# Is it possible to perform a meta-analysis of multiple outcomes and multiple predictors?

I have a pool of 20-ish quantitative studies that report odds ratios for a particular outcome (e.g. homelessness) but most studies will also report a few more outcomes. All of these studies report the multivariate odds for lots of predictor of these outcomes. I have narrowed down the predictors and outcomes that I am interested in across the 20-ish studies and I am wanting to see the pattern of relationships between predictors and outcomes.

How do I account for having multiple predictors in the meta-analysis? I know that I don't want to do n(outcomes) x n(predictors) univariate meta-analyses or a multi-level meta-analysis to account for correlated and dependent outcomes (which there will be in the sample of studies I have).

The outcome I am looking for is a matrix of effect sizes that would let me see the relationships between a number of variables. For example, I am looking to create a table of odds ratios (and 95% CIs) similar to the following:

Homelessness Outcome B Outcome C Outcome D Outcome E
Predictor A 2.2 [1.8-2.5] 2.2 3.8 0.3 0.2
Predictor B 6 4.2 N/A* 0.5 0.3
Predictor C 2.0 2.4 3.2 0.3 0.1
Predictor D 0.4 0.1 N/A 5.2 3.8
Predictor E 0.1 0.3 N/A 4.4 9.6
• N/A = not enough studies to perform a meta-analysis

#### Approach

Probably the most flexible framework for meta-analysis would be meta-analytic structural equation modeling (MASEM). MASEM essentially merges meta-analysis and structural equation modeling (SEM), wherein you enter effect sizes (usually correlations) from multiple studies into a covariance matrix and then construct regression paths based off what pre-specified relationships are considered. In this sense it would help you for your suggested use-case, as it allows you to estimate as many predictors and outcomes as you want (versus a normal bivariate meta-analysis).

MASEM requires a heavy understanding of regression, meta-analysis, and SEM. I would definitely recommend educating yourself on all these topics before conducting one. If you don't have a strong math background, I recommend reading Gelman's Regression and Other Studies, Kline's Principles and Practice of Structural Equation Modeling, and the the articles on MASEM linked below. The MASEM articles sometimes have Supplementary Materials that include the R code necessary for running an analysis. I also know that Instats has an excellent course on this topic which includes many readings and explanation about what MASEM is and is taught by the principal author of this technique.

#### Related Works

• Cheung, M. W.-L. (2015). metaSEM: An R package for meta-analysis using structural equation modeling. Frontiers in Psychology, 5. https://doi.org/10.3389/fpsyg.2014.01521
• Cheung, M. W.-L., & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10(1), 40–64. https://doi.org/10.1037/1082-989X.10.1.40
• Gelman, A., Hill, J., & Vehtari, A. (2022). Regression and other stories. Cambridge University Press.
• Jak, S., & Cheung, M. W.-L. (2020). Meta-analytic structural equation modeling with moderating effects on SEM parameters. Psychological Methods, 25(4), 430–455. https://doi.org/10.1037/met0000245
• Kline, R. B. (2023). Principles and practice of structural equation modeling (5th ed.). The Guilford Press.
• Valentine, J. C., Cheung, M. W.-L., Smith, E. J., Alexander, O., Hatton, J. M., Hong, R. Y., Huckaby, L. T., Patton, S. C., Pössel, P., & Seely, H. D. (2022). A primer on meta-analytic structural equation modeling: The case of depression. Prevention Science, 23(3), 346–365. https://doi.org/10.1007/s11121-021-01298-5