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Published in: BMC Medical Research Methodology 1/2011

Open Access 01-12-2011 | Research article

Network meta-analysis of survival data with fractional polynomials

Author: Jeroen P Jansen

Published in: BMC Medical Research Methodology | Issue 1/2011

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Abstract

Background

Pairwise meta-analysis, indirect treatment comparisons and network meta-analysis for aggregate level survival data are often based on the reported hazard ratio, which relies on the proportional hazards assumption. This assumption is implausible when hazard functions intersect, and can have a huge impact on decisions based on comparisons of expected survival, such as cost-effectiveness analysis.

Methods

As an alternative to network meta-analysis of survival data in which the treatment effect is represented by the constant hazard ratio, a multi-dimensional treatment effect approach is presented. With fractional polynomials the hazard functions of interventions compared in a randomized controlled trial are modeled, and the difference between the parameters of these fractional polynomials within a trial are synthesized (and indirectly compared) across studies.

Results

The proposed models are illustrated with an analysis of survival data in non-small-cell lung cancer. Fixed and random effects first and second order fractional polynomials were evaluated.

Conclusion

(Network) meta-analysis of survival data with models where the treatment effect is represented with several parameters using fractional polynomials can be more closely fitted to the available data than meta-analysis based on the constant hazard ratio.
Appendix
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Literature
1.
go back to reference Higgins JPT, Whitehead A: Borrowing strength from external trials in a meta-analysis. Statistics in Medicine. 1996, 15: 2733-2749. 10.1002/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0.CrossRefPubMed Higgins JPT, Whitehead A: Borrowing strength from external trials in a meta-analysis. Statistics in Medicine. 1996, 15: 2733-2749. 10.1002/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0.CrossRefPubMed
2.
go back to reference Lumley T: Network meta-analysis for indirect treatment comparisons. Statistics in Medicine. 2002, 21: 2313-2324. 10.1002/sim.1201.CrossRefPubMed Lumley T: Network meta-analysis for indirect treatment comparisons. Statistics in Medicine. 2002, 21: 2313-2324. 10.1002/sim.1201.CrossRefPubMed
3.
go back to reference Lu G, Ades AE: Combination of direct and indirect evidence in mixed treatment comparisons. Statistics in Medicine. 2004, 23: 3105-3124. 10.1002/sim.1875.CrossRefPubMed Lu G, Ades AE: Combination of direct and indirect evidence in mixed treatment comparisons. Statistics in Medicine. 2004, 23: 3105-3124. 10.1002/sim.1875.CrossRefPubMed
4.
go back to reference Caldwell DM, Ades AE, Higgins JPT: Simultaneous comparison of multiple treatments: combining direct and indirect evidence. British Medical Journal. 2005, 331: 897-900. 10.1136/bmj.331.7521.897.CrossRefPubMedPubMedCentral Caldwell DM, Ades AE, Higgins JPT: Simultaneous comparison of multiple treatments: combining direct and indirect evidence. British Medical Journal. 2005, 331: 897-900. 10.1136/bmj.331.7521.897.CrossRefPubMedPubMedCentral
5.
go back to reference Royston P, Altman DG: Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion). Applied Statistics. 1994, 43: 429-467. 10.2307/2986270.CrossRef Royston P, Altman DG: Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion). Applied Statistics. 1994, 43: 429-467. 10.2307/2986270.CrossRef
6.
