In the absence of sufficient data directly comparing multiple treatments, indirect comparisons using network meta-analyses (NMAs) can provide useful information. Under current contrast-based (CB) methods for binary outcomes, the patient-centered measures including the treatment-specific event rates and risk differences (RDs) are not provided, which may create some unnecessary obstacles for patients to comprehensively trade-off efficacy and safety measures.

We aim to develop NMA to accurately estimate the treatment-specific event rates.

A Bayesian hierarchical model is developed to illustrate how treatment-specific event rates, RDs, and risk ratios (RRs) can be estimated. We first compare our approach to alternative methods using two hypothetical NMAs assuming a fixed RR or RD, and then use two published NMAs to illustrate the improved reporting.

In the hypothetical NMAs, our approach outperforms current CB NMA methods in terms of bias. In the two published NMAs, noticeable differences are observed in the magnitude of relative treatment effects and several pairwise statistical significance tests from previous report.

First, to facilitate the estimation, each study is assumed to hypothetically compare all treatments, with unstudied arms being missing at random. It is plausible that investigators may have selected treatment arms on purpose based on the results of previous trials, which may lead to ‘nonignorable missingness’ and potentially bias our estimates. Second, we have not considered methods to identify and account for potential inconsistency between direct and indirect comparisons.

The proposed NMA method can accurately estimate treatment-specific event rates, RDs, and RRs and is recommended.

