Novel and existing flexible survival methods for network meta-analyses
Publication: Journal of Comparative Effectiveness Research
Abstract
Aim: Technical Support Document 21 discusses trial-based, flexible relative survival models. The authors generalized flexible relative survival models to the network meta-analysis (NMA) setting while accounting for different treatment-effect specifications. Methods: The authors compared the standard parametric model with mixture, mixture cure and nonmixture cure, piecewise, splines and fractional polynomial models. The optimal treatment-effect parametrization was defined in two steps. First, all models were run with treatment effects on all parameters and subsequently the optimal model was defined by removing uncertain treatment effects, for which the parameter was smaller than its standard deviation. The authors used a network in previously treated advanced non-small-cell lung cancer. Results: Flexible model-based NMAs impact fit and incremental mean survival and they increase corresponding uncertainty. Treatment-effect specification impacts incremental survival, reduces uncertainty and improves the fit statistic. Conclusion: Extrapolation techniques already available for individual trials can now be used for NMAs to ensure that the most plausible extrapolations are being used for health technology assessment submissions.
Supplementary Material
References
1.
NICE DSU Technical Support Document 2: A Generalised Linear Modelling Framework for Pairwise and Network Meta-analysis of Randomised Controlled Trials. NICE, London, UK (2011).
2.
NICE DSU Technical Support Document 14: Survival Analysis for Economic Evaluations alongside Clinical Trials – Extrapolation with Patient-Level Data. NICE, London, UK (2011).
3.
Guidelines for the Economic Evaluation of Health Technologies: Canada. Canadian Agency for Drugs and Technologies in Health. Ottowa, Canada (2017).
4.
Guidelines for Preparing Submissions to the Pharmaceutical Benefits Advisory Committee (PBAC). Version 5.0, September 2016. Department of Health, Canberra Australia (2016).
5.
Technology Appraisal Guidance [TA517] – Avelumab for Treating Metastatic Merkel Cell Carcinoma. NICE, London, UK (2021).
6.
Technology Appraisal Guidance [TA519] – Pembrolizumab for Treating Locally Advanced or Metastatic Urothelial Carcinoma after Platinum-Containing Chemotherapy. NICE, London, UK (2018).
7.
Technology Appraisal Guidance [TA520] – Atezolizumab for Treating Locally Advanced or Metastatic Non-small-cell Lung Cancer after Chemotherapy. NICE, London, UK (2018).
8.
Technology Appraisal Guidance [TA531] – Pembrolizumab for Untreated PD-L1-Positive Metastatic Non-small-cell Lung Cancer NICE, London, UK (2018).
9.
Technology Appraisal Guidance [TA554] – Tisagenlecleucel for Treating Relapsed or Refractory B-cell Acute Lymphoblastic Leukaemia in People Aged Up to 25 Years. NICE, London, UK (2018).
10.
Technology Appraisal Guidance [TA545] – Gemtuzumab Ozogamicin for Untreated Acute Myeloid Leukaemia. NICE, London, UK (2018).
11.
Technology Appraisal Guidance [TA589] – Blinatumomab for Treating Acute Lymphoblastic Leukaemia in Remission with Minimal Residual Disease Activity. NICE, London, UK (2019).
12.
Technology Appraisal Guidance [TA559] – Axicabtagene Ciloleucel for Treating Diffuse Large B-cell Lymphoma and Primary Mediastinal Large B-cell Lymphoma after 2 or More Systemic Therapies. NICE, London, UK (2019).
13.
Technology Appraisal Guidance [TA552] – Liposomal Cytarabine-Daunorubicin for Untreated Acute Myeloid Leukaemia. NICE, London, UK (2018).
14.
Lambert PC, Thompson JR, Weston CL, Dickman PW. Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics 8(3), 576–594 (2006).
15.
Swain PK, Grover G, Goel K. Mixture and non-mixture cure fraction models based on generalized Gompertz distribution under Bayesian approach. Tatra Mt. 66(1), 121–135 (2016).
16.
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. Biomet. J. 49(3), 453–473 (2007).
17.
Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat. Med. 21(15), 2175–2197 (2002).
18.
Ducros F, Pamphile P. Bayesian estimation of Weibull mixture in heavily censored data setting. Reliabil. Eng. Syst. Saf. 180, 453–462 (2018).
19.
Mohammed YA, Yatim B, Ismail S. A simulation study of a parametric mixture model of three different distributions to analyze heterogeneous survival data. Modern App. Sci. 7(7), 1–9 (2013).
20.
Ouwens MJNM, Mukhopadhyay P, Zhang Y, Huang M, Latimer N, Briggs A. Estimating lifetime benefits associated with immuno-oncology therapies: challenges and approaches for overall survival extrapolations. Pharmacoeconomics 37(9), 1129–1138 (2019).
21.
Cislo PR, Emir B, Cabrera J, Li B, Alemayehu D. Finite mixture models, a flexible alternative to standard modeling techniques for extrapolated mean survival times needed for cost–effectiveness analyses. Value Health 24(11), 1643–1650 (2021).
22.
NICE DSU Technical Support Document 21. Flexible Methods for Survival Analysis. NICE, London, UK (2020).
23.
Jansen JP. Network meta-analysis of survival data with fractional polynomials. BMC Med. Res. Methodol. 11(1), 61 (2011).
24.
Ouwens MJNM, Philips Z, Jansen JP. Network meta-analysis of parametric survival curves. Res. Synth. Methods 1(3–4), 258–271 (2010).
25.
Freeman SC, Carpenter JR. Bayesian one-step IPD network meta-analysis of time-to-event data using Royston-Parmar models. Res. Synth. Methods 8(4), 451–464 (2017).
