An extended mixed-effects framework for meta-analysis.

Francesco Sera, Benedict Armstrong, Marta Blangiardo, Antonio Gasparrini
Author Information
  1. Francesco Sera: Department of Public Health Environments and Society, London School of Hygiene & Tropical Medicine, London, UK. ORCID
  2. Benedict Armstrong: Department of Public Health Environments and Society, London School of Hygiene & Tropical Medicine, London, UK. ORCID
  3. Marta Blangiardo: Department of Epidemiology and Biostatistics, Imperial College London, London, UK. ORCID
  4. Antonio Gasparrini: Department of Public Health Environments and Society, London School of Hygiene & Tropical Medicine, London, UK. ORCID

Abstract

Standard methods for meta-analysis are limited to pooling tasks in which a single effect size is estimated from a set of independent studies. However, this setting can be too restrictive for modern meta-analytical applications. In this contribution, we illustrate a general framework for meta-analysis based on linear mixed-effects models, where potentially complex patterns of effect sizes are modeled through an extended and flexible structure of fixed and random terms. This definition includes, as special cases, a variety of meta-analytical models that have been separately proposed in the literature, such as multivariate, network, multilevel, dose-response, and longitudinal meta-analysis and meta-regression. The availability of a unified framework for meta-analysis, complemented with the implementation in a freely available and fully documented software, will provide researchers with a flexible tool for addressing nonstandard pooling problems.

Keywords

References

  1. Borenstein M, Hedges LV, Higgins J, Rothstein HR. Introduction to Meta-Analysis. Hoboken, NJ: John Wiley & Sons; 2009.
  2. Jackson D, Riley R, White IR. Multivariate meta-analysis: potential and promise. Statist Med. 2011;30(20):2481-2498.
  3. Gasparrini A, Armstrong B, Kenward MG. Multivariate meta-analysis for non-linear and other multi-parameter associations. Statist Med. 2012;31(29):3821-3839.
  4. Riley RD, Jackson D, Salanti G, et al. Multivariate and network meta-analysis of multiple outcomes and multiple treatments: rationale, concepts, and examples. BMJ. 2017;358:j3932.
  5. Stevens JR, Taylor AM. Hierarchical dependence in meta-analysis. J Educ Behav Stat. 2009;34(1):46-73.
  6. Orsini N, Li R, Wolk A, Khudyakov P, Spiegelman D. Meta-analysis for linear and nonlinear dose-response relations: examples, an evaluation of approximations, and software. Am J Epidemiol. 2011;175(1):66-73.
  7. Crippa A, Discacciati A, Bottai M, Spiegelman D, Orsini N. One-stage dose-response meta-analysis for aggregated data. Stat Methods Med Res. 2019;28(5):1579-1596.
  8. Ishak K, Platt RW, Joseph L, Hanley JA, Caro JJ. Meta-analysis of longitudinal studies. Clinical Trials. 2007;4(5):525-539.
  9. Goldstein H, Yang M, Omar R, Turner R, Thompson S. Meta-analysis using multilevel models with an application to the study of class size effects. J R Stat Soc Ser C Appl Stat. 2000;49(3):399-412.
  10. Thompson SG, Turner RM, Warn DE. Multilevel models for meta-analysis, and their application to absolute risk differences. Stat Methods Med Res. 2001;10(6):375-392.
  11. Turner RM, Omar RZ, Yang M, Goldstein H, Thompson SG. A multilevel model framework for meta-analysis of clinical trials with binary outcomes. Statist Med. 2000;19(24):3417-3432.
  12. Berkey CS, Hoaglin DC, Antczak-Bouckoms A, Mosteller F, Colditz GA. Meta-analysis of multiple outcomes by regression with random effects. Statist Med. 1998;17(22):2537-2550.
  13. Konstantopoulos S. Fixed effects and variance components estimation in three-level meta-analysis. Res Synth Methods. 2011;2(1):61-76.
  14. Stram DO. Meta-analysis of published data using a linear mixed-effects model. Biometrics. 1996;52(2):536-544.
  15. Bagos PG. Meta-analysis in Stata using gllamm. Res Synth Methods. 2015;6(4):310-332.
  16. Van den Noortgate W, L��pez-L��pez JA, Mar��n-Mart��nez F, S��nchez-Meca J. Three-level meta-analysis of dependent effect sizes. Behav Res Methods. 2013;45(2):576-594.
  17. Van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Statist Med. 2002;21(4):589-624.
  18. Pinheiro JC, Bates DM. Mixed-Effects Models in S and S-Plus. New York, NY: Springer Verlag; 2000.
  19. Harville DA. Maximum likelihood approaches to variance component estimation and to related problems. J Am Stat Assoc. 1977;72(358):320-338.
  20. Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. New York, NY: Springer; 1997.
  21. Goldstein H. Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika. 1986;73(1):43-56.
  22. Goldstein H. Restricted unbiased iterative generalized least-squares estimation. Biometrika. 1989;76(3):622-623.
  23. Goldstein H. Multilevel Statistical Models. Vol 922. Hoboken, NJ: John Wiley & Sons; 2011.
  24. DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7(3):177-188.
  25. Higgins J, Thompson SG. Quantifying heterogeneity in a meta-analysis. Statist Med. 2002;21(11):1539-1558.
  26. Riley RD, Higgins JPT, Deeks JJ. Interpretation of random effects meta-analyses. BMJ. 2011;342:d549.
  27. Higgins J, Thompson SG, Spiegelhalter DJ. A re-evaluation of random-effects meta-analysis. J R Stat Soc Ser A Stat Soc. 2009;172(1):137-159.
  28. Rice K, Higgins J, Lumley T. A re-evaluation of fixed effect (s) meta-analysis. J R Stat Soc Ser A Stat Soc. 2018;181(1):205-227.
  29. Berkey CS, Hoaglin DC, Mosteller F, Colditz GA. A random-effects regression model for meta-analysis. Statist Med. 1995;14(4):395-411.
  30. Colditz GA, Brewer TF, Berkey CS, et al. Efficacy of BCG vaccine in the prevention of tuberculosis: meta-analysis of the published literature. JAMA. 1994;271(9):698-702.
  31. Olkin I, Gleser L. Stochastically dependent effect sizes. In: Cooper H, Hedges LV, Valentine JC, eds. The Handbook of Research Synthesis and Meta-Analysis. New York, NY: Russell Sage Foundation; 2009:357-376.
  32. Ma X, Nie L, Cole SR, Chu H. Statistical methods for multivariate meta-analysis of diagnostic tests: an overview and tutorial. Stat Methods Med Res. 2016;25(4):1596-1619.
  33. White IR, Barrett JK, Jackson D, Higgins J. Consistency and inconsistency in network meta-analysis: model estimation using multivariate meta-regression. Res Synth Methods. 2012;3(2):111-125.
  34. Fiore MC, Bailey WC, Cohen SJ, et al. Smoking cessation: clinical practice guideline no. 18. AHCPR Publication No. 96-0692, Agency for Health Care Policy and Research, U.S. Department of Health and Human Services; 1996.
  35. White IR. Multivariate random-effects meta-regression: updates to mvmeta. Stata J. 2011;11(2):255-270.
  36. 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.
  37. Cooper H, Valentine JC, Charlton K, Melson A. The effects of modified school calendars on student achievement and on school and community attitudes. Rev Educ Res. 2003;73(1):1-52.
  38. Boersma E, Maas ACP, Deckers JW, Simoons ML. Early thrombolytic treatment in acute myocardial infarction: reappraisal of the golden hour. Lancet. 1996;348(9030):771-775.
  39. Berlin JA, Longnecker MP, Greenland S. Meta-analysis of epidemiologic dose-response data. Epidemiology. 1993;4(3):218-228.
  40. Liu Q, Cook NR, Bergstr��m A, Hsieh CC. A two-stage hierarchical regression model for meta-analysis of epidemiologic nonlinear dose-response data. Comput Stat Data Anal. 2009;53(12):4157-4167.
  41. Rota M, Bellocco R, Scotti L, et al. Random-effects meta-regression models for studying nonlinear dose-response relationship, with an application to alcohol and esophageal squamous cell carcinoma. Statist Med. 2010;29(26):2679-2687.
  42. Crippa A, Orsini N. Multivariate dose-response meta-analysis: the dosresmeta R package. J Stat Softw. 2016;72(1):1-15.
  43. Cho E, Smith-Warner SA, Ritz J, et al. Alcohol intake and colorectal cancer: a pooled analysis of 8 cohort studies. Ann Intern Med. 2004;140(8):603-613.
  44. Peters JL, Mengersen KL. Meta-analysis of repeated measures study designs. J Eval Clin Pract. 2008;14(5):941-950.
  45. Musekiwa A, Manda SOM, Mwambi HG, Chen DG. Meta-analysis of effect sizes reported at multiple time points using general linear mixed model. PloS One. 2016;11(10):e0164898.
  46. Trikalinos TA, Olkin I. Meta-analysis of effect sizes reported at multiple time points: a multivariate approach. Clinical Trials. 2012;9(5):610-620.
  47. Ahn JE, French JL. Longitudinal aggregate data model-based meta-analysis with NONMEM: approaches to handling within treatment arm correlation. J Pharmacokinet Pharmacodyn. 2010;37(2):179-201.
  48. Fine HA, Dear KBG, Loeffler JS, Mc Black PL, Canellos GP. Meta-analysis of radiation therapy with and without adjuvant chemotherapy for malignant gliomas in adults. Cancer. 1993;71(8):2585-2597.
  49. Riley RD, Lambert PC, Abo-Zaid G. Meta-analysis of individual participant data: rationale, conduct, and reporting. BMJ. 2010;340:c221.
  50. Burke DL, Ensor J, Riley RD. Meta-analysis using individual participant data: one-stage and two-stage approaches, and why they may differ. Statist Med. 2017;36(5):855-875.
  51. Platt RW, Leroux BG, Breslow N. Generalized linear mixed models for meta-analysis. Statist Med. 1999;18(6):643-654.
  52. Stijnen T, Hamza TH, ��zdemir P. Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statist Med. 2010;29(29):3046-3067.
  53. Jackson D, Law M, Stijnen T, Viechtbauer W, White IR. A comparison of seven random-effects models for meta-analyses that estimate the summary odds ratio. Statist Med. 2018;37(7):1059-1085.
  54. Bakbergenuly I, Kulinskaya E. Meta-analysis of binary outcomes via generalized linear mixed models: a simulation study. BMC Med Res Methodol. 2018;18(1):70.
  55. Wei Y, Higgins J. Estimating within-study covariances in multivariate meta-analysis with multiple outcomes. Statist Med. 2013;32(7):1191-1205.
  56. Greenland S, Longnecker MP. Methods for trend estimation from summarized dose-response data, with applications to meta-analysis. Am J Epidemiol. 1992;135(11):1301-1309.
  57. Orsini N, Bellocco R, Greenland S. Generalized least squares for trend estimation of summarized dose-response data. Stata J. 2006;6(1):40-57.
  58. Hamling J, Lee P, Weitkunat R, Ambuhl M. Facilitating meta-analyses by deriving relative effect and precision estimates for alternative comparisons from a set of estimates presented by exposure level or disease category. Statist Med. 2008;27(7):954-970.
  59. Van den Noortgate W, L��pez-L��pez JA, Mar��n-Mart��nez F, S��nchez-Meca J. Meta-analysis of multiple outcomes: a multilevel approach. Behav Res Methods. 2015;47(4):1274-1294.
  60. Molenberghs G, Kenward M. Missing Data in Clinical Studies. Vol 61. Hoboken, NJ: John Wiley & Sons; 2007.
  61. Heisterkamp SH, van Willigen E, Diderichsen PM, Maringwa J. Update of the NLME package to allow a fixed standard deviation of the residual error. R J. 2017;9(1):239-251.
  62. Orsini N. DRMETA: Stata module for dose-response meta-analysis. Statistical Software Components, Boston College Department of Economics; 2018.
  63. Viechtbauer W. Conducting meta-analyses in R with the metafor package. J Stat Softw. 2010;36(3):1-48.
  64. Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 1997:983-997.
  65. Kalaian HA, Raudenbush SW. A multivariate mixed linear model for meta-analysis. Psychol Methods. 1996;1(3):227.
  66. Riley RD, Abrams KR, Lambert PC, Sutton AJ, Thompson JR. An evaluation of bivariate random-effects meta-analysis for the joint synthesis of two correlated outcomes. Statist Med. 2007;26(1):78-97.
  67. Follmann DA, Proschan MA. Valid inference in random effects meta-analysis. Biometrics. 1999;55(3):732-737.
  68. Morris TP, Fisher DJ, Kenward MG, Carpenter JR. Meta-analysis of Gaussian individual patient data: two-stage or not two-stage? Statist Med. 2018;37(9):1419-1438.
  69. Sutton AJ, Abrams KR. Bayesian methods in meta-analysis and evidence synthesis. Stat Methods Med Res. 2001;10(4):277-303.
  70. Nam IS, Mengersen K, Garthwaite P. Multivariate meta-analysis. Statist Med. 2003;22(14):2309-2333.
  71. Wei Y, Higgins J. Bayesian multivariate meta-analysis with multiple outcomes. Statist Med. 2013;32(17):2911-2934.
  72. Sutton AJ, Higgins J. Recent developments in meta-analysis. Statist Med. 2008;27(5):625-650.
  73. Rhodes KM, Turner RM, Payne RA, White IR. Computationally efficient methods for fitting mixed models to electronic health records data. Statist Med. 2018;37(29):4557-4570.

Grants

  1. MR/M022625/1/Medical Research Council
  2. MR/R013349/1/Medical Research Council
  3. MR/S019669/1/Medical Research Council

MeSH Term

Biostatistics
Computer Simulation
Humans
Likelihood Functions
Linear Models
Longitudinal Studies
Meta-Analysis as Topic
Models, Statistical
Multivariate Analysis
Network Meta-Analysis As Topic
Software

Word Cloud

Created with Highcharts 10.0.0meta-analysisframeworkmixed-effectsmodelspoolingeffectmeta-analyticalextendedflexibledose-responselongitudinalStandardmethodslimitedtaskssinglesizeestimatedsetindependentstudiesHoweversettingcanrestrictivemodernapplicationscontributionillustrategeneralbasedlinearpotentiallycomplexpatternssizesmodeledstructurefixedrandomtermsdefinitionincludesspecialcasesvarietyseparatelyproposedliteraturemultivariatenetworkmultilevelmeta-regressionavailabilityunifiedcomplementedimplementationfreelyavailablefullydocumentedsoftwarewillprovideresearcherstooladdressingnonstandardproblems

Similar Articles

Cited By