Background and Problem
I have a question concerning a meta-analysis combining effects from between- and within-subject designs using log-odds ratios (OR) as the metric of interest. I am familiar with conducting meta-analyses and will be undertaking my calculations in R (using the
lme4 packages). To provide greater context, the studies in question ask research subjects to make a binary decision with respect to a personal preference across one of two conditions. In some cases, each participant is assigned to a single condition (making only a single binary response); in others, each subject takes part in both conditions (making two binary responses). For now, presume I have the raw data in all cases. The issue I face is how best to calculate an OR that is comparable across design and whether I should take the correlation between conditions into account for the within-subject designs.
My Current Approach
I presently use logistic regression to estimate the OR for between-subject designs. The slope represents the OR and the sampling variance can be calculated by squaring the SE of the slope coefficient. Using this approach produces estimates comparable to equations reported in common texts such The Handbook of Research Synthesis and Meta-Analysis, 2nd Edition (p. 243). I then extend this approach to use a multilevel logistic regression model including a random intercept by subject to estimate the OR for within-subject designs while account for the dependency between conditions. The OR and sampling variance are otherwise calculated in the same fashion.
With this in mind, I would like to ask:
- Is it reasonable to meta-analytically aggregate OR calculated using standard and multilevel logistic regression?
- Would it be better to use standard logistic regression for both designs (ignoring the correlation between conditions for the within-subject designs)?