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Abstract
In metaanalysis of odds ratios (${\OR}s$), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative random effects model for ${\OR}s$ uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intraclass correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves betadistributed, resulting in betabinomial distributions. We propose two new estimators of the ICC for metaanalysis in this setting. One is based on the inverted BreslowDay test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's $Q$. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the MantelHaenszel approach to estimation of odds ratios is extended to the betabinomial model, and we study performance of various ICC estimators when used in the MantelHaenszel or the inversevariance method to combine odds ratios in metaanalysis. The results of the simulations show that the improved gammabased estimator of ICC is superior for small sample sizes, and the BreslowDaybased estimator is the best for $n\geq100$. The MantelHaenszelbased estimator of ${\OR}$ is very biased and is not recommended. The inversevariance approach is also somewhat biased for ${\OR}s\neq1$, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the betabinomial model a feasible alternative to the standard REM for metaanalysis of odds ratios.
Original language  English 

Pages (fromto)  17151734 
Number of pages  20 
Journal  Statistics in Medicine 
Volume  36 
Issue number  11 
Early online date  25 Jan 2017 
DOIs  
Publication status  Published  20 May 2017 
Keywords
 Intracluster correlation
 odds ratio
 fixedeffect model
 randomeffects model
 betabinomial distribution
 overdispersion
 heterogeneity
Profiles

Elena Kulinskaya
 School of Computing Sciences  Emeritus Professor
 Norwich Epidemiology Centre  Member
 Data Science and Statistics  Member
Person: Honorary, Research Group Member
Projects
 1 Finished

Smart Data Analytics for Business and Local Government
Hancock, R., Sena, V., Coakley, J., Cornford, J., De La Iglesia, B., Fasli, M., Fearne, A., Forder, J., Harwood, A., Hviid, M., Jones, A., Kulinskaya, E., Laurie, H., Lovett, A., Schofield, G., Appleton, K., Morciano, M. & Sunnenberg, G.
Economic and Social Research Council
31/01/14 → 31/10/20
Project: Research