1. Egger, M, Smith, GD, Altman, D. Systematic Reviews in Health Care: Meta-Analysis in Context (2nd edn). BMJ Publishing Group, London, 2001.
Google Scholar | Crossref
2. Guyatt, GH, Sackett, DL, Sinclair, JC. Users’ guides to the medical literature. JAMA 1995; 274(22): 180004.
Google Scholar | Crossref | Medline | ISI
3. Li, T, Puhan, MA, Vedula, SS, Singh, S, Dickersin, K. Network meta-analysis-highly attractive but more methodological research is needed. BMC Med 2011; 9: 79.
Google Scholar | Crossref | Medline | ISI
4. Higgins, JPT, Whitehead, A. Borrowing strength from external trials in a meta-analysis. Stat Med 1996; 15(24): 273349.
Google Scholar | Crossref | Medline | ISI
5. Caldwell, DM, Ades, A, Higgins, J. Simultaneous comparison of multiple treatments: Combining direct and indirect evidence. BMJ 2005; 331: 897900.
Google Scholar | Crossref | Medline
6. Cipriani, A, Furukawa, TA, Salanti, G. Comparative efficacy and acceptability of 12 new-generation antidepressants: A multiple-treatments meta-analysis. Lancet 2009; 373: 74658.
Google Scholar | Crossref | Medline | ISI
7. Cipriani, A, Barbui, C, Salanti, G. Comparative efficacy and acceptability of antimanic drugs in acute mania: A multiple-treatments meta-analysis. Lancet 2011; 378: 130615.
Google Scholar | Crossref | Medline | ISI
8. Elliott, WJ, Meyer, PM. Incident diabetes in clinical trials of antihypertensive drugs: A network meta-analysis. Lancet 2007; 369(9557): 20107.
Google Scholar | Crossref | Medline | ISI
9. Pahor, M, Psaty, BM, Alderman, MH. Health outcomes associated with calcium antagonists compared with other first-line antihypertensive therapies: A meta-analysis of randomised controlled trials. Lancet 2000; 356(9246): 194954.
Google Scholar | Crossref | Medline | ISI
10. Song, F, Loke, YK, Walsh, T. Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: Survey of published systematic reviews. BMJ 2009; 338: b1147.
Google Scholar | Crossref | Medline
11. Palmerini, T, Biondi-Zoccai, G, Riva, DD. Stent thrombosis with drug-eluting and bare-metal stents: Evidence from a comprehensive network meta-analysis. Lancet 2012; 379: 1393402.
Google Scholar | Crossref | Medline | ISI
12. Daniels, J, Middleton, L, Champaneria, R. Second generation endometrial ablation techniques for heavy menstrual bleeding: Network meta-analysis. BMJ 2012; 344: e2564.
Google Scholar | Crossref | Medline
13. Wang, SY, Chu, H, Shamliyan, T. Network meta-analysis of margin threshold for women with ductal carcinoma in situ. J Natl Cancer Inst 2012; 104(7): 50716.
Google Scholar | Crossref | Medline
14. Altman, DG, Deeks, JJ, Sackett, DL. Odds ratios should be avoided when events are common. BMJ 1998; 317: 1318.
Google Scholar | Crossref | Medline
15. Deeks, J . When can odds ratios mislead? Odds ratios should be used only in case-control studies and logistic regression analyses. BMJ 1998; 317: 115557.
Google Scholar | Crossref | Medline
16. Sackett, DL, Deeks, JJ, Altman, DG. Down with odds ratios!Evid Based Med 1996; 1: 16466.
Google Scholar
17. Davies, HTO, Crombie, IK, Tavakoli, M. When can odds ratios mislead?BMJ 1998; 316: 98991.
Google Scholar | Crossref | Medline
18. Borenstein, M, Hedges, LV, Higgins, JPT, Rothstein, HR. Introduction to Meta-Analysis. Wiley, West Sussex, 2011.
Google Scholar
19. Psaty, BM, Lumley, T, Furberg, CD. Health outcomes associated with various antihypertensive therapies used as first-line agents. JAMA 2003; 289(19): 253444.
Google Scholar | Crossref | Medline | ISI
20. Trikalinos, TA, Alsheikh-Ali, AA, Tatsioni, A, Nallamothu, BK, Kent, DM. Percutaneous coronary interventions for non-acute coronary artery disease: A quantitative 20-year synopsis and a network meta-analysis. Lancet 2009; 373(9667): 91118.
Google Scholar | Crossref | Medline | ISI
21. Lumley, T . Network meta-analysis for indirect treatment comparisons. Stat Med 2002; 21(16): 231324.
Google Scholar | Crossref | Medline | ISI
22. Salanti, G, Ades, AE, Ioannidis, JPA. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: An overview and tutorial. J Clin Epidemiol 2011; 64(2): 16371.
Google Scholar | Crossref | Medline | ISI
23. Chung, H, Lumley, T. Graphical exploration of network meta-analysis data: The use of multidimensional scaling. Clin Trials 2008; 5(4): 30107.
Google Scholar | SAGE Journals | ISI
24. Lu, G, Ades, AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med 2004; 23: 310524.
Google Scholar | Crossref | Medline | ISI
25. Lu, G, Ades, AE. Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc 2006; 101: 44759.
Google Scholar | Crossref | ISI
26. Lu, G, Ades, AE, Sutton, AJ. Meta-analysis of mixed treatment comparisons at multiple follow-up times. Stat Med 2007; 26: 368199.
Google Scholar | Crossref | Medline | ISI
27. Lu, G, Ades, AE. Modeling between-trial variance structure in mixed treatment comparisons. Biostatistics 2009; 10: 792805.
Google Scholar | Crossref | Medline | ISI
28. Jones, B, Roger, J, Lane, PW. Statistical approaches for conducting network meta-analysis in drug development. Pharm Stat 2011; 10(6): 52331.
Google Scholar | Crossref | Medline | ISI
29. White, IR . Multivariate random-effects meta-regression: Updates to mvmeta. Stata J 2011; 11(2): 25570.
Google Scholar | SAGE Journals | ISI
30. Manzoli, L, Vito, CD, Salanti, G. Meta-analysis of the immunogenicity and tolerability of pandemic influenza A 2009 (H1N1) vaccines. PloS One 2011; 6(9): e24384.
Google Scholar | Crossref | Medline | ISI
31. Dias, S, Welton, NJ, Sutton, AJ, Ades, AE. Nice DSU technical support document 2: A generalised linear modelling framework for pairwise and network meta-analysis of randomised controlled trials. Report, National Institute for Health and Clinical Excellence, London, UK, August 2011.
Google Scholar
