Approximate Bayesian inference for random effects meta-analysis

Statistics in Medicine

Volumn 17, Issue 2, 1998, Pages 201-218

  Abrams, Keith ^a   Sansó, Bruno ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BAYES THEOREM; MATHEMATICAL COMPUTING; META ANALYSIS; SAMPLING;

ANTIBIOTIC PROPHYLAXIS; BAYES THEOREM; DENTAL CARIES; DENTIFRICES; DIGESTIVE SYSTEM; HUMANS; LOGISTIC MODELS; META-ANALYSIS; MODELS, STATISTICAL; ODDS RATIO;

EID: 0032579591     PISSN: 02776715     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0258(19980130)17:2<201::AID-SIM736>3.0.CO;2-9     Document Type: Article

References (51)

1. Jones D. R. 'Meta-analysis: weighing the evidence', Statistics in Medicine, 14, 137-149 (1995).
2. Fleiss, J. L. 'The statistical basis of meta-analysis', Statistical Methods in Medical Research, 2, 121-145 (1993).
3. Cochran, W. G. 'Problems arising in the analysis of a series of similar experiments', Journal of the Royal Statistical Society, 4, 102-118 supplement (1937).
4. Rao, P. S. R. S., Kaplan, J. and Cochran, W. G. 'Estimators for the one-way random effects model with unequal error variances', Journal of the American Statistical Association, 76(373), 89-97 (1981).
5. DerSimonian, R. D. and Laird, N. 'Meta-analysis in clinical trials', Controlled Clinical Trials, 7, 177-188 (1986).
6. Whitehead, A. and Whitehead, J. 'A general parametric approach to meta-analysis of randomised clinical trials', Statistics in Medicine, 10, 1665-1677 (1991).
7. Thompson, S. G. 'Why sources of heterogeneity in meta-analysis should be investigated', British Medical Journal, 309, 1351-1355 (1994).
8. Breslow, N. E. and Clayton, D. G. 'Approximate inference in generalized linear mixed models', Journal of the American Statistical Association, 88, 9-25 (1993).
9. DuMouchel, W. 'Bayesian meta analysis, in Berry, D. (ed.), Statistical Methodology in Pharmaceutical Sciences, Marcel-Dekker, New York, 1990, pp. 509-529.
10. Morris, C. 'Parametric Empirical Bayes inference: theory and applications (with discussion)', Journal of the American Statistical Association, 78, 47-65 (1983).
11. Carlin, J. B. 'Meta-analysis for 2 x 2 tables: a Bayesian approach', Statistic in Medicine, 11, 141-158 (1992).
12. Lambert, P. C. and Abrams, K. R. 'Meta-analysis using multi-level models', ML3 Newsletter, 7, 2, 17-19 (1995).
13. Hardy, R. J. and Thompson, S. G. 'A likelihood approach to meta-analysis with random effects', Statistics in Medicine, 15(6), 619-629 (1996).
14. Lau, J., Antman, E. M., Jimenez-Silva, J., Kupelnick, B., Mosteller, F. and Chlmers, T. C. 'Cumulative meta-analysis of therapeutic trials for myocardial infarction', New England Journal of Medicine, 327, 248-254 (1992).
15. DuMouchel, W. and Harris, J. E. 'Bayes methods for combining the results of cancer studies in humans and other species', Journal of the American Statistical Association, 78, 293-315 (1983).
16. Pocock, S. J. and Hughes, M. D. 'Estimation issues in clinical trials and overviews', Statistics in Medicine, 9, 657-671 (1990).
17. Morris, C. N. and Mormand, S. L. 'Hierarchical models for combining information and for meta-analysis', in Bernardo, J. M., Berger, J. O., Lindsey, D. V. and Smith, A. F. M. (eds), Bayesian Statistics 4, Oxford University Press, Oxford, 1992.
18. Malec, D. and Sedransk, J. 'Bayesian methodology for combining the results from dofferent experiments when the specifications for pooling are uncertain', Biometrica, 79(3), 593-601 (1992).
19. Lindsey, D. V. and Smith, A. F. M. 'Bayes estimates for the linear model (with discusion)', Journal of the Royal Statistical Society, Series A, 34, 1-41 (1972).
20. Skene, A. M. and Wakefield, J. C. 'Hierarchical models for multicentre binary response studies', Statistics in Medicine, 9, 919-929 (1990).
21. Rogatko, A. 'Bayesian approach for meta-analysis of controlled clinical trials', Communication in Statistics - Theory and Methods, 21, 1441-1462 (1991).
22. Smith, T., Spiegelhalter, D. J. and Thomas, A. Bayesian graphical modelling fro random-effects meta-analysis: a comparative study', Statistics in Medicine, 14(24), 2685-2699 (1995).
23. Tierney, L. and Kadane, J. B. 'Accurate approximations for posterior moments and marginal densities', Journal of the American Statisitcal Association, 81, 82-86 (1986).
