Statistics and Computing

, Volume 22, Issue 5, pp 1099–1111 | Cite as

Algorithmic parameterization of mixed treatment comparisons

  • Gert van Valkenhoef
  • Tommi Tervonen
  • Bert de Brock
  • Hans Hillege
Open Access
Article

Abstract

Mixed Treatment Comparisons (MTCs) enable the simultaneous meta-analysis (data pooling) of networks of clinical trials comparing ≥2 alternative treatments. Inconsistency models are critical in MTC to assess the overall consistency between evidence sources. Only in the absence of considerable inconsistency can the results of an MTC (consistency) model be trusted. However, inconsistency model specification is non-trivial when multi-arm trials are present in the evidence structure. In this paper, we define the parameterization problem for inconsistency models in mathematical terms and provide an algorithm for the generation of inconsistency models. We evaluate running-time of the algorithm by generating models for 15 published evidence structures.

Keywords

Mixed treatment comparison Network meta-analysis Indirect comparisons Evidence consistency Model generation Algorithm 

Supplementary material

11222_2011_9281_MOESM1_ESM.pdf (109 kb)
Evidence Structures (PDF 109 kB)

References

  1. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001) MATHGoogle Scholar
  2. Deo, N., Prabhu, G.M., Krishnamoorthy, M.S.: Algorithms for generating fundamental cycles in a graph. ACM Trans. Math. Softw. 8(1), 26–42 (1982). doi:10.1145/355984.355988 MathSciNetMATHCrossRefGoogle Scholar
  3. Gabow, H.N., Myers, E.W.: Finding all spanning trees of directed and undirected graphs. SIAM J. Comput. 7(3), 280–287 (1978). doi:10.1137/0207024 MathSciNetMATHCrossRefGoogle Scholar
  4. Hedges, L.V., Vevea, J.L.: Fixed- and random-effects models in meta-analysis. Psychol. Methods 3(4), 486–504 (1998). doi:10.1037/1082-989X.3.4.486 CrossRefGoogle Scholar
  5. Higgins, J.P.T., Whitehead, A.: Borrowing strength from external trials in a meta-analysis. Stat. Med. 15(24), 2733–2749 (1996). doi:10.1002/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0 CrossRefGoogle Scholar
  6. Lu, G., Ades, A.E.: Assessing evidence inconsistency in mixed treatment comparisons. J. Am. Stat. Assoc. 101(474), 447–459 (2006). doi:10.1198/016214505000001302 MathSciNetMATHCrossRefGoogle Scholar
  7. Lu, G., Ades, A.: Modeling between-trial variance structure in mixed treatment comparisons. Biostatistics 10(4), 792–805 (2009). doi:10.1093/biostatistics/kxp032 CrossRefGoogle Scholar
  8. Lumley, T.: Network meta-analysis for indirect treatment comparisons. Stat. Med. 21(16), 2313–2324 (2002). doi:10.1002/sim.1201 CrossRefGoogle Scholar
  9. Normand, S.: Meta-analysis: formulating, evaluating, combining, and reporting. Stat. Med. 18(3), 321–359 (1999). doi:10.1002/(SICI)1097-0258(19990215)18:3<273::AID-SIM19>3.0.CO;2-7 CrossRefGoogle Scholar
  10. Salanti, G., Higgins, J.P.T., Ades, A.E., Ioannidis, J.P.A.: Evaluation of networks of randomized trials. Stat. Methods Med. Res. 17(3), 279–301 (2008a). doi:10.1177/0962280207080643 MathSciNetCrossRefGoogle Scholar
  11. Salanti, G., Kavvoura, F.K., Ioannidis, J.P.A.: Exploring the geometry of treatment networks. Ann. Intern. Med. 148(7), 544–553 (2008b) Google Scholar
  12. Sutton, A.J., Higgins, J.P.T.: Recent developments in meta-analysis. Stat. Med. 27(5), 625–650 (2008). doi:10.1002/sim.2934 MathSciNetCrossRefGoogle Scholar
  13. Wu, P., Wilson, K., Dimoulas, P., Mills, E.J.: Effectiveness of smoking cessation therapies: a systematic review and meta-analysis. BMC Public Health 6, 300 (2006). doi:10.1186/1471-2458-6-300 CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Gert van Valkenhoef
    • 1
    • 2
  • Tommi Tervonen
    • 3
  • Bert de Brock
    • 2
  • Hans Hillege
    • 1
  1. 1.Dept. of EpidemiologyUniversity Medical Center GroningenRB GroningenThe Netherlands
  2. 2.Faculty of Economics and BusinessUniversity of GroningenGroningenThe Netherlands
  3. 3.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands

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