go back to reference Lambert PC, Smith LK, Jones DR, Botha JL: Additive and multiplicative covariate regression models for relative survival incorporating fractional polynomials for time-dependent effects. Statistics in Medicine. 2005, 24: 3871-3885. 10.1002/sim.2399.CrossRefPubMed Lambert PC, Smith LK, Jones DR, Botha JL: Additive and multiplicative covariate regression models for relative survival incorporating fractional polynomials for time-dependent effects. Statistics in Medicine. 2005, 24: 3871-3885. 10.1002/sim.2399.CrossRefPubMed
7.
go back to reference Bossard N, Descotes F, Bremond AG, Bobin Y, De Saint Hilaire P, Golfier F, et al: Keeping data continuous when analyzing the prognostic impact of a tumor marker: an example with cathepsin D in breast cancer. Breast Cancer Research and Treatment. 2003, 82: 47-59. 10.1023/B:BREA.0000003919.75055.e8.CrossRefPubMed Bossard N, Descotes F, Bremond AG, Bobin Y, De Saint Hilaire P, Golfier F, et al: Keeping data continuous when analyzing the prognostic impact of a tumor marker: an example with cathepsin D in breast cancer. Breast Cancer Research and Treatment. 2003, 82: 47-59. 10.1023/B:BREA.0000003919.75055.e8.CrossRefPubMed
8.
go back to reference Berger U, Schafer J, Ulm K: Dynamic Cox modelling based on fractional polynomials: time-variations in gastric cancer prognosis. Statistics in Medicine. 2003, 22: 1163-1180. 10.1002/sim.1411.CrossRefPubMed Berger U, Schafer J, Ulm K: Dynamic Cox modelling based on fractional polynomials: time-variations in gastric cancer prognosis. Statistics in Medicine. 2003, 22: 1163-1180. 10.1002/sim.1411.CrossRefPubMed
9.
go back to reference Bagnardi V, Zambon A, Quatto P, Corrao G: Flexible meta-regression functions for modeling aggregate dose response data, with an application to alcohol and mortality. American Journal of Epidemiology. 2004, 159: 1077-1086. 10.1093/aje/kwh142.CrossRefPubMed Bagnardi V, Zambon A, Quatto P, Corrao G: Flexible meta-regression functions for modeling aggregate dose response data, with an application to alcohol and mortality. American Journal of Epidemiology. 2004, 159: 1077-1086. 10.1093/aje/kwh142.CrossRefPubMed
10.
go back to reference Sauerbrei W, Royston P: Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. JRSSA. 1999, 162: 71-94.CrossRef Sauerbrei W, Royston P: Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. JRSSA. 1999, 162: 71-94.CrossRef
11.
go back to reference Sauerbrei W, Royston P, Look M: A new proposal for multivariable modelling of time-varying effects in survival data based on fractional polynomial time-transformation. Biom J. 2007, 9: 453-473.CrossRef Sauerbrei W, Royston P, Look M: A new proposal for multivariable modelling of time-varying effects in survival data based on fractional polynomial time-transformation. Biom J. 2007, 9: 453-473.CrossRef
12.
go back to reference Lu G, Ades AE: Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc. 2006, 101: 447-459. 10.1198/016214505000001302.CrossRef Lu G, Ades AE: Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc. 2006, 101: 447-459. 10.1198/016214505000001302.CrossRef
13.
go back to reference Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ: Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med. 2009, 28: 1861-81. 10.1002/sim.3594.CrossRefPubMed Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ: Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med. 2009, 28: 1861-81. 10.1002/sim.3594.CrossRefPubMed
14.
go back to reference Akaike H: Information theory and an extension of the maximum likelihood principle. Second International Symposium on Information Theory. 1973, 1: 267-281. Akaike H: Information theory and an extension of the maximum likelihood principle. Second International Symposium on Information Theory. 1973, 1: 267-281.
