The Conditional Random-Effects Variance Component in Meta-regression

1. The Conditional Random-Effects Variance Component in Meta-regression Michael T. Brannick Guy Cafri University of South Florida

2. Background • What is the random-effects variance component (REVC)? • What is the conditional random-effects variance component (CREVC)? • Who cares? (Tells whether we are done!)

3. Fixed and Mixed Regression Fixed Mixed CREVC = 0 CREVC > 0

4. Items of Interest Point Estimators of the CREVC Method of Moments (WLS) Maximum Likelihood (iterated WLS) Significance tests Fixed chi-square Random chi-square (2 of these) Lower bound > 0 (3 of these) Confidence Intervals (3 types) ML, bootstrap, bootstrap adjusted • Bias • RMSE • Type I error • Power • Coverage probability • Width

5. Monte Carlo Method • Effect size: d • Conditions (based on literature) • REVC: 0, .04, .10, .19, .35, .52 • Proportion A/C: 0, .02, .18, .50 • K studies: 13, 22, 30, 69, 112, 234 • Average N (skewed): 53, 231, 730 • Reps: 10k times each for 378 cells

6. Results – Point Estimates Note: results are averages over cells Method of moments is less biased than max like until k > 100

7. Results – Point Estimates Meta-analysis results for one cell (10k trials for each method)

8. Results – Significance Tests

9. Results – Confidence Intervals Bias corrected bootstrap has best coverage; similar width Coverage Width

10. Implications • Slight preference for method of moments WLS when k is small • Use the fixed-effects chi-square for testing the CREVC • Use the bias-corrected bootstrap for constructing confidence intervals

11. Conclusions • Please indicate the uncertainty of the estimates when reporting a meta-analysis (confidence intervals and/or standard errors of parameter estimates) • Free software: • http://luna.cas.usf.edu/~mbrannic/files/meta/MetaRegsMB1.sas