Skip to main content
Top
Published in: Systematic Reviews 1/2012

Open Access 01-12-2012 | Methodology

Sample size and power considerations in network meta-analysis

Authors: Kristian Thorlund, Edward J Mills

Published in: Systematic Reviews | Issue 1/2012

Login to get access

Abstract

Background

Network meta-analysis is becoming increasingly popular for establishing comparative effectiveness among multiple interventions for the same disease. Network meta-analysis inherits all methodological challenges of standard pairwise meta-analysis, but with increased complexity due to the multitude of intervention comparisons. One issue that is now widely recognized in pairwise meta-analysis is the issue of sample size and statistical power. This issue, however, has so far only received little attention in network meta-analysis. To date, no approaches have been proposed for evaluating the adequacy of the sample size, and thus power, in a treatment network.

Findings

In this article, we develop easy-to-use flexible methods for estimating the ‘effective sample size’ in indirect comparison meta-analysis and network meta-analysis. The effective sample size for a particular treatment comparison can be interpreted as the number of patients in a pairwise meta-analysis that would provide the same degree and strength of evidence as that which is provided in the indirect comparison or network meta-analysis. We further develop methods for retrospectively estimating the statistical power for each comparison in a network meta-analysis. We illustrate the performance of the proposed methods for estimating effective sample size and statistical power using data from a network meta-analysis on interventions for smoking cessation including over 100 trials.