15.
go back to reference Dempster AP: The direct use of likelihood for significance testing. Statistics and Computing. 1997, 7: 247-252. 10.1023/A:1018598421607.CrossRef Dempster AP: The direct use of likelihood for significance testing. Statistics and Computing. 1997, 7: 247-252. 10.1023/A:1018598421607.CrossRef
16.
go back to reference Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B. 2002, 64: 583-639. 10.1111/1467-9868.00353.CrossRef Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B. 2002, 64: 583-639. 10.1111/1467-9868.00353.CrossRef
17.
go back to reference Molina JR, Yang P, Cassivi SD, Schild SE, Adjei AA: Non-small cell lung cancer: epidemiology, risk factors, treatment, and survivorship. Mayo Clin Proc. 2008, 83: 584-94. 10.4065/83.5.584.CrossRefPubMedPubMedCentral Molina JR, Yang P, Cassivi SD, Schild SE, Adjei AA: Non-small cell lung cancer: epidemiology, risk factors, treatment, and survivorship. Mayo Clin Proc. 2008, 83: 584-94. 10.4065/83.5.584.CrossRefPubMedPubMedCentral
18.
go back to reference De Lima Araújo LH, Ferreira CG: Platinum-based second-line treatment in non-small-cell lung cancer: an old new kid on the block?. J Clin Oncol. 2010, 10 (28): e24-5.CrossRef De Lima Araújo LH, Ferreira CG: Platinum-based second-line treatment in non-small-cell lung cancer: an old new kid on the block?. J Clin Oncol. 2010, 10 (28): e24-5.CrossRef
19.
go back to reference Chang A, Parikh P, Thongprasert S, Tan E, Perng R, Ganzon D, et al: Gefitinib IRESSA in patients of Asian origin with refractory advanced non-small cell lung cancer: subset analysis from the ISEL study. Journal of thoracic oncology: official publication of theInternational Association for the Study of Lung Cancer. 2006, 1: 847-55.CrossRef Chang A, Parikh P, Thongprasert S, Tan E, Perng R, Ganzon D, et al: Gefitinib IRESSA in patients of Asian origin with refractory advanced non-small cell lung cancer: subset analysis from the ISEL study. Journal of thoracic oncology: official publication of theInternational Association for the Study of Lung Cancer. 2006, 1: 847-55.CrossRef
20.
go back to reference Cufer T, Vrdoljak E, Gaafar R, Erensoy I, Pemberton K, SIGN Study Group: Phase II, open-label, randomized study SIGN of single-agent gefitinib IRESSA or docetaxel as second-line therapy in patients with advanced stage IIIb or IV non-small-cell lung cancer. Anti-cancer drugs. 2006, 17: 401-9. 10.1097/01.cad.0000203381.99490.ab.CrossRefPubMed Cufer T, Vrdoljak E, Gaafar R, Erensoy I, Pemberton K, SIGN Study Group: Phase II, open-label, randomized study SIGN of single-agent gefitinib IRESSA or docetaxel as second-line therapy in patients with advanced stage IIIb or IV non-small-cell lung cancer. Anti-cancer drugs. 2006, 17: 401-9. 10.1097/01.cad.0000203381.99490.ab.CrossRefPubMed
21.
go back to reference Hanna N, Shepherd FA, Fossella FV, Pereira JR, De Marinis F, von Pawel J, et al: Randomized phase III trial of pemetrexed versus docetaxel in patients with non-small-cell lung cancer previously treated with chemotherapy. J Clin Oncol. 2004, 22: 1589-97. 10.1200/JCO.2004.08.163.CrossRefPubMed Hanna N, Shepherd FA, Fossella FV, Pereira JR, De Marinis F, von Pawel J, et al: Randomized phase III trial of pemetrexed versus docetaxel in patients with non-small-cell lung cancer previously treated with chemotherapy. J Clin Oncol. 2004, 22: 1589-97. 10.1200/JCO.2004.08.163.CrossRefPubMed
22.
go back to reference Kim E, Hirsh V, Mok T, Socinski M, Gervais R, Wu Y, et al: Gefitinib versus docetaxel in previously treated non-small-cell lung cancer INTEREST: a randomised phase III trial. Lancet. 2008, 372: 1809-18. 10.1016/S0140-6736(08)61758-4.CrossRefPubMed Kim E, Hirsh V, Mok T, Socinski M, Gervais R, Wu Y, et al: Gefitinib versus docetaxel in previously treated non-small-cell lung cancer INTEREST: a randomised phase III trial. Lancet. 2008, 372: 1809-18. 10.1016/S0140-6736(08)61758-4.CrossRefPubMed
