No retraction, correction or concern found when last checked on Oct 30, 2026.

Multivariate meta‐analysis for non‐linear and other multi‐parameter associations

A. Gasparrini, B. Armstrong, M. G. Kenward

Statistics in Medicine · 2012

doi:10.1002/sim.5471 (opens in a new tab)

Abstract

In this paper, we formalize the application of multivariate meta‐analysis and meta‐regression to synthesize estimates of multi‐parameter associations obtained from different studies. This modelling approach extends the standard two‐stage analysis used to combine results across different sub‐groups or populations. The most straightforward application is for the meta‐analysis of non‐linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta‐analysis is implemented in the package mvmeta within the statistical environment R . As an illustrative example, we propose a two‐stage analysis for investigating the non‐linear exposure–response relationship between temperature and non‐accidental mortality using time‐series data from multiple cities. Multivariate meta‐analysis represents a useful analytical tool for studying complex associations through a two‐stage procedure. Copyright © 2012 John Wiley & Sons, Ltd.

Shown for reading. Its publisher allows quoting it, not republishing it.

References 75

1.
Normand SLT. Meta-analysis: formulating, evaluating, combining, and reporting. Statistics in Medicine. 1999;18(3):321-359.
Not in our library10.1002/(sici)1097-0258(19990215)18:3<321::aid-sim28>3.0.co;2-p (opens in a new tab)
2.
Sutton AJ, Higgins JP. Recent developments in meta-analysis. Statistics in Medicine. 2008;27(5):625-650.
Not in our library10.1002/sim.2934 (opens in a new tab)
3.
Stukel TA, Demidenko E, Dykes J, Karagas MR. Two-stage methods for the analysis of pooled data. Statistics in Medicine. 2001;20(14):2115-2130.
Not in our library10.1002/sim.852 (opens in a new tab)
4.
Simmonds MC, Higgins J, Stewart LA, Tierney JF, Clarke MJ, Thompson SG. Meta-analysis of individual patient data from randomized trials: a review of methods used in practice. Clinical Trials. 2005;2(3):209-217.
Not in our library10.1191/1740774505cn087oa (opens in a new tab)
5.
Thompson S, Kaptoge S, White I, Wood A, Perry P, Danesh J. Statistical methods for the time-to-event analysis of individual participant data from multiple epidemiological studies. International Journal of Epidemiology. 2010;39:1345-1359.
Not in our library10.1093/ije/dyq063 (opens in a new tab)
6.
Dominici F, Samet JM, Zeger SL. Combining evidence on air pollution and daily mortality from the 20 largest US cities: a hierarchical modelling strategy. Journal of the Royal Statistical Society: Series A. 2000;163(3):263-302.
Not in our library
7.
Berkey CS, Anderson JJ, Hoaglin DC. Multiple-outcome meta-analysis of clinical trials. Statistics in Medicine. 1996;15(5):537-557.
Not in our library10.1002/(sici)1097-0258(19960315)15:5<537::aid-sim176>3.0.co;2-s (opens in a new tab)
8.
Berkey CS, Hoaglin DC, Antczak-Bouckoms A, Mosteller F, Colditz GA. Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine. 1998;17(22):2537-2550.
Not in our library10.1002/(sici)1097-0258(19981130)17:22<2537::aid-sim953>3.0.co;2-c (opens in a new tab)
9.
Arends LR, Vokó Z, Stijnen T. Combining multiple outcome measures in a meta-analysis: an application. Statistics in Medicine. 2003;22(8):1335-1353.
Not in our library10.1002/sim.1370 (opens in a new tab)
10.
Gasparrini A, Armstrong B, Kenward MG. Multivariate meta-analysis: a method to summarize non-linear associations. Statistics in Medicine. 2011;30(20):2504-2506.
Not in our library10.1002/sim.4226 (opens in a new tab)
11.
Multivariate meta‐analysis: Potential and promise · 2011
No notice
12.
R: A Language and Environment for Statistical Computing. 2012.
Not in our library
13.
Gasparrini A, Armstrong B. Time series analysis on the health effects of temperature: advancements and limitations. Environmental Research. 2010;110(6):633-638.
Not in our library10.1016/j.envres.2010.06.005 (opens in a new tab)
14.
Basu R, Samet JM. Relation between elevated ambient temperature and mortality: a review of the epidemiologic evidence. Epidemiologic Reviews. 2002;24(2):190-202.
Not in our library10.1093/epirev/mxf007 (opens in a new tab)
15.
Armstrong B. Models for the relationship between ambient temperature and daily mortality. Epidemiology. 2006;17(6):624-631.
Not in our library10.1097/01.ede.0000239732.50999.8f (opens in a new tab)
16.
McMichael AJ, Wilkinson P, Kovats RS, Pattenden S, Hajat S, Armstrong B, Vajanapoom N, Niciu EM, Mahomed H, Kingkeow C, Kosnik M, O'Neill MS, Romieu I, Ramirez-Aguilar M, Barreto ML, Gouveia N, Nikiforov B. International study of temperature, heat and urban mortality: the ‘ISOTHURM’ project. International Journal of Epidemiology. 2008;37(5):1121.