Conclusion

The proposed methods are easy to use and will be of high value to regulatory agencies and decision makers who must assess the strength of the evidence supporting comparative effectiveness estimates.
Appendix
Available only for authorised users
Literature
1.
go back to reference Sutton AJ, Higgins JP: Recent developments in meta-analysis. Stat Med. 2008, 27: 625-650. 10.1002/sim.2934.CrossRefPubMed Sutton AJ, Higgins JP: Recent developments in meta-analysis. Stat Med. 2008, 27: 625-650. 10.1002/sim.2934.CrossRefPubMed
2.
go back to reference Ioannidis JP: Integration of evidence from multiple meta-analyses: a primer on umbrella reviews, treatment networks and multiple treatments meta-analyses. Cmaj. 2009, 181: 488-493. 10.1503/cmaj.081086.CrossRefPubMedPubMedCentral Ioannidis JP: Integration of evidence from multiple meta-analyses: a primer on umbrella reviews, treatment networks and multiple treatments meta-analyses. Cmaj. 2009, 181: 488-493. 10.1503/cmaj.081086.CrossRefPubMedPubMedCentral
3.
go back to reference Jansen JP, Crawford B, Bergman G, Stam W: Bayesian meta-analysis of multiple treatment comparisons: an introduction to mixed treatment comparisons. Value Health. 2008, 11: 956-964. 10.1111/j.1524-4733.2008.00347.x.CrossRefPubMed Jansen JP, Crawford B, Bergman G, Stam W: Bayesian meta-analysis of multiple treatment comparisons: an introduction to mixed treatment comparisons. Value Health. 2008, 11: 956-964. 10.1111/j.1524-4733.2008.00347.x.CrossRefPubMed
4.
go back to reference Lu G, Ades AE: Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med. 2004, 23: 3105-3124. 10.1002/sim.1875.CrossRefPubMed Lu G, Ades AE: Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med. 2004, 23: 3105-3124. 10.1002/sim.1875.CrossRefPubMed
5.
go back to reference Mills EJ, Bansback N, Ghement I, Thorlund K, Kelly S, Puhan MA, Wright J: Multiple treatment comparison meta-analyses: a step forward into complexity. Clin Epidemiol. 2011, 3: 193-202.CrossRefPubMedPubMedCentral Mills EJ, Bansback N, Ghement I, Thorlund K, Kelly S, Puhan MA, Wright J: Multiple treatment comparison meta-analyses: a step forward into complexity. Clin Epidemiol. 2011, 3: 193-202.CrossRefPubMedPubMedCentral
6.
go back to reference Salanti G, Higgins JP, Ades AE, Ioannidis JP: Evaluation of networks of randomized trials. Stat Methods Med Res. 2008, 17: 279-301.CrossRefPubMed Salanti G, Higgins JP, Ades AE, Ioannidis JP: Evaluation of networks of randomized trials. Stat Methods Med Res. 2008, 17: 279-301.CrossRefPubMed
7.
go back to reference Sutton A, Ades AE, Cooper N, Abrams K: Use of indirect and mixed treatment comparisons for technology assessment. Pharmacoeconomics. 2008, 26: 753-767. 10.2165/00019053-200826090-00006.CrossRefPubMed Sutton A, Ades AE, Cooper N, Abrams K: Use of indirect and mixed treatment comparisons for technology assessment. Pharmacoeconomics. 2008, 26: 753-767. 10.2165/00019053-200826090-00006.CrossRefPubMed
8.
go back to reference Glenny AM, Altman DG, Song F, Sakarovitch C, Deeks JJ, D'Amico R, Bradburn M, Eastwood AJ: Indirect comparisons of competing interventions. Health Technol Assess. 2005, 9: 1-134. iii-ivCrossRefPubMed Glenny AM, Altman DG, Song F, Sakarovitch C, Deeks JJ, D'Amico R, Bradburn M, Eastwood AJ: Indirect comparisons of competing interventions. Health Technol Assess. 2005, 9: 1-134. iii-ivCrossRefPubMed
9.
go back to reference Song F, Altman DG, Glenny AM, Deeks JJ: Validity of indirect comparison for estimating efficacy of competing interventions: empirical evidence from published meta-analyses. BMJ. 2003, 326: 472-10.1136/bmj.326.7387.472.CrossRefPubMedPubMedCentral Song F, Altman DG, Glenny AM, Deeks JJ: Validity of indirect comparison for estimating efficacy of competing interventions: empirical evidence from published meta-analyses. BMJ. 2003, 326: 472-10.1136/bmj.326.7387.472.CrossRefPubMedPubMedCentral
10.
go back to reference Song F, Loke YK, Walsh T, Glenny AM, Eastwood AJ, Altman DG: Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews. BMJ. 2009, 338: b1147-10.1136/bmj.b1147.CrossRefPubMedPubMedCentral Song F, Loke YK, Walsh T, Glenny AM, Eastwood AJ, Altman DG: Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews. BMJ. 2009, 338: b1147-10.1136/bmj.b1147.CrossRefPubMedPubMedCentral
11.
