BMC Medical Research Methodology | |
Visualizing inconsistency in network meta-analysis by independent path decomposition | |
Jochem König1  Harald Binder1  Ulrike Krahn1  | |
[1] Institute of Medical Biostatistics, Epidemiology and Informatics, University Medical Center Johannes Gutenberg University Mainz, Langenbeckstr. 1, 55101 Mainz, Germany | |
关键词: Forest plot; Influence diagnostics; Inconsistency; Mixed treatment comparison meta-analysis; Multiple treatments comparison meta-analysis; Network meta-analysis; | |
Others : 1090314 DOI : 10.1186/1471-2288-14-131 |
|
received in 2014-08-07, accepted in 2014-10-28, 发布年份 2014 | |
【 摘 要 】
Background
In network meta-analysis, several alternative treatments can be compared by pooling the evidence of all randomised comparisons made in different studies. Incorporated indirect conclusions require a consistent network of treatment effects. An assessment of this assumption and of the influence of deviations is fundamental for the validity evaluation.
Methods
We show that network estimates for single pairwise treatment comparisons can be approximated by the evidence of a subnet that is decomposable into independent paths. Path-based estimates and the estimate of the residual evidence can be used with their contribution to the network estimate to set up a forest plot for the consistency assessment. Using a network meta-analysis of twelve antidepressants and controlled perturbations in the real and constructed consistent data, we discuss the consistency assessment by the independent path decomposition in contrast to an approach using a recently presented graphical tool, the net heat plot. In addition, we define influence functions that describe how changes in study effects are translated into network estimates.
Results
While the consistency assessment by the net heat plot comprises all network estimates, an independent path decomposition and visualisation in a forest plot is tailored to one specific treatment comparison. It allows for the recognition as to whether inconsistencies between different paths of evidence and outlier effects do affect the considered treatment comparison.
Conclusions
The approximation of the network estimate for a single comparison by the evidence of a subnet and the visualisation of the decomposition into independent paths provide the applicability of a graphical validation instrument that is known from classical meta-analysis.
【 授权许可】
2014 Krahn et al.; licensee BioMed Central.
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
20150128160002517.pdf | 934KB | download | |
Figure 5. | 49KB | Image | download |
Figure 4. | 108KB | Image | download |
Figure 3. | 82KB | Image | download |
Figure 2. | 158KB | Image | download |
Fig. 4. | 76KB | Image | download |
【 图 表 】
Fig. 4.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
【 参考文献 】
- [1]Salanti G: Indirect and mixed-treatment comparison, network, or multiple-treatments meta-analysis: many names, many benefits, many concerns for the next generation evidence synthesis tool. Res Synth Methods 2012, 3(2):80-97.
- [2]Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE: Evidence synthesis for decision making4: inconsistency in networks of evidence based on randomised controlled trials. Med Decis Making 2013, 33:641-656.
- [3]Sutton AJ, Higgins JPT: Recent developments in meta-analysis. Stat Med 2008, 27:625-650.
- [4]Lewis S, Clarke M: Forest plots: trying to see the wood and the trees. BMJ 2001, 322(7300):1479-1480.
- [5]Salanti G, Marinho V, Higgins JPT: A case study of multiple-treatments meta-analysis demonstrates that covariates should be considered. J Clin Epidemiol 2009, 62(8):857-864.
- [6]Dias S, Welton NJ, Sutton AJ, Caldwell DM, Guobing L, Ades AE: NICE DSU Technical Support Document 4: Inconsistency in Networks of Evidence Based on Randomised Controlled Trials. 2011. [http://www.nicedsu.org.uk webcite]
- [7]Lu G, Ades AE: Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc 2006, 101(474):447-459.
- [8]Dias S, Welton NJ, Caldwell DM, Ades AE: Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010, 29:932-944.
- [9]Piepho HP: Network meta-analysis made easy: detection of inconsistency using factorial analysis-of-variance models. BMC Med Res Methodol 2014, 14:61. BioMed Central Full Text
- [10]Krahn U, Binder H, König J: A graphical tool for locating inconsistency in network meta-analyses. BMC Med Res Methodol 2013, 13:35. BioMed Central Full Text
- [11]Cipriani A, Furukawa TA, Salanti G, Geddes JR, Higgins JP, Churchill R, Watanabe N, Nakagawa A, Omori IM, McGuire H, Tansella M, Barbui C: Comparative efficacy and acceptability of 12 new-generation antidepressants: a multiple-treatments meta-analysis. Lancet 2009, 373(9665):746-758.
- [12]Higgins JPT, Jackson D, Barrett JK, Lu G, Ades AE, White IR: Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Res Synth Methods 2012, 3(2):98-110.
- [13]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):111-125.
- [14]Caldwell DM, Welton NJ, Ades AE: Mixed treatment comparison analysis provides internally coherent treatment effect estimates based on overviews of reviews and can reveal inconsistency. J Clin Epidemiol 2010, 63(8):875-882.
- [15]Bucher HC, Guyatt GH, Griffith LE, Walter SD: The results of direct and indirect treatment comparisons in meta-analysis of randomised controlled trials. J Clin Epidemiol 1997, 50(6):683-691.
- [16]König J, Krahn U, Binder H: Visualizing the flow of evidence in network meta-analysis and characterizing mixed treatment comparisons. Stat Med 2013, 32:5414-5429.
- [17]Dijkstra EW: A note on two problems in connexion with graphs. Numerische Mathematik 1959, 1:269-271.
- [18]Schwarzer G: meta: Meta-Analysis with R. R package version 3.0-1, 2013. [http://CRAN.R-project.org/package=meta webcite]
- [19]Rücker G, Schwarzer G, Krahn U, König J: netmeta: Network meta-analysis with R. R package version 0.5-0, 2014. [http://CRAN.R-project.org/package=netmeta webcite]
- [20]Song F, Harvey I, Lilford R: Adjusted indirect comparison may be less biased than direct comparison for evaluating new pharmaceutical interventions. J Clin Epidemiol 2008, 61(5):455-463.
- [21]Lu G, Ades AE: Modeling between-trial variance structure in mixed treatment comparisons. Biostatistics 2009, 10(4):792-805.
- [22]Cook RD, Weisberg S: Residuals and Influence in Regression . New York: Chapman and Hall; 1982.
- [23]Belsley DA, Kuh E, Welsch RE: Regression Diagnostics: Identifying Influential Data and Sources of Collinearity . New Jersey: John Wiley & Sons; 2004.
- [24]Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A: Bayesian measures of model compelxity and fit. J R Stat Soc B 2002, 64:583-639.
- [25]Senn S, Gavini F, Magrez D, Scheen A: Issues in performing a network meta-analysis. Stat Methods Med Res 2012, 22(2):169-189.
- [26]Lu G, Welton NJ, Higgins J, White I, Ades A: Linear inference for mixed treatment comparison meta-analysis: a two-stage approach. Res Synth Methods 2011, 2(1):43-60.
- [27]Sturtz S, Bender R: Unsolved issues of mixed treatment comparison meta-analysis: network size and inconsistency. Res Synth Methods 2012, 3:300-311.