title: The binomial distribution of meta-analysis was preferred to model within-study variability.
abstract: OBJECTIVE
  When studies report proportions such as sensitivity or specificity, it is customary to meta-analyze them using the DerSimonian and Laird random effects model. This method approximates the within-study variability of the proportion by a normal distribution, which may lead to bias for several reasons. Alternatively an exact likelihood approach based on the binomial within-study distribution can be used. This method can easily be performed in standard statistical packages. We investigate the performance of the standard method and the alternative approach.
  
  
  METHODS
  We compare the two approaches through a simulation study, in terms of bias, mean-squared error, and coverage probabilities. We varied the size of the overall sensitivity or specificity, the between-studies variance, the within-study sample sizes, and the number of studies. The methods are illustrated using a published meta-analysis data set.
  
  
  RESULTS
  The exact likelihood approach performs always better than the approximate approach and gives unbiased estimates. The coverage probability, in particular for the profile likelihood, is also reasonably acceptable. In contrast, the approximate approach gives huge bias with very poor coverage probability in many cases.
  
  
  CONCLUSIONS
  The exact likelihood approach is the method of preference and should be used whenever feasible.
authors: Department of Epidemiology and Biostatistics, Erasmus MC-Erasmus University Medical Center, Rotterdam, The Netherlands. t.hussienhamza@erasmusmc.nl
authors: Taye H
authors: TH
authors: Hamza
authors: Hans C
authors: HC
authors: van Houwelingen
authors: Theo
authors: T
authors: Stijnen
mesh_terms: D000544:Alzheimer Disease / Q000000981:diagnostic imaging; D016010:Binomial Distribution; D003627:Data Interpretation, Statistical; D019937:Diagnostic Techniques and Procedures; D019788:Fluorodeoxyglucose F18; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D049268:Positron-Emission Tomography; D019275:Radiopharmaceuticals
chemical_list: D019275:Radiopharmaceuticals; D019788:Fluorodeoxyglucose F18