24. Lindley, D. V. 'The estimation of many parameters', in Godamle, V. P. and Sprott, D. A. (eds), Foundations of Statistics Inferrence, 1971, pp. 435-455.
25. Gelfand, A. E., and Smith, A. F. m. 'Sampling-based approaches to calculating narginal densities', Journal of the American Statistical Association, 85, 398-409 (1990).
26. Digestive Tract Trialists' Collaborative Group, 'Meta-analysis of randormised controlled trials of selective decontamination of the digestive tract', British Medical Journal, 307, 525-532 (1993).
27. Smith, T. C., Spiegelhalter, D. J. and Parmar, M. K. B. 'Bayesian meta-analysis of randomised trials using graphical models and BUGS', in Berry, D. and Stangl, D. (eds), Bayesian Biostatistics, Marcel Dekker, Oxford, 1995, pp. 411-427.
28. Johnson, M. F. 'Comparative efficacy of NaF and SMFP dentifrices in caries prevention; a meta-analytic overview', Caries Research, 27, 328-336 (1993).
29. Cohen, B. and Kramer, I. R. H. Scientific Foundations of Dentistry, William Heinemann, London, 1976.
30. Cox, D. R. and Snell, E. J. Analysis of Binary Data, 2nd edn, Chapman and Hall, London, 1989.
31. Raiffa, H. and Schlaifer, R. Applied Statistical Decision Theory, Havard Business School, Boston, 1961.
32. Box, G. E. P. and Tiao, G. C. 'Bayesian estimation of means for the random effects model', Journal of the American Statistics Association, 63, 174-181 (1968).
33. Box, G. E. P. and Tiao, G. C. Bayesian Inference in Statistical Analysis, Addison-Wesley, Massachusetts, 1973 .
34. Bernardo, J. M. and Smith, A. F. M. Bayesian Theory, Wiley, Chichester, 1994.
35. Sansó, B. 'Approximations for the posterior moments of the location of a normal likelihood with unknown scale', Technical Report 94-01, CESMa, Universidad Simón Bolivar, 1994.
36. Harville, D. A. 'Maximum likelihood approaches to variance component estimation and to related problems', Journal of the American Statistical Association, 72, 320-338 (1977).
37. Smith, A. F. M. and Roberts, G. O. 'Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods', Journal of the Royal Statistical Society, Series B, 55, 3-23 (1993).
38. Eddy, D. M., Hasselblad, V. and Shachter, R. 'A Bayesian method for synthesizing evidence: the Confidence Profile Method', International Journal of Technology Assessment in Health Care, 6, 31-55 (1990).
39. Smith, T. C., Abrams, K. R. and Jones, D. R. 'Hierarchical models in generalised synthesis of evidence - a breast cancer screening example' Technical Report (Statistics) 95-02, Department of Epidemiology and Public Health, University of Leicester, 1995.
40. Davey-Smith, G., Song, F. and Sheldon, T. 'Cholesterol lowering and mortality: the importance of considering initial level of risk', British Medical Journal, 306, 1367-1373 (1993).
41. Thompson, S. G. and Pocock, S. J. 'Can meta-analyses be trusted?', Lancet, 338, 1127-1130 (1991).
42. Kass, R. R. 'Bayes factors in practice', Statistician, 42, 551-560 (1993).
43. Berger, J. O. and Pericchi, L. R. 'The intrinsic Bayes factor for linear models', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 5, Oxford University Press, Oxford, 1996, pp. 25-44.
44. Abrams, K. R. and Sansó, B. 'Model discrimination in meta-analysis - a Bayesian perspective', Technical Report (Statistics) 95-03, Department of Epidemiology and Public Health, University of Leicester, 1995.
45. Gilks, W. R., Thomas, A. and Spiegelhalter, D. J. 'A language and program for complex Bayesian modelling', Statistician, 43(1), 169-178 (1994).
46. Geweke, J. 'Evaluating the accuracy of sampling based approaches to the calculation of posterior moments', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 169-193.
47. Roberts, G. O. 'Convergence diagnostics of the Gibbs sampler', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 775-782.
48. Raftery, A. E. and Lewis, S. M. 'How many iterations in the Gibbs sampler?', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 763-773.
49. Gelman, A. and Rubin, D. R. 'A single series from the Gibbs sampler provides a false sense of security', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 625-631.
50. O'Hagan, A. Bayesian Inference, Volume 2b of Kendall's Advanced Theory of Statistics, Edward Arnold, London, 1994.
51. Pericchi, L. R. and Sansó, B. 'A note on bounded influence in Bayesian analysis', Biometrika, 82, 1, 223-225 (1995).