[R-sig-ME] Duplicating meta-regression results from PROC MIXED with lmer

[Viechtbauer Wolfgang (STAT)]

I have not followed the discussion fully, but I have a hunch that may be useful to examine. 

Suppose you want to meta-analyze k 2x2 table data using the odds ratio as the outcome measure. One approach is to calculate the log odds ratio with the corresponding sampling variances (or to be precise: estimates thereof) for those k tables and apply one of the usual meta-analytic models. Moderators can be added and van Houwelingen, Arends, and Stijnen (2002) nicely demonstrate how those types of models can be fitted with SAS.

An alternative approach is not to rely on the normal approximation and instead formulate a logistic regression model. An "equivalent" fixed-effects model then should include *dummy variables for the k tables* and a dummy variable for the group variable (e.g., bcg vaccinated = 1; not bcg vaccinated = 0). A constant term should also be in the model. If you want to add a moderator variable to this model, then one should add *the interaction between the group variable and the moderator variable* to the model (but NOT the main effect for the moderator variable, since then the model would be overparameterized).

If one wants a random-effects model, one should STILL add the *dummy variables for the k tables* and the dummy variable for the group variable, plus a random effect along with that group dummy variable (so that we get a random treatment effect). Again, moderators are included via an interaction term between the moderator variable and the group variable.

These could be considered the "equivalent" models to the usual meta-anaytic fixed-, random-, and mixed-effects models. 

As far as I can tell, Brant, there are no dummies in your model for the tables. Give that a try. And then, when you throw in moderators, just include the interaction between the moderator and the bcg variable. I'll be interested in what you find!

Best,

-- 
Wolfgang Viechtbauer
 Department of Methodology and Statistics
 University of Maastricht, The Netherlands
 http://www.wvbauer.com/