title: Methods for calculating confidence and credible intervals for the residual between-study variance in random effects meta-regression models.
abstract: BACKGROUND
  Meta-regression is becoming increasingly used to model study level covariate effects. However this type of statistical analysis presents many difficulties and challenges. Here two methods for calculating confidence intervals for the magnitude of the residual between-study variance in random effects meta-regression models are developed. A further suggestion for calculating credible intervals using informative prior distributions for the residual between-study variance is presented.
  
  
  METHODS
  Two recently proposed and, under the assumptions of the random effects model, exact methods for constructing confidence intervals for the between-study variance in random effects meta-analyses are extended to the meta-regression setting. The use of Generalised Cochran heterogeneity statistics is extended to the meta-regression setting and a Newton-Raphson procedure is developed to implement the Q profile method for meta-analysis and meta-regression. WinBUGS is used to implement informative priors for the residual between-study variance in the context of Bayesian meta-regressions.
  
  
  RESULTS
  Results are obtained for two contrasting examples, where the first example involves a binary covariate and the second involves a continuous covariate. Intervals for the residual between-study variance are wide for both examples.
  
  
  CONCLUSIONS
  Statistical methods, and R computer software, are available to compute exact confidence intervals for the residual between-study variance under the random effects model for meta-regression. These frequentist methods are almost as easily implemented as their established counterparts for meta-analysis. Bayesian meta-regressions are also easily performed by analysts who are comfortable using WinBUGS. Estimates of the residual between-study variance in random effects meta-regressions should be routinely reported and accompanied by some measure of their uncertainty. Confidence and/or credible intervals are well-suited to this purpose.
authors.affiliation: MRC Biostatistics Unit, Cambridge, UK. dan.jackson@mrc-bsu.cam.ac.uk.
authors.forename: Dan
authors.initials: D
authors.lastname: Jackson
authors.forename: Rebecca
authors.initials: R
authors.lastname: Turner
authors.forename: Kirsty
authors.initials: K
authors.lastname: Rhodes
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Viechtbauer
mesh_terms: D000082:Acetaminophen / Q000627:therapeutic use*; D000704:Analysis of Variance; D001499:Bayes Theorem; D016001:Confidence Intervals; D006801:Humans; D015233:Models, Statistical; D008964:Molar, Third; D010146:Pain / Q000188:drug therapy*; D059408:Pain Management / Q000379:methods*; D012044:Regression Analysis; D014081:Tooth Extraction
chemical_list: D000082:Acetaminophen