Modeling between-trial variance structure in mixed treatment comparisons

Biostatistics

Volumn 10, Issue 4, 2009, Pages 792-805

  Lu, Guobing ^a   Ades, Ae ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Bayesian hierarchical model; Between trial heterogeneity; Equivalent prior sample method; Evidence consistency; Markov chain Monte Carlo; Mixed treatment comparison meta analysis; Triangle inequality

Indexed keywords

ANALYSIS OF VARIANCE; ARTICLE; BAYES THEOREM; BIOSTATISTICS; CLINICAL TRIAL (TOPIC); COMPARATIVE STUDY; GASTROESOPHAGEAL REFLUX; HUMAN; META ANALYSIS (TOPIC); METHODOLOGY; MONTE CARLO METHOD; PROBABILITY; SMOKING CESSATION; STATISTICAL MODEL; STATISTICS;

ANALYSIS OF VARIANCE; BAYES THEOREM; BIOSTATISTICS; CLINICAL TRIALS AS TOPIC; GASTROESOPHAGEAL REFLUX; HUMANS; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; META-ANALYSIS AS TOPIC; MODELS, STATISTICAL; MONTE CARLO METHOD; SMOKING CESSATION;

EID: 74349083543     PISSN: 14654644     EISSN: 14684357     Source Type: Journal    
DOI: 10.1093/biostatistics/kxp032     Document Type: Article

References (32)

1. ADES, A. E., LU, G. AND HIGGINS, J. P. T. (2005). The interpretation of random effects meta-analysis in decision models. Medical Decision Making 25, 646-654.
2. ANDERSON, T. W., OLKIN, I. AND UNDERHILL, L. G. (1987). Generation of random orthogonal matrices. SIAM Journal on Scientific and Statistical Computing 8, 625-629.
3. BARNARD, J., McCULLOCH, R. AND MENG, X. L. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica 10, 1281-1311.
4. BEDFORD, T. AND COOKE, R. (2001). Probability Risk Analysis: Foundations and Methods. Cambridge: Cambridge University Press.
5. CALDWELL, D. M., ADES, A. E. AND HIGGINS, J. P. T. (2005). Simultaneous comparison of multiple treatments: combining direct and indirect evidence. British Medical Journal 331, 897-900.
6. DANIELS, M. J. AND KASS, R. E. (1999). Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. Journal of the American Statistical Association 94, 1254-1263.
7. DEMPSTER, A. P. (1972). Covariance selection. Biometrics 28, 157-175.
8. EATON, M. L. AND OLKIN, I. (1987). Best equivariant estimators of a Cholesky decomposition. Annals of Statistics 15, 1639-1665.
9. FIORE, M. C., BAILEY, W. C., COHEN, S. J., DORFMAN, S. F., GOLDSTEIN, M. G., GRITZ, E. R., HEYMAN, R. B., HOLBROOK, J., JAEN, C. R., KOTTKE, T. E. and others (1996). Smoking Cessation. Clinical Practice Guideline No. 18. Rockville, MD: Agency for Health Care Policy and Research, U.S. Department of Health and Human Services. AHCPR Publication No. 96-0692.
10. GELMAN, A. (2006). Prior distributions for variance parameters in hierarchical Models. Bayesian Analysis 1, 515-533.
11. GELMAN, A. (2007). Running WinBugs and Open Bugs from R. http://www.stat.columbia.edu/~gelman/bugsR/runningbugs.html.
12. GOEREE, R., O'BRIEN, B., HUNT, R., BLACKHOUSE, G., WILLAN, A. AND WATSON, J. (1999). Economic evaluation of long term management strategies for erosive oesophagitis. Pharmacoeconomics 16, 679-697.
13. HASSELBLAD, V. (1998). Meta-analysis of multi-treatment studies. Medical Decision Making 18, 37-43.
14. HIGGINS, J. P. T. AND WHITEHEAD, A. (1996). Borrowing strength from external trials in a meta-analysis. Statistics in Medicine 15, 2733-2749.
15. LEONARD, T. AND HSU, J. S. (1992). Bayesian inference for a covariance matrix. Annals of Statistics 20, 1669-1696.
16. LIU, C. (1993). Bartlett's decomposition of the posterior distribution of the covariance for normal monotone ignorable missing data. Journal of Multivariate Analysis 46, 497-512.
17. LU, G. AND ADES, A. E. (2004). Combination of direct and indirect evidence in mixed treatment comparisons. Statistics in Medicine 23, 3105-3124.
18. LU, G. AND ADES, A. E. (2006). Assessing evidence inconsistency in mixed treatment comparisons. Journal of the American Statistical Association 101, 447-459.
19. LU, G., ADES, A. E., SUTTON, A. J., COPPER, N. J., BRIGGS, A. H. AND CALDWELL, D. M. (2007). Meta-analysis of mixed treatment comparisons at multiple follow-up times. Statistics in Medicine 26, 3681-3699.
20. LUMLEY, T. (2002). Network meta-analysis for indirect treatment comparisons. Statistics in Medicine 21, 2313-2324.
21. O'HAGAN, A., BUCK, C. E., DANESHKHAH, A., EISER, J. R., GARTHWAITE, P. H., JENKINSON, D. J., OAKLEY, J. E. AND RAKOW, T. (2006). Uncertain Judgments: Eliciting Experts' Probabilities. Chichester, UK: Wiley.
22. PINHEIRO, J. C. AND BATES, D. M. (1996). Unconstrained parameterisations for variance-covariance matrices. Statistics and Computing 6, 289-296.
23. SMITH, T. C., SPIEGELHALTER, D. J. AND THOMAS, A. (1995). Bayesian approaches to random-effects meta-analysis: a comparative study. Statistics in Medicine 14, 2685-2699.
24. SPIEGELHALTER, D. J., ABRAMS, K. R. AND MYLES, J. P. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Chichester, Chichester, UK: Wiley.
25. SPIEGELHALTER, D. J., BEST, N. G., CARLIN, B. P. AND VAN DER LINDE, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society B 64, 1-34.
26. SPIEGELHALTER, D. J., THOMAS, A., BEST, N. AND LUNN, D. (2001). WinBUGS User Manual. Version 1.4. Cambridge: MRC Biostatistics Unit.
27. SUN, D. AND SUN, X. (2005). Estimation of the multivariate normal precision and covariance matrices in a star-shape model. Annals of the Institute of Statistical Mathematics 57, 455-484. (Pubitemid 43004420)
28. SUTTON, A. J. AND HIGGINS, J. P. T. (2008). Recent developments in meta-analysis. Statistics in Medicine 27, 625-650.
29. THOMPSON, S. G., SMITH, T. C. AND SHARP, S. J. (1997). Investigating underlying risk as a source of heterogeneity in meta-analysis. Statistics in Medicine 16, 2741-2758.
30. WARN, D. E., THOMPSON, S. G. AND SPIEGELHALTER, D. J. (2002). Bayesian random effects meta-analysis of trials with binary outcomes: method for absolute risk difference and relative risk scales. Statistics in Medicine 21, 1601-1623.
31. WINKLER, R. L. (1967). The assessment of prior distributions in Bayesian analysis. Journal of the American Statistical Association 67, 776-800
32. YANG, R. AND BERGER, J. O. (1994). Estimation of a covariance matrix using the reference prior. Annals of Statistics 22, 1195-1211.