title: Pooling overdispersed binomial data to estimate event rate.
abstract: BACKGROUND
  The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research.
  
  
  METHODS
  We describe the statistical theories behind the beta-binomial model and the associated estimation methods. We supply information about statistical software that can provide beta-binomial estimations. Using a published example, we illustrate the application of the beta-binomial model when pooling overdispersed binomial data.
  
  
  RESULTS
  In an example regarding the safety of oral antifungal treatments, we had 41 treatment arms with event rates varying from 0% to 13.89%. Using the beta-binomial model, we obtained a summary event rate of 3.44% with a standard error of 0.59%. The parameters of the beta-binomial model took the values of 1.24 for alpha and 34.73 for beta.
  
  
  CONCLUSIONS
  The beta-binomial model can provide a robust estimate for the summary event rate by pooling overdispersed binomial data from different studies. The explanation of the method and the demonstration of its applications should help researchers incorporate the beta-binomial method as they aggregate probabilities of events from heterogeneous studies.
authors: EpiPatterns, Haverhill, NH, USA. yyoungxu@hotmail.com
authors: Yinong
authors: Y
authors: Young-Xu
authors: K Arnold
authors: KA
authors: Chan
mesh_terms: D000284:Administration, Oral; D000293:Adolescent; D000328:Adult; D000935:Antifungal Agents / Q000008:administration & dosage / Q000009:adverse effects*; D001499:Bayes Theorem; D016010:Binomial Distribution; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D015233:Models, Statistical; D009281:Naphthalenes / Q000008:administration & dosage / Q000009:adverse effects*; D000077291:Terbinafine
chemical_list: D000935:Antifungal Agents; D009281:Naphthalenes; D000077291:Terbinafine