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On the Q statistic with constant weights in meta-analysis of binary outcomes
Elena Kulinskaya1, David C Hoaglin2
1School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ, Norwich, UK. e.kulinskaya@uea.ac.uk.
BMC Medical Research Methodology
|June 21, 2023
Summary
This study introduces a new Q statistic for meta-analysis heterogeneity testing, using sample sizes instead of estimated variances. Recommended approximations improve accuracy for log-odds-ratio, log-relative-risk, and risk difference measures.
Area of Science:
- Biostatistics
- Medical Research Methodology
- Statistical Modeling
Background:
- Cochran's Q statistic is standard for meta-analysis heterogeneity testing.
- Current methods often use estimated variances in weights, complicating distribution approximations.
- This complexity impacts the accuracy of between-study variance estimators.
Approach:
- Investigated an alternative Q statistic using constant weights based on sample sizes.
- Evaluated distribution approximations for this new statistic and the standard Q statistic via simulation.
- Focused on log-odds-ratio (LOR), log-relative-risk (LRR), and risk difference (RD) effect measures.
Key Points:
- For LOR and LRR, gamma and Farebrother approximations are effective for the new Q statistic.
- For RD, the Farebrother approximation shows excellent performance across sample sizes.
- The standard chi-square approximation for Q is inadequate for all three binary effect measures.
Conclusions:
- The standard chi-square approximation for Q is unreliable for binary effect measures.
- Recommended alternative approximations for heterogeneity testing based on the new Q statistic.
- Provided practical guidelines for selecting appropriate tests at the 0.05 significance level.
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