32. Dias, S, Welton, NJ, Sutton, AJ, Ades, AE. Nice DSU technical support document 5: Evidence synthesis in the baseline natural history model. Report, National Institute for Health and Clinical Excellence, London, UK, August 2012.
Google Scholar
33. Dias, S, Welton, NJ, Sutton, AJ, Ades, AE. Nice DSU technical support document 6: Embedding evidence synthesis in probabilistic cost-effectiveness analysis: Software choices. Report, National Institute for Health and Clinical Excellence, London, UK, May 2011.
Google Scholar
34. Ibrahim, JG, Chu, H, Chen, MH. Missing data in clinical studies: Issues and methods. J Clin Oncol 2012. 30(26): 3297303.
Google Scholar | Crossref | Medline | ISI
35. Little, RJA, Rubin, DB. Statistical Analysis With Missing Data (2nd edn). John Wiley & Sons, New Jersey, 2002.
Google Scholar | Crossref
36. Rubin, DB . Inference and missing data. Biometrika 1976; 63(3): 58192.
Google Scholar | Crossref | ISI
37. Rubin, DB . Multiple Imputation for Nonresponse in Surveys. Wiley Online Library, New York, 1987.
Google Scholar | Crossref
38. Schafer, JL . Analysis of Incomplete Multivariate Data. Chapman & Hall/CRC, New York, 1997.
Google Scholar | Crossref
39. Salanti, G, Higgins, JPT, Ades, AE, Ioannidis, JPA. Evaluation of networks of randomized trials. Stat Methods Med Res 2008; 17(3): 279301.
Google Scholar | SAGE Journals | ISI
40. White, IR, Barrett, JK, Jackson, D, Higgins, JPT. Consistency and inconsistency in network meta-analysis: Model estimation using multivariate meta-regression. Res Synth Methods 2012; 3(2): 11125.
Google Scholar | Crossref | Medline | ISI
41. Chu, H, Nie, L, Chen, Y, Huang, Y, Sun, W. Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: Methods for the absolute risk difference and relative risk. Stat Methods Med Res 2012; 21(6): 62133.
Google Scholar | SAGE Journals | ISI
42. Gelman, A . Prior distributions for variance parameters in hierarchical models. Bayesian Anal 2006; 1(3): 51533.
Google Scholar | Crossref | ISI
43. Gustafson, P . The utility of prior information and stratification for parameter estimation with two screening tests but no gold standard. Stat Med 2005; 24(8): 120317.
Google Scholar | Crossref | Medline | ISI
44. Gustafson, P, Hossain, S, Macnab, YC. Conservative prior distributions for variance parameters in hierarchical models. Can J Stat 2006; 34(4): 37790.
Google Scholar | Crossref | ISI
45. Natarajan, R, McCulloch, CE. Gibbs sampling with diffuse proper priors: A valid approach to data-driven inference?J Comput Graph Stat 1998; 7(3): 26777.
Google Scholar | ISI
46. Lunn, DJ, Thomas, A, Best, N, Spiegelhalter, D. A Bayesian modeling framework: Concepts, structure, and extensibility. Stat Comput 2000; 10(4): 32537.
Google Scholar | Crossref | ISI
47. Lunn, D, Spiegelhalter, D, Thomas, A, Best, N. The BUGS project: Evolution, critique and future directions. Stat Med 2009; 28(25): 304967.
Google Scholar | Crossref | Medline | ISI
48. Gelfand, AE, Smith, AFM. Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 1990; 85(410): 398409.
Google Scholar | Crossref | ISI
49. Gilks, WR, Best, N, Tan, K. Adaptive rejection metropolis sampling within Gibbs sampling. Appl Stat 1995; 44(4): 45572.
Google Scholar | Crossref | ISI
50. Brooks, SP, Gelman, A. General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 1998; 7(4): 43455.
Google Scholar | ISI
51. Gelman, A, Rubin, DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992; 7(4): 45772.
Google Scholar | Crossref
52. Goodman, SN . Toward evidence-based medical statistics. 1: The P value fallacy. Ann Intern Med 1999; 130(12): 9951004.
Google Scholar | Crossref | Medline | ISI
53. Yusuf, S, Peto, R, Lewis, J, Collins, R, Sleight, P. Beta blockade during and after myocardial infarction: An overview of the randomized trials. Prog Cardiovasc Dis 1985; 27(5): 33571.
Google Scholar | Crossref | Medline | ISI
54. Hong, H, Chu, H, Zhang, J, Carlin, BP. A Bayesian missing data framework for generalized multiple outcome mixed treatment comparisons. Research Report 2012-018, 2012. Minneapolis, MN: Division of Biostatistics, University of Minnesota.
Google Scholar
55. Zhang, J, Yu, KF. What’s the relative risk?JAMA 1998; 280(19): 169091.
Google Scholar | Crossref | Medline | ISI
56. Zeger, SL, Liang, KY, Albert, PS. Models for longitudinal data: A generalized estimating equation approach. Biometrics 1988; 44(4): 104960.
Google Scholar | Crossref | Medline | ISI
57. Caldwell, DM, Welton, NJ, Dias, S, Ades, AE. Selecting the best scale for measuring treatment effect in a network meta-analysis: A case study in childhood nocturnal enuresis. Res Synth Methods 2012; 3(2): 12641.
Google Scholar | Crossref | Medline | ISI
58. Achana, FA, Cooper, NJ, Dias, S. Extending methods for investigating the relationship between treatment effect and baseline risk from pairwise meta-analysis to network meta-analysis. Stat Med 2012; 32(5): 75271.
Google Scholar | Crossref | Medline | ISI
59. Dias, S, Welton, NJ, Caldwell, DM, Ades, AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010; 29: 93244.
Google Scholar | Crossref | Medline | ISI
60. Higgins, JPT, Jackson, D, Barrett, JK. Consistency and inconsistency in network meta-analysis: Concepts and models for multi-arm studies. Res Synth Methods 2012; 3: 98110.
Google Scholar | Crossref | Medline | ISI
61. van Valkenhoef, G, Tervonen, T, de Brock, B, Hillege, H. Algorithmic parameterization of mixed treatment comparisons. Stat Comput 2012; 22: 1099111.
Google Scholar | Crossref | ISI
62. Jansen, JP . Network meta-analysis of individual and aggregate level data. Res Synth Methods 2012; 3: 17790.
Google Scholar | Crossref | Medline | ISI
63. Saramago, P, Sutton, AJ, Cooper, NJ, Manca, A. Mixed treatment comparisons using aggregate and individual participant level data. Stat Med 2012; 31: 351636.
Google Scholar | Crossref | Medline | ISI
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