Approximate Bayesian inference for random effects meta-analysis.

Whilst meta-analysis is becoming a more commonplace statistical technique, Bayesian inference in meta-analysis requires complex computational techniques to be routinely applied. We consider simple approximations for the first and second moments of the parameters of a Bayesian random effects model for meta-analysis. These computationally inexpensive methods are based on simple analytical formulae that provide an efficient tool for a qualitative analysis and a quick numerical estimation of posterior quantities. They are shown to lead to sensible approximations in two examples of meta-analyses and to be in broad agreement with the more computationally intensive Gibbs sampling.

[1]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[2]  Ross D. Shachter,et al.  A Bayesian Method for Synthesizing Evidence: The Confidence Profile Method , 1990, International Journal of Technology Assessment in Health Care.

[3]  David Lindley,et al.  THE ESTIMATION OF MANY PARAMETERS , 1970 .

[4]  A Whitehead,et al.  A general parametric approach to the meta-analysis of randomized clinical trials. , 1991, Statistics in medicine.

[5]  M. F. Johnson,et al.  Comparative efficacy of NaF and SMFP dentifrices in caries prevention: a meta-analytic overview. , 1993, Caries research.

[6]  T C Chalmers,et al.  Cumulative meta-analysis of therapeutic trials for myocardial infarction. , 1992, The New England journal of medicine.

[7]  F. Song,et al.  Cholesterol lowering and mortality: the importance of considering initial level of risk. , 1993, BMJ.

[8]  S. Pocock,et al.  Estimation issues in clinical trials and overviews. , 1990, Statistics in medicine.

[9]  R. Kass.  Bayes Factors in Practice , 1993 .

[10]  C. Morris.  Parametric Empirical Bayes Inference: Theory and Applications , 1983 .

[11]  Donald Malec,et al.  Bayesian methodology for combining the results from different experiments when the specifications for pooling are uncertain , 1992 .

[12]  A note on bounded influence in Bayesian analysis , 1995 .

[13]  Joong-Kweon Sohn,et al.  Convergence Diagnostics for the Gibbs Sampler , 1996 .

[14]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[15]  André Rogatko,et al.  Bayesian approach for meta - analysis of controlled clinical trials , 1992 .

[16]  J. Carlin.  Meta-analysis for 2 x 2 tables: a Bayesian approach. , 1992, Statistics in medicine.

[17]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[18]  D. Angus,et al.  Selective decontamination of the digestive tract. , 1990 .

[19]  Jack Kaplan,et al.  Estimators for the One-Way Random Effects Model with Unequal Error Variances , 1981 .

[20]  David R. Cox.  The analysis of binary data , 1970 .

[21]  G. C. Tiao,et al.  Bayesian Estimation of Means for the Random Effect Model , 1968 .

[22]  J. Fleiss,et al.  The statistical basis of meta-analysis. , 1993, Statistical methods in medical research.

[23]  S G Thompson,et al.  A likelihood approach to meta-analysis with random effects. , 1996, Statistics in medicine.

[24]  Howard Raiffa,et al.  Applied Statistical Decision Theory. , 1961 .

[25]  J. Fleiss.  Review papers : The statistical basis of meta-analysis , 1993 .

[26]  W. G. Cochran.  Problems arising in the analysis of a series of similar experiments , 1937 .

[27]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[28]  David R. Jones,et al.  Meta-analysis: weighing the evidence. , 1995, Statistics in medicine.

[29]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[30]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[31]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[32]  Bertram Cohen,et al.  Scientific foundations of dentistry , 1976 .

[33]  S G Thompson,et al.  Systematic Review: Why sources of heterogeneity in meta-analysis should be investigated , 1994, BMJ.

[34]  Jeffrey E. Harris,et al.  Bayes Methods for Combining the Results of Cancer Studies in Humans and other Species , 1983 .

[35]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[36]  J C Wakefield,et al.  Hierarchical models for multicentre binary response studies. , 1990, Statistics in medicine.

[37]  Walter R. Gilks,et al.  A Language and Program for Complex Bayesian Modelling , 1994 .

[38]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[39]  S. Pocock,et al.  Can meta-analyses be trusted? , 1991, The Lancet.

[40]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .