of course you have to make sure that all the studies use the same scale when analysing the effect of the variable of interest. It would not be valid to compare a log transformed variable with its raw counterpart and so on.

You also have to discuss the different data sets used. The differences in the observed coefficients might simple be a result of different preprocessing steps and sample compositions. But this should in general be an important point to discuss in any meta analysis.

Hope this helps.

With kind regards,

Alex