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)?

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The Conditional Random-Effects Variance Component in Meta-regression

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The conditional random effects variance component in meta regression

The Conditional Random-Effects Variance Component in Meta-regression

Michael T. Brannick

Guy Cafri

University of South Florida


Background

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 and mixed regression

Fixed and Mixed Regression

Fixed

Mixed

CREVC = 0

CREVC > 0


Items of interest

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


Monte carlo method

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

Results – Point Estimates

Note: results are averages over cells

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


Results point estimates1

Results – Point Estimates

Meta-analysis results for one cell

(10k trials for each method)


Results significance tests

Results – Significance Tests


Results confidence intervals

Results – Confidence Intervals

Bias corrected bootstrap has best coverage; similar width

Coverage

Width


Implications

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

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


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