go back to reference Song F, Xiong T, Parekh-Bhurke S, Loke YK, Sutton AJ, Eastwood AJ, Holland R, Chen YF, Glenny AM, Deeks JJ, Altman DG: Inconsistency between direct and indirect comparisons of competing interventions: meta-epidemiological study. BMJ. 2011, 343: d4909-10.1136/bmj.d4909.CrossRefPubMedPubMedCentral Song F, Xiong T, Parekh-Bhurke S, Loke YK, Sutton AJ, Eastwood AJ, Holland R, Chen YF, Glenny AM, Deeks JJ, Altman DG: Inconsistency between direct and indirect comparisons of competing interventions: meta-epidemiological study. BMJ. 2011, 343: d4909-10.1136/bmj.d4909.CrossRefPubMedPubMedCentral
12.
go back to reference Higgins JPT, Green S (editors): Cochrane Handbook for Systematic Reviews of Interventions Version 5.0.2 [updated September 2009]. The Cochrane Collaboration. 2009 Higgins JPT, Green S (editors): Cochrane Handbook for Systematic Reviews of Interventions Version 5.0.2 [updated September 2009]. The Cochrane Collaboration. 2009
13.
go back to reference Mills EJ, Ioannidis JPA, Thorlund K, Schünemann HJ, Puhan MA, Guyatt GH: How to use an article reporting a multiple treatment comparison meta-analysis. JAMA. 2012, 308: 1246-53. 10.1001/2012.jama.11228.CrossRefPubMed Mills EJ, Ioannidis JPA, Thorlund K, Schünemann HJ, Puhan MA, Guyatt GH: How to use an article reporting a multiple treatment comparison meta-analysis. JAMA. 2012, 308: 1246-53. 10.1001/2012.jama.11228.CrossRefPubMed
14.
go back to reference Brok J, Thorlund K, Gluud C, Wetterslev J: Trial sequential analysis reveals insufficient information size and potentially false positive results in many meta-analyses. J Clin Epidemiol. 2008, 61: 763-769. 10.1016/j.jclinepi.2007.10.007.CrossRefPubMed Brok J, Thorlund K, Gluud C, Wetterslev J: Trial sequential analysis reveals insufficient information size and potentially false positive results in many meta-analyses. J Clin Epidemiol. 2008, 61: 763-769. 10.1016/j.jclinepi.2007.10.007.CrossRefPubMed
15.
go back to reference Brok J, Thorlund K, Wetterslev J, Gluud C: Apparently conclusive meta-analyses may be inconclusive–Trial sequential analysis adjustment of random error risk due to repetitive testing of accumulating data in apparently conclusive neonatal meta-analyses. Int J Epidemiol. 2009, 38: 287-298.CrossRefPubMed Brok J, Thorlund K, Wetterslev J, Gluud C: Apparently conclusive meta-analyses may be inconclusive–Trial sequential analysis adjustment of random error risk due to repetitive testing of accumulating data in apparently conclusive neonatal meta-analyses. Int J Epidemiol. 2009, 38: 287-298.CrossRefPubMed
16.
go back to reference Guyatt GH, Oxman AD, Kunz R, Brozek J, Alonso-Coello P, Rind D, Devereaux PJ, Montori VM, Freyschuss B, Vist G: GRADE guidelines 6. Rating the quality of evidence--imprecision. J Clin Epidemiol. 2011, 64: 1283-1293. 10.1016/j.jclinepi.2011.01.012.CrossRefPubMed Guyatt GH, Oxman AD, Kunz R, Brozek J, Alonso-Coello P, Rind D, Devereaux PJ, Montori VM, Freyschuss B, Vist G: GRADE guidelines 6. Rating the quality of evidence--imprecision. J Clin Epidemiol. 2011, 64: 1283-1293. 10.1016/j.jclinepi.2011.01.012.CrossRefPubMed
17.
go back to reference Higgins JP, Whitehead A, Simmonds M: Sequential methods for random-effects meta-analysis. Stat Med. 2011, 30: 903-921. 10.1002/sim.4088.CrossRefPubMed Higgins JP, Whitehead A, Simmonds M: Sequential methods for random-effects meta-analysis. Stat Med. 2011, 30: 903-921. 10.1002/sim.4088.CrossRefPubMed
18.
go back to reference Ioannidis J, Lau J: Evolution of treatment effects over time: empirical insight from recursive cumulative metaanalyses. Proc Natl Acad Sci USA. 2001, 98: 831-836. 10.1073/pnas.98.3.831.CrossRefPubMedPubMedCentral Ioannidis J, Lau J: Evolution of treatment effects over time: empirical insight from recursive cumulative metaanalyses. Proc Natl Acad Sci USA. 2001, 98: 831-836. 10.1073/pnas.98.3.831.CrossRefPubMedPubMedCentral
19.
go back to reference Pogue J, Yusuf S: Overcoming the limitations of current meta-analysis of randomised controlled trials. Lancet. 1998, 351: 47-52. 10.1016/S0140-6736(97)08461-4.CrossRefPubMed Pogue J, Yusuf S: Overcoming the limitations of current meta-analysis of randomised controlled trials. Lancet. 1998, 351: 47-52. 10.1016/S0140-6736(97)08461-4.CrossRefPubMed
20.