23.
go back to reference Lee D, Park K, Kim J, Lee J, Shin S, Kang J, et al: Randomized Phase III trial of gefitinib versus docetaxel in non-small cell lung cancer patients who have previously received platinum-based chemotherapy. Clinical cancer research. 2010, 16: 1307-14. 10.1158/1078-0432.CCR-09-1903.CrossRefPubMed Lee D, Park K, Kim J, Lee J, Shin S, Kang J, et al: Randomized Phase III trial of gefitinib versus docetaxel in non-small cell lung cancer patients who have previously received platinum-based chemotherapy. Clinical cancer research. 2010, 16: 1307-14. 10.1158/1078-0432.CCR-09-1903.CrossRefPubMed
24.
go back to reference Maruyama R, Nishiwaki Y, Tamura T, Yamamoto N, Tsuboi M, Nakagawa K, et al: Phase III study, V-15-32, of gefitinib versus docetaxel in previously treated Japanese patients with non-small-cell lung cancer. Journal of clinical oncology: official journal of the AmericanSociety of Clinical Oncology. 2008, 26: 4244-52.CrossRef Maruyama R, Nishiwaki Y, Tamura T, Yamamoto N, Tsuboi M, Nakagawa K, et al: Phase III study, V-15-32, of gefitinib versus docetaxel in previously treated Japanese patients with non-small-cell lung cancer. Journal of clinical oncology: official journal of the AmericanSociety of Clinical Oncology. 2008, 26: 4244-52.CrossRef
25.
go back to reference Shepherd FA, Dancey J, Ramlau R, et al: Prospective randomized trial of docetaxel versus best supportive care in patients with non-small-cell lung cancer previously treated with platinum-based chemotherapy. J Clin Oncol. 2000, 18: 2095-103.PubMed Shepherd FA, Dancey J, Ramlau R, et al: Prospective randomized trial of docetaxel versus best supportive care in patients with non-small-cell lung cancer previously treated with platinum-based chemotherapy. J Clin Oncol. 2000, 18: 2095-103.PubMed
26.
go back to reference Ades AE, Sculpher M, Sutton AJ, Abrams K, Cooper N, Welton N, Lu G: Bayesian Methods for Evidence Synthesis in Cost-Effectiveness Analysis. Pharmacoeconomics. 2006, 24: 1-19. 10.2165/00019053-200624010-00001.CrossRefPubMed Ades AE, Sculpher M, Sutton AJ, Abrams K, Cooper N, Welton N, Lu G: Bayesian Methods for Evidence Synthesis in Cost-Effectiveness Analysis. Pharmacoeconomics. 2006, 24: 1-19. 10.2165/00019053-200624010-00001.CrossRefPubMed
27.
go back to reference Spiegelhalter DJ, Abrams KR, Myles JP: Bayesian approaches to clinical trials and health-care evaluations. 2004, Chichester: John Wiley & Sons, 80-85. Spiegelhalter DJ, Abrams KR, Myles JP: Bayesian approaches to clinical trials and health-care evaluations. 2004, Chichester: John Wiley & Sons, 80-85.
28.
go back to reference Spiegelhalter DJ, Abrams KR, Myles JP: Bayesian approaches to clinical trials and health-care evaluations. 2004, Chichester: John Wiley & Sons, 286- Spiegelhalter DJ, Abrams KR, Myles JP: Bayesian approaches to clinical trials and health-care evaluations. 2004, Chichester: John Wiley & Sons, 286-
29.
go back to reference Spiegelhalter D, Thomas A, Best N, Lunn D: WinBUGS User Manual: Version 1.4. 2003, MRC Biostatistics Unit: Cambridge Spiegelhalter D, Thomas A, Best N, Lunn D: WinBUGS User Manual: Version 1.4. 2003, MRC Biostatistics Unit: Cambridge
Metadata
Title
Network meta-analysis of survival data with fractional polynomials
Author
Jeroen P Jansen
Publication date
01-12-2011
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2011
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-11-61

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