Not in our library10.1093/ije/dyn086 (opens in a new tab)
17.
Baccini M, Biggeri A, Accetta G, Kosatsky T, Katsouyanni K, Analitis A, Anderson HR, Bisanti L, D'Ippoliti D, Danova J, Forsberg B, Medina S, Paldy A, Rabczenko D, Schindler C, Michelozzi P. Heat effects on mortality in 15 European cities. Epidemiology. 2008;19(5):711-719.
Not in our library10.1097/ede.0b013e318176bfcd (opens in a new tab)
18.
Anderson BG, Bell ML. Weather-related mortality: how heat, cold, and heat waves affect mortality in the United States. Epidemiology. 2009;20(2):205-213.
Not in our library10.1097/ede.0b013e318190ee08 (opens in a new tab)
19.
Ruppert D, Wand MP, Carroll RJ. Semiparametric Regression. 2003.
Not in our library
20.
Royston P, Altman DG. Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. Journal of the Royal Statistical Society: Series C. 1994;43(3):429-467.
Not in our library
21.
Muggeo VM. Estimating regression models with unknown break-points. Statistics in Medicine. 2003;22(19):3055-3071.
Not in our library10.1002/sim.1545 (opens in a new tab)
22.
Dominici F, Sheppard L, Clyde M. Health effects of air pollution: a statistical review. International Statistical Review. 2003;71(2):243-276.
Not in our library
23.
Cao J, Valois MF, Goldberg MS. An S-Plus function to calculate relative risks and adjusted means for regression models using natural splines. Computer Methods and Programs in Biomedicine. 2006;84(1):58-62.
Not in our library10.1016/j.cmpb.2006.08.004 (opens in a new tab)
24.
Peng RD, Dominici F, Louis TA. Model choice in time series studies of air pollution and mortality. Journal of the Royal Statistical Society: Series A. 2006;169(2):179-203.
Not in our library
25.
Harrell FE. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. 2001.
Not in our library
26.
A Re-Evaluation of Random-Effects Meta-Analysis · 2008
No notice
27.
Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. 2000.
Not in our library
28.
White IR. Multivariate random-effects meta-analysis. Stata Journal. 2009;9(1):40-56.
Not in our library
29.
Ritz J, Demidenko E, Spiegelman D. Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling projects. Journal of Statistical Planning and Inference. 2008;139(7):1919-1933.
Not in our library
30.
Dear KBG. Iterative generalized least squares for meta-analysis of survival data at multiple times. Biometrics. 1994;50:989-1002.
Not in our library
31.
Nam IS, Mengersen K, Garthwaite P. Multivariate meta-analysis. Statistics in Medicine. 2003;22(14):2309-2333.
Not in our library10.1002/sim.1410 (opens in a new tab)
32.
Jackson D, White IR, Thompson SG. Extending DerSimonian and Laird's methodology to perform multivariate random effects meta-analyses. Statistics in Medicine. 2010;29(12):1282-1297.
Not in our library10.1002/sim.3602 (opens in a new tab)
33.
Harville DA. Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association. 1977;72(358):320-338.
Not in our library
34.
Pinheiro JC, Bates DM. Mixed-Effects Models in S and S-PLUS. 2000.
Not in our library
35.
Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 1997;53(3):983-997.
Not in our library
36.
Kenward MG, Roger JH. An improved approximation to the precision of fixed effects from restricted maximum likelihood. Computational Statistics and Data Analysis. 2009;53(7):2583-2595.
Not in our library
37.
Stram DO, Lee JW. Variance components testing in the longitudinal mixed effects model. Biometrics. 1994;50(4):1171-1177.
Not in our library
38.
Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Statistics in Medicine. 2002;21(11):1539-1558.
Not in our library10.1002/sim.1186 (opens in a new tab)
39.
Undue reliance on I 2 in assessing heterogeneity may mislead · 2008
No notice
40.
White IR. Multivariate random-effects meta-regression: updates to mvmeta. Stata Journal. 2011;11(2):255-270.
Not in our library
41.
Riley R, Higgins J, Deeks JJ. The interpretation of random-effects meta-analysis. British Medical Journal. 2011;342:d549.
Not in our library10.1136/bmj.d549 (opens in a new tab)
42.
Viechtbauer W, Cheung MWL. Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods. 2010;1(2):112-125.
Not in our library10.1002/jrsm.11 (opens in a new tab)
43.
Ades AE. A chain of evidence with mixed comparisons: models for multi-parameter synthesis and consistency of evidence. Statistics in Medicine. 2003;22(19):2995-3016.
Not in our library10.1002/sim.1566 (opens in a new tab)
44.
Ades AE, Sutton AJ. Multiparameter evidence synthesis in epidemiology and medical decision-making: current approaches. Journal of the Royal Statistical Society: Series A. 2006;169(1):5-35.
Not in our library
45.
Hedges LV, Tipton E, Johnson MC. Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods. 2010;1(1):