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Biometrical journal. Biometrische Zeitschrift
Feb, 2025;67 (1): e70037.

Network Meta-Analysis of Time-to-Event Endpoints With Individual Participant Data Using Restricted Mean Survival Time Regression.

Kaiyuan Hua, Xiaofei Wang, Hwanhee Hong
Author Information
  1. Kaiyuan Hua: Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, North Carolina, USA. ORCID
  2. Xiaofei Wang: Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, North Carolina, USA.
  3. Hwanhee Hong: Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, North Carolina, USA.
PMID: 39967285 DOI: 10.1002/bimj.70037

Abstract

Network meta-analysis (NMA) extends pairwise meta-analysis to compare multiple treatments simultaneously by combining "direct" and "indirect" comparisons of treatments. The availability of individual participant data (IPD) makes it possible to evaluate treatment effect moderation and to draw inferences about treatment effects by taking the full utilization of individual covariates from multiple clinical trials. In IPD-NMA, restricted mean survival time (RMST) models have gained popularity when analyzing time-to-event outcomes because RMST models offer more straightforward interpretations of treatment effects with fewer assumptions than hazard ratios commonly estimated from Cox models. Existing approaches estimate RMST within each study and then combine by using aggregate-level NMA methods. However, these methods cannot incorporate individual covariates to evaluate the effect moderation. In this paper, we propose advanced RMST NMA models when IPD are available. Our models allow us to study treatment effect moderation and provide a comprehensive understanding about comparative effectiveness of treatments and subgroup effects. The methods are evaluated by an extensive simulation study and illustrated using a real NMA example about treatments for patients with atrial fibrillation.

Keywords

effect moderation individual participant data network‐meta analysis restricted mean survival time

References

  1. Andersen, P., M. Hansen, and J. Klein. 2004. “Regression Analysis of Restricted Mean Survival Time Based on Pseudo‐Observations.” Lifetime Data Analysis 10, no. 4: 335–350.
  2. Bellamy, S. L., Y. Li, X. Lin, and L. M. Ryan. 2005. “Quantifying PQL Bias in Estimating Cluster‐Level Covariate Effects in Generalized Linear Mixed Models for Group‐Randomized Trials.” Statistica Sinica 15, no. 4: 1015–1032.
  3. Bowden, J., J. F. Tierney, M. Simmonds, A. J. Copas, and J. P. Higgins. 2011. “Individual Patient Data Meta‐Analysis of Time‐to‐Event Outcomes: One‐Stage Versus Two‐Stage Approaches for Estimating the Hazard Ratio Under a Random Effects Model.” Research Synthesis Methods 2, no. 3: 150–162.
  4. Breslow, N. 2004. “Whither PQL?” In Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data, 1–22. Springer.
  5. Breslow, N. E., and D. G. Clayton. 1993. “Approximate Inference in Generalized Linear Mixed Models.” Journal of the American Statistical Association 88, no. 421: 9–25.
  6. Burke, D., J. Ensor, and R. Riley. 2017. “Meta‐Analysis Using Individual Participant Data: One‐Stage and Two‐Stage Approaches, and Why They may Differ.” Statistics in Medicine 36, no. 5: 855–875.
  7. Carnicelli, A., H. Hong, R. P. Giugliano, et al. 2021. “Individual Patient Data from the Pivotal Randomized Controlled Trials of Non‐Vitamin K Antagonist Oral Anticoagulants in Patients With Atrial Fibrillation (COMBINE AF): Design and Rationale: From the COMBINE AF (A Collaboration Between Multiple Institutions to Better Investigate Non‐vitamin K Antagonist Oral Anticoagulant use in Atrial Fibrillation) Investigators.” American Heart Journal 233: 48–58.
  8. Carnicelli, A. P., H. Hong, S. J. Connolly, et al. 2022. “Direct Oral Anticoagulants Versus Warfarin in Patients With Atrial Fibrillation: Patient‐Level Network Meta‐Analyses of Randomized Clinical Trials With Interaction Testing by Age and Sex.” Circulation 145, no. 4: 242–255.
  9. Chen, H., A. Manning, and J. Dupuis. 2012. “A Method of Moments Estimator for Random Effect Multivariate Meta‐Analysis.” Biometrics 68, no. 4: 1278–1284.
  10. Chu, H., L. Lin, Z. Wang, Z. Wang, Y. Chen, and J. C. Cappelleri. 2024. “A Review and Comparison of Arm‐Based Versus Contrast‐Based Network Meta‐Analysis for Binary Outcomes—Understanding Their Differences and Limitations.” Wiley Interdisciplinary Reviews: Computational Statistics 16, no. 1: e1639.
  11. Cox, D. 1972. “Regression Models and Life‐Tables.” Journal of the Royal Statistical Society: Series B (Methodological) 34, no. 2: 187–202.
  12. Crowther, M. J., R. D. Riley, J. A. Staessen, J. Wang, F. Gueyffier, and P. C. Lambert. 2012. “Individual Patient Data Meta‐Analysis of Survival Data Using Poisson Regression Models.” BMC Medical Research Methodology 12, no. 1: 1–14.
  13. Debray, T. P., K. G. Moons, G. M. A. Abo‐Zaid, H. Koffijberg, and R. D. Riley. 2013. “Individual Participant Data Meta‐Analysis for a Binary Outcome: One‐Stage or Two‐Stage?” PLoS One 8, no. 4: e60650.
  14. Debray, T. P. A., K. G. Moons, G. van Valkenhoef, et al. 2015. “Get Real in Individual Participant Data (IPD) Meta‐Analysis: A Review of the Methodology.” Research Synthesis Methods 6, no. 4: 293–309.
  15. DerSimonian, R., and N. Laird. 1986. “Meta‐Analysis in Clinical Trials.” Controlled Clinical Trials 7, no. 3: 177–188.
  16. Dias, S., and A. Ades. 2016. “Absolute or Relative Effects? Arm‐Based Synthesis of Trial Data.” Research Synthesis Methods 7, no. 1: 23–28.
  17. Donegan, S., P. Williamson, U. D'Alessandro, P. Garner, and C. T. Smith. 2013. “Combining Individual Patient Data and Aggregate Data in Mixed Treatment Comparison Meta‐Analysis: Individual Patient Data May Be Beneficial If Only for a Subset of Trials.” Statistics in Medicine 32, no. 6: 914–930.
  18. Donegan, S., P. Williamson, U. D'Alessandro, and C. T. Smith. 2012. “Assessing the Consistency Assumption by Exploring Treatment by Covariate Interactions in Mixed Treatment Comparison Meta‐Analysis: Individual Patient‐Level Covariates Versus Aggregate Trial‐Level Covariates.” Statistics in Medicine 31, no. 29: 3840–3857.
  19. Elfadaly, F. G., A. Adamson, J. Patel, et al. 2021. “BIMAM—A Tool for Imputing Variables Missing Across Datasets Using a Bayesian Imputation and Analysis Model.” International Journal of Epidemiology 50, no. 5: 1419–1425.
  20. Freeman, S. C., D. Fisher, I. R. White, A. Auperin, and J. R. Carpenter. 2019. “Identifying Inconsistency in Network Meta‐Analysis: Is the Net Heat Plot a Reliable Method?” Statistics in Medicine 38, no. 29: 5547–5564.
  21. Gardiner, J. 2021. “Restricted Mean Survival Time Estimation: Nonparametric and Regression Methods.” Journal of Statistical Theory and Practice 15, no. 1: 1–15.
  22. Gasparrini, A., B. Armstrong, and M. G. Kenward. 2012. “Multivariate meta‐analysis for non‐linear and other multi‐parameter associations.” Statistics in Medicine 31, no. 29: 3821–3839.
  23. Hawkins, N., D. A. Scott, and B. Woods. 2016. “Arm‐Based‐Parameterization for Network Meta‐Analysis.” Research Synthesis Methods 7, no. 3: 306–313.
  24. Higgins, J., D. Jackson, J. Barrett, G. Lu, A. Ades, and I. White. 2012. “Consistency and Inconsistency in Network Meta‐Analysis: Concepts and Models for Multi‐Arm Studies.” Research Synthesis Methods 3, no. 2: 98–110.
  25. Hong, H., H. Chu, J. Zhang, and B. P. Carlin. 2016a. “A Bayesian Missing Data Framework for Generalized Multiple Outcome Mixed Treatment Comparisons.” Research Synthesis Methods 7, no. 1: 6–22.
  26. Hong, H., H. Chu, J. Zhang, and B. P. Carlin. 2016b. “Rejoinder to the Discussion of ‘A Bayesian Missing Data Framework for Generalized Multiple Outcome Mixed Treatment Comparisons,’ by S. Dias and AE Ades.” Research Synthesis Methods 7, no. 1: 29–33.
  27. Hong, H., H. Fu, K. L. Price, and B. P. Carlin. 2015. “Incorporation of Individual‐Patient Data in Network Meta‐Analysis for Multiple Continuous Endpoints, With Application to Diabetes Treatment.” Statistics in Medicine 34, no. 20: 2794–2819.
  28. Hua, H., D. L. Burke, M. J. Crowther, J. Ensor, C. Tudur Smith, and R. D. Riley. 2017. “One‐Stage Individual Participant Data Meta‐Analysis Models: Estimation of Treatment‐Covariate Interactions Must Avoid Ecological Bias by Separating Out Within‐Trial and Across‐Trial Information.” Statistics in Medicine 36, no. 5: 772–789.
  29. Hua, K., D. Wojdyla, A. Carnicelli, C. Granger, X. Wang, and H. Hong. 2024. “Network Meta‐Analysis With Individual Participant‐Level Data of Time‐to‐Event Outcomes Using Cox Regression.” Statistics in Medicine, https://doi.org/10.1002/sim.70027.
  30. Irwin, J. 1949. “The Standard Error of an Estimate of Expectation of Life, With Special Reference to Expectation of Tumourless Life in Experiments With Mice.” Epidemiology & Infection 47, no. 2: 188–189.
  31. Jackson, D., R. Riley, and I. R. White. 2011. “Multivariate Meta‐Analysis: Potential and Promise.” Statistics in Medicine 30, no. 20: 2481–2498.
  32. Jackson, D., I. White, and R. Riley. 2013. “A Matrix‐Based Method of Moments for Fitting the Multivariate Random Effects Model for Meta‐Analysis and Meta‐Regression.” Biometrical Journal 55, no. 2: 231–245.
  33. Jang, W., and J. Lim. 2009. “A Numerical Study of PQL Estimation Biases in Generalized Linear Mixed Models Under Heterogeneity of Random Effects.” Communications in Statistics ‐ Simulation and Computation 38, no. 4: 692–702.
  34. Jansen, J. P. 2011. “Network Meta‐Analysis of Survival Data With Fractional Polynomials.” BMC Medical Research Methodology 11, no. 1: 1–14.
  35. Jiang, J., and T. Nguyen. 2007. Linear and Generalized Linear Mixed Models and Their Applications. Vol. 1. Springer.
  36. Jolani, S., T. P. Debray, H. Koffijberg, S. van Buuren, and K. G. Moons. 2015. “Imputation of Systematically Missing Predictors in an Individual Participant Data Meta‐Analysis: A Generalized Approach Using MICE.” Statistics in Medicine 34, no. 11: 1841–1863.
  37. Kim, D., H. Uno, and L. Wei. 2017. “Restricted Mean Survival Time as a Measure to Interpret Clinical Trial Results.” JAMA Cardiology 2, no. 11: 1179–1180.
  38. Kontopantelis, E. 2018. “A Comparison of One‐Stage vs Two‐Stage Individual Patient Data Meta‐Analysis Methods: A Simulation Study.” Research Synthesis Methods 9, no. 3: 417–430.
  39. Lin, D., and L. Wei. 1989. “The Robust Inference for the Cox Proportional Hazards Model.” Journal of the American Statistical Association 84, no. 408: 1074–1078.
  40. Lin, X. 2007. “Estimation Using Penalized Quasilikelihood and Quasi‐Pseudo‐Likelihood in Poisson Mixed Models.” Lifetime Data Analysis 13: 533–544.
  41. Lin, X., and N. E. Breslow. 1996. “Bias Correction in Generalized Linear Mixed Models With Multiple Components of Dispersion.” Journal of the American Statistical Association 91, no. 435: 1007–1016.
  42. Little, R. J., and D. B. Rubin. 2019. Statistical Analysis With Missing Data. Vol. 793. Wiley.
  43. Liu, Q., and D. A. Pierce. 1994. “A Note on Gauss–Hermite Quadrature.” Biometrika 81, no. 3: 624–629.
  44. Lu, G., and A. E. Ades. 2004. “Combination of Direct and Indirect Evidence in Mixed Treatment Comparisons.” Statistics in Medicine 23, no. 20: 3105–3124.
  45. Lueza, B., A. Mauguen, J.‐P. Pignon, O. Rivero‐Arias, J. Bonastre, and M.‐L. C. Group. 2016. “Difference in Restricted Mean Survival Time for Cost‐Effectiveness Analysis Using Individual Patient Data Meta‐Analysis: Evidence From a Case Study.” PLoS One 11, no. 3: e0150032.
  46. Lyman, G. H., and N. M. Kuderer. 2005. “The Strengths and Limitations of Meta‐Analyses Based on Aggregate Data.” BMC Medical Research Methodology 5, no. 1: 1–7.
  47. McCullagh, P. 2019. Generalized Linear Models. Routledge.
  48. Mills, E. J., K. Thorlund, and J. P. Ioannidis. 2013. “Demystifying Trial Networks and Network Meta‐Analysis.” BMJ 346: f2914.
  49. Nugent, J., B. Doone, and K. Kleinman. 2019. “Bias Induced by Fitting Glmms With Dichotomous Outcomes Using Penalized Quasi‐Likelihood.” https://joshua‐nugent.github.io/pql/main.pdf.
  50. Perego, C., M. Sbolli, C. Specchia, et al. 2020. “Utility of Restricted Mean Survival Time Analysis for Heart Failure Clinical Trial Evaluation and Interpretation.” Heart Failure 8, no. 12: 973–983.
  51. Piepho, H.‐P. 2014. “Network Meta‐Analysis Made Easy: Detection of Inconsistency Using Factorial Analysis‐of‐Variance Models.” BMC Medical Research Methodology 14: 1–9.
  52. Piepho, H.‐P., and L. V. Madden. 2022. “How to Observe the Principle of Concurrent Control in an Arm‐Based Meta‐Analysis Using SAS Procedures GLIMMIX and BGLIMM.” Research Synthesis Methods 13, no. 6: 821–828.
  53. Piepho, H.‐P., L. V. Madden, J. Roger, R. Payne, and E. R. Williams. 2018. “Estimating the Variance for Heterogeneity in Arm‐Based Network Meta‐Analysis.” Pharmaceutical Statistics 17, no. 3: 264–277.
  54. Piepho, H.‐P., L. V. Madden, and E. R. Williams. 2024. “The Use of Fixed Study Main Effects in Arm‐Based Network Meta‐Analysis.” Research Synthesis Methods 15, no. 5: 747–750.
  55. Pinheiro, J. C., and D. M. Bates. 1995. “Approximations to the Log‐Likelihood Function in the Nonlinear Mixed‐Effects Model.” Journal of Computational and Graphical Statistics 4, no. 1: 12–35.
  56. Press, S. J. 2005. Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. Courier Corporation.
  57. Resche‐Rigon, M., and I. R. White. 2018. “Multiple Imputation by Chained Equations for Systematically and Sporadically Missing Multilevel Data.” Statistical Methods in Medical Research 27, no. 6: 1634–1649.
  58. Riley, R. D., P. C. Lambert, and G. Abo‐Zaid. 2010. “Meta‐Analysis of Individual Participant Data: Rationale, Conduct, and Reporting.” BMJ 340: c221.
  59. Ripley, B., B. Venables, D. M. Bates, et al. 2013. “Package ‘mass’.” Cran R 538: 113–120.
  60. Royston, P., and M. Parmar. 2002. “Flexible Parametric Proportional‐Hazards and Proportional‐Odds Models for Censored Survival Data, With Application to Prognostic Modelling and Estimation of Treatment Effects.” Statistics in Medicine 21, no. 15: 2175–2197.
  61. Royston, P., and M. K. Parmar. 2013. “Restricted Mean Survival Time: An Alternative to the Hazard Ratio for the Design and Analysis of Randomized Trials With a Time‐to‐Event Outcome.” BMC Medical Research Methodology 13, no. 1: 1–15.
  62. Rubin, D. B. 2018. “Multiple Imputation.” In Flexible Imputation of Missing Data, Second Edition, 29–62. Chapman and Hall/CRC.
  63. Salanti, G., J. P. Higgins, A. Ades, and J. P. Ioannidis. 2008. “Evaluation of Networks of Randomized Trials.” Statistical Methods in Medical Research 17, no. 3: 279–301.
  64. Saramago, P., L.‐H. Chuang, and M. O. Soares. 2014. “Network Meta‐Analysis of (Individual Patient) Time to Event Data Alongside (Aggregate) Count Data.” BMC Medical Research Methodology 14, no. 1: 1–11.
  65. Schwarzer, G., J. R. Carpenter, and G. Rücker. 2015. Meta‐Analysis With R. Vol. 4784. Springer.
  66. Simmonds, M. C., J. P. Higginsa, L. A. Stewartb, J. F. Tierneyb, M. J. Clarke, and S. G. Thompson. 2005. “Meta‐Analysis of Individual Patient Data From Randomized Trials: A Review of Methods Used in Practice.” Clinical Trials 2, no. 3: 209–217.
  67. Smith, C. T., P. R. Williamson, and A. G. Marson. 2005. “Investigating Heterogeneity in an Individual Patient Data Meta‐Analysis of Time to Event Outcomes.” Statistics in Medicine 24, no. 9: 1307–1319.
  68. Steingrimsson, J. A., D. H. Barker, R. Bie, and I. J. Dahabreh. 2024. “Systematically Missing Data in Causally Interpretable Meta‐Analysis.” Biostatistics 25, no. 2: 289–305.
  69. Stewart, G. B., D. G. Altman, L. M. Askie, L. Duley, M. C. Simmonds, and L. A. Stewart. 2012. “Statistical Analysis of Individual Participant Data Meta‐Analyses: A Comparison of Methods and Recommendations for Practice.” PLoS One 7, no. 10: e46042.
  70. Tang, X., and L. Trinquart. 2022. “Bayesian Multivariate Network Meta‐Analysis Model for the Difference in Restricted Mean Survival Times.” Statistics in Medicine 41, no. 3: 595–611.
  71. Tian, L., L. Zhao, and L. Wei. 2014. “Predicting the Restricted Mean Event Time With the Subject's Baseline Covariates in Survival Analysis.” Biostatistics 15, no. 2: 222–233.
  72. Uno, H., B. Claggett, L. Tian, et al. 2014. “Moving Beyond the Hazard Ratio in Quantifying the Between‐Group Difference in Survival Analysis.” Journal of Clinical Oncology 32, no. 22: 2380–2385.
  73. Wang, X., and D. E. Schaubel. 2018. “Modeling Restricted Mean Survival Time Under General Censoring Mechanisms.” Lifetime Data Analysis 24: 176–199.
  74. Wei, Y., and J. P. Higgins. 2013. “Bayesian Multivariate Meta‐Analysis With Multiple Outcomes.” Statistics in Medicine 32, no. 17: 2911–2934.
  75. Wei, Y., P. Royston, J. Tierney, and M. Parmar. 2015. “Meta‐Analysis of Time‐to‐Event Outcomes From Randomized Trials Using Restricted Mean Survival Time: Application to Individual Participant Data.” Statistics in Medicine 34, no. 21: 2881–2898.
  76. Weir, I., L. Tian, and L. Trinquart. 2021. “Multivariate Meta‐Analysis Model for the Difference in Restricted Mean Survival Times.” Biostatistics 22, no. 1: 82–96.
  77. White, I. R. 2015. “Network Meta‐Analysis.” Stata Journal 15, no. 4: 951–985.
  78. White, I. R., J. K. Barrett, D. Jackson, and J. P. Higgins. 2012. “Consistency and Inconsistency in Network Meta‐Analysis: Model Estimation Using Multivariate Meta‐Regression.” Research Synthesis Methods 3, no. 2: 111–125.
  79. White, I. R., R. M. Turner, A. Karahalios, and G. Salanti. 2019. “A Comparison of Arm‐Based and Contrast‐Based Models for Network Meta‐Analysis.” Statistics in Medicine 38, no. 27: 5197–5213.
  80. Wolfinger, R., and M. O'Connell. 1993. “Generalized Linear Mixed Models a Pseudo‐Likelihood Approach.” Journal of Statistical Computation and Simulation 48, no. 3‐4: 233–243.
  81. Xie, L., and L. V. Madden. 2014. “%HPGLIMMIX: A High‐Performance SAS Macro for GLMM Estimation.” Journal of Statistical Software 58, no. 8: 1–25.
  82. Zhong, Y., and D. E. Schaubel. 2022. “Restricted Mean Survival Time as a Function of Restriction Time.” Biometrics 78, no. 1: 192–201.

Grants

  1. R01 AG066883/NIA NIH HHS
  2. ME-2020C3-21145/Patient-Centered Outcomes Research Institute
  3. R01MH126856/NIMH NIH HHS
  4. P01 CA142538/NCI NIH HHS

MeSH Term

Humans
Biometry
Survival Analysis
Models, Statistical
Regression Analysis
Atrial Fibrillation
Time Factors
Endpoint Determination
Journal Article Network Meta-Analysis
Article has an altmetric score of 1

Word Cloud

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