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# The Conditional Random-Effects Variance Component in Meta-regression PowerPoint PPT Presentation

The Conditional Random-Effects Variance Component in Meta-regression. Michael T. Brannick Guy Cafri University of South Florida. Background. What is the random-effects variance component (REVC)? What is the conditional random-effects variance component (CREVC)?

The Conditional Random-Effects Variance Component in Meta-regression

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## The Conditional Random-Effects Variance Component in Meta-regression

Michael T. Brannick

Guy Cafri

University of South Florida

### 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!)

Fixed

Mixed

CREVC = 0

CREVC > 0

### 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)

• Bias

• RMSE

• Type I error

• Power

• Coverage probability

• Width

### 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

### Results – Point Estimates

Note: results are averages over cells

Method of moments is less biased than max like until k > 100

### Results – Point Estimates

Meta-analysis results for one cell

(10k trials for each method)

### Results – Confidence Intervals

Bias corrected bootstrap has best coverage; similar width

Coverage

Width

### 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

### 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