go back to reference Pogue JM, Yusuf S: Cumulating evidence from randomized trials: utilizing sequential monitoring boundaries for cumulative meta-analysis. Control Clin Trials. 1997, 18: 580-593. 10.1016/S0197-2456(97)00051-2. discussion 661–586CrossRefPubMed Pogue JM, Yusuf S: Cumulating evidence from randomized trials: utilizing sequential monitoring boundaries for cumulative meta-analysis. Control Clin Trials. 1997, 18: 580-593. 10.1016/S0197-2456(97)00051-2. discussion 661–586CrossRefPubMed
21.
go back to reference Thorlund K, Devereaux PJ, Wetterslev J, Guyatt G, Ioannidis JP, Thabane L, Gluud LL, Als-Nielsen B, Gluud C: Can trial sequential monitoring boundaries reduce spurious inferences from meta-analyses?. Int J Epidemiol. 2009, 38: 276-286.CrossRefPubMed Thorlund K, Devereaux PJ, Wetterslev J, Guyatt G, Ioannidis JP, Thabane L, Gluud LL, Als-Nielsen B, Gluud C: Can trial sequential monitoring boundaries reduce spurious inferences from meta-analyses?. Int J Epidemiol. 2009, 38: 276-286.CrossRefPubMed
22.
go back to reference Thorlund K, Imberger G, Walsh M, Chu R, Gluud C, Wetterslev J, Guyatt G, Devereaux PJ, Thabane L: The number of patients and events required to limit the risk of overestimation of intervention effects in meta-analysis–a simulation study. PLoS One. 2011, 6: e25491-10.1371/journal.pone.0025491.CrossRefPubMedPubMedCentral Thorlund K, Imberger G, Walsh M, Chu R, Gluud C, Wetterslev J, Guyatt G, Devereaux PJ, Thabane L: The number of patients and events required to limit the risk of overestimation of intervention effects in meta-analysis–a simulation study. PLoS One. 2011, 6: e25491-10.1371/journal.pone.0025491.CrossRefPubMedPubMedCentral
23.
go back to reference Wetterslev J, Thorlund K, Brok J, Gluud C: Trial sequential analysis may establish when firm evidence is reached in cumulative meta-analysis. J Clin Epidemiol. 2008, 61: 64-75. 10.1016/j.jclinepi.2007.03.013.CrossRefPubMed Wetterslev J, Thorlund K, Brok J, Gluud C: Trial sequential analysis may establish when firm evidence is reached in cumulative meta-analysis. J Clin Epidemiol. 2008, 61: 64-75. 10.1016/j.jclinepi.2007.03.013.CrossRefPubMed
24.
go back to reference Wetterslev J, Thorlund K, Brok J, Gluud C: Estimating required information size by quantifying diversity in random-effects model meta-analyses. BMC Med Res Methodol. 2009, 9: 86-10.1186/1471-2288-9-86.CrossRefPubMedPubMedCentral Wetterslev J, Thorlund K, Brok J, Gluud C: Estimating required information size by quantifying diversity in random-effects model meta-analyses. BMC Med Res Methodol. 2009, 9: 86-10.1186/1471-2288-9-86.CrossRefPubMedPubMedCentral
25.
go back to reference van der Tweel I, Bollen C: Sequential meta-analysis: an efficient decision-making tool. Clin Trials. 2010, 7: 136-146. 10.1177/1740774509360994.CrossRefPubMed van der Tweel I, Bollen C: Sequential meta-analysis: an efficient decision-making tool. Clin Trials. 2010, 7: 136-146. 10.1177/1740774509360994.CrossRefPubMed
26.
go back to reference Thorlund K, Anema A, Mills E: Interpreting meta-analysis according to the adequacy of sample size. An example using isoniazid chemoprophylaxis for tuberculosis in purified protein derivative negative HIV-infected individuals. Clin Epidemiol. 2010, 2: 57-66.PubMedPubMedCentral Thorlund K, Anema A, Mills E: Interpreting meta-analysis according to the adequacy of sample size. An example using isoniazid chemoprophylaxis for tuberculosis in purified protein derivative negative HIV-infected individuals. Clin Epidemiol. 2010, 2: 57-66.PubMedPubMedCentral
27.
go back to reference Pereira TV, Ioannidis JP: Statistically significant meta-analyses of clinical trials have modest credibility and inflated effects. J Clin Epidemiol. 2011, 64: 1060-1069. 10.1016/j.jclinepi.2010.12.012.CrossRefPubMed Pereira TV, Ioannidis JP: Statistically significant meta-analyses of clinical trials have modest credibility and inflated effects. J Clin Epidemiol. 2011, 64: 1060-1069. 10.1016/j.jclinepi.2010.12.012.CrossRefPubMed
28.
go back to reference Thorlund K, Engstrom J, Wetterslev J, Brok J, Imberger G, Gluud C: User manual for trial sequential analysis (TSA). In Book User manual for trial sequential analysis (TSA). 2011, Copenhagen Trial Unit, City Thorlund K, Engstrom J, Wetterslev J, Brok J, Imberger G, Gluud C: User manual for trial sequential analysis (TSA). In Book User manual for trial sequential analysis (TSA). 2011, Copenhagen Trial Unit, City
29.