26.
Astrazeneca. National Institute for Health and Care Excellence (NICE). Technology Appraisal Guidance [TA503] – Fulvestrant for Untreated Locally Advanced or Metastatic Oestrogen-Receptor Positive Breast Cancer NICE, London, UK (2018).
27.
Wiecek W, Karcher H. Nivolumab versus cabozantinib: comparing overall survival in metastatic renal cell carcinoma. PLOS ONE 11(6), 1–11 (2016).
28.
Cope S, Jansen JP. Quantitative summaries of treatment effect estimates obtained with network meta-analysis of survival curves to inform decision-making. BMC Med. Res. Methodol. 13, 1–11 (2013).
29.
Cope S, Ouwens MJNM, Jansen JP, Schmid P. Progression-free survival with fulvestrant 500 mg and alternative endocrine therapies as second-line treatment for advanced breast cancer: a network meta-analysis with parametric survival models. Value Health 16(2), 403–417 (2013).
30.
Kim J, Cho J, Lee MH, Lim JH. Relative efficacy of checkpoint inhibitors for advanced NSCLC according to programmed death-ligand-1 expression: a systematic review and network meta-analysis. Sci. Rep. 8(1), 1–8 (2018).
31.
Borghaei H, Gettinger S, Vokes EE et al. Five-year outcomes from the randomized, phase III trials CheckMate 017 and 057: nivolumab versus docetaxel in previously treated non-small-cell lung cancer. J. Clin. Oncol. 39(7), 723–733 (2021).
32.
Herbst RS, Garon EB, Kim DW et al. Long-term outcomes and retreatment among patients with previously treated, programmed death-ligand 1-positive, advanced non-small-cell lung cancer in the KEYNOTE-010 study. J. Clin. Oncol. 38(14), 1580–1590 (2020).
33.
Fehrenbacher L, Von Pawel J, Park K et al. Updated efficacy analysis including secondary population results for OAK: a randomized phase III study of atezolizumab versus docetaxel in patients with previously treated advanced non-small cell lung cancer. J. Thorac. Oncol. 13(8), 1156–1170 (2018).
34.
Fehrenbacher L, Spira A, Ballinger M et al. Atezolizumab versus docetaxel for patients with previously treated non-small-cell lung cancer (POPLAR): a multicentre, open-label, phase 2 randomised controlled trial. Lancet 387(10030), 1837–1846 (2016).
35.
Rittmeyer A, Barlesi F, Waterkamp D et al. Atezolizumab versus docetaxel in patients with previously treated non-small-cell lung cancer (OAK): a phase 3, open-label, multicentre randomised controlled trial. Lancet 389(10066), 255–265 (2017).
36.
Mitchell M, Muftakhidinov B, Winchen T. Engauge digitizer software (2020). https://markummitchell.github.io/engauge-digitizer/
37.
Guyot P, Ades AE, Ouwens MJNM, Welton NJ. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan–Meier survival curves. BMC Med. Res. Methodol. 12(1), 9 (2012).
38.
Demiris N, Lunn D, Sharples LD. Survival extrapolation using the poly-Weibull model. Stat. Methods Med. Res. 24(2), 287–301 (2015).
39.
Crowther MJ, Lambert PC. stgenreg: a Stata package for general parametric survival analysis. J. Stat. Software 53(12), 1–17 (2013).
40.
O'Hara B, Sillanpää M. A review of Bayesian variable selection methods: what, how and which. Bayesian Analysis 4, 85–117 (2009).
41.
Vehtari A, Gelman A, Gabry J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 27(5), 1413–1432 (2017).
42.
Stone M. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. Royal Stat. Soc. B 39(1), 44–47 (1977).
43.
National life tables, UK: 2016 to 2018. www.ons.gov.uk/releases/nationallifetablesuk2016to2018
44.
Andersson TML, Dickman PW, Eloranta S, Lambe M, Lambert PC. Estimating the loss in expectation of life due to cancer using flexible parametric survival models. Stat. Med. 32(30), 5286–5300 (2013).
45.
Van Oostrum I, Ouwens M, Remiro-Azócar A et al. Comparison of parametric survival extrapolation approaches incorporating general population mortality for adequate health technology assessment of new oncology drugs. Value Health 24(9), 1294–1301 (2021).
46.
rstan®, package insert. Available at: https://cran.r-project.org/web/packages/rstan/rstan.pdf.
47.
Betancourt M. How the Shape of a Weakly Informative Prior Affects Inferences. R package version 2(1), (2017). https://mc-stan.org/users/documentation/case-studies/weakly_informative_shapes.html
48.
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Statist. Sci. 7(4), 457–472 (1992).
49.
Schoenfeld DA, Hui Z, Finkelstein DM. Bayesian design using adult data to augment pediatric trials. Clin. Trials 6(4), 297–304 (2009).
50.
Dias S, Ades AE, Welton NJ, Jansen JP, Sutton AJ. Network Meta-analysis for Decision-Making. John Wiley & Sons, Hoboken, NJ, USA (2018).
51.
Phillippo DM, Dias S, Ades AE et al. Multilevel network meta-regression for population-adjusted treatment comparisons. J. Royal Stat. Soc. Ser. A Stat. Soc. 183(3), 1189–1210 (2020).
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© 2022 Cytel. This work is licensed under the Attribution-NonCommercial-NoDerivatives 4.0 Unported License
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Received: 28 February 2022
Accepted: 8 August 2022
Published online: 12 September 2022
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Novel and existing flexible survival methods for network meta-analyses. (2022) Journal of Comparative Effectiveness Research. DOI: 10.2217/cer-2022-0044
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