go back to reference Mills EJ, Ghement I, O'Regan C, Thorlund K: Estimating the power of indirect comparisons: a simulation study. PLoS One. 2011, 6: e16237-10.1371/journal.pone.0016237.CrossRefPubMedPubMedCentral Mills EJ, Ghement I, O'Regan C, Thorlund K: Estimating the power of indirect comparisons: a simulation study. PLoS One. 2011, 6: e16237-10.1371/journal.pone.0016237.CrossRefPubMedPubMedCentral
30.
go back to reference Lumley T: Network meta-analysis for indirect treatment comparisons. Stat Med. 2002, 21: 2313-2324. 10.1002/sim.1201.CrossRefPubMed Lumley T: Network meta-analysis for indirect treatment comparisons. Stat Med. 2002, 21: 2313-2324. 10.1002/sim.1201.CrossRefPubMed
31.
go back to reference Mills EJ, Wu P, Lockhart I, Thorlund K, Puhan MA, Ebbert JO: Comparison of high-dose and combination nicotine replacement therapy, varenicline, and buproprion for smoking cessation: A systematic review and multiple treatment meta-analysis. Ann Med. 2012, 44: 588-97. 10.3109/07853890.2012.705016.CrossRefPubMed Mills EJ, Wu P, Lockhart I, Thorlund K, Puhan MA, Ebbert JO: Comparison of high-dose and combination nicotine replacement therapy, varenicline, and buproprion for smoking cessation: A systematic review and multiple treatment meta-analysis. Ann Med. 2012, 44: 588-97. 10.3109/07853890.2012.705016.CrossRefPubMed
32.
go back to reference Bucher HC, Guyatt GH, Griffith LE, Walter SD: The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol. 1997, 50: 683-691. 10.1016/S0895-4356(97)00049-8.CrossRefPubMed Bucher HC, Guyatt GH, Griffith LE, Walter SD: The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol. 1997, 50: 683-691. 10.1016/S0895-4356(97)00049-8.CrossRefPubMed
33.
go back to reference Higgins JP, Whitehead A: Borrowing strength from external trials in a meta-analysis. Stat Med. 1996, 15: 2733-2749. 10.1002/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0.CrossRefPubMed Higgins JP, Whitehead A: Borrowing strength from external trials in a meta-analysis. Stat Med. 1996, 15: 2733-2749. 10.1002/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0.CrossRefPubMed
34.
go back to reference Higgins JP, Thompson SG: Quantifying heterogeneity in a meta-analysis. Stat Med. 2002, 21: 1539-1558. 10.1002/sim.1186.CrossRefPubMed Higgins JP, Thompson SG: Quantifying heterogeneity in a meta-analysis. Stat Med. 2002, 21: 1539-1558. 10.1002/sim.1186.CrossRefPubMed
35.
go back to reference Borenstein M, Hedges L, Higgins JP: Introduction to meta-analysis. 2009, John Wiley and Sons, Chichester, 25CrossRef Borenstein M, Hedges L, Higgins JP: Introduction to meta-analysis. 2009, John Wiley and Sons, Chichester, 25CrossRef
36.
go back to reference Thorlund K, Imberger G, Johnston B, Walsh M, Awad T, Thabane L, Gluud C, Devereaux PJ, Wetterslev J: Evolution of heterogeneity (I2) estimates and their 95% confidence intervals in large meta-analyses. PLoS One. 2012, 7: e39471-10.1371/journal.pone.0039471.CrossRefPubMedPubMedCentral Thorlund K, Imberger G, Johnston B, Walsh M, Awad T, Thabane L, Gluud C, Devereaux PJ, Wetterslev J: Evolution of heterogeneity (I2) estimates and their 95% confidence intervals in large meta-analyses. PLoS One. 2012, 7: e39471-10.1371/journal.pone.0039471.CrossRefPubMedPubMedCentral
37.
go back to reference Whitehead A, Whitehead J: A general parametric approach to the meta-analysis of randomized clinical trials. Stat Med. 1991, 10: 1665-1677. 10.1002/sim.4780101105.CrossRefPubMed Whitehead A, Whitehead J: A general parametric approach to the meta-analysis of randomized clinical trials. Stat Med. 1991, 10: 1665-1677. 10.1002/sim.4780101105.CrossRefPubMed
38.
go back to reference Thorlund K, Imberger G, Wetterslev J, Brok J, Gluud C: Comments on 'Sequential meta-analysis: an efficient decision-making tool' by I van der Tweel and C Bollen. Clin Trials. 2010, 7: 752-753. 10.1177/1740774510386255. author reply 754CrossRefPubMed Thorlund K, Imberger G, Wetterslev J, Brok J, Gluud C: Comments on 'Sequential meta-analysis: an efficient decision-making tool' by I van der Tweel and C Bollen. Clin Trials. 2010, 7: 752-753. 10.1177/1740774510386255. author reply 754CrossRefPubMed
Metadata
Title
Sample size and power considerations in network meta-analysis
Authors
Kristian Thorlund
Edward J Mills
Publication date
01-12-2012
Publisher
BioMed Central
Published in
Systematic Reviews / Issue 1/2012
Electronic ISSN: 2046-4053
DOI
https://doi.org/10.1186/2046-4053-1-41

Other articles of this Issue 1/2012

Systematic Reviews 1/2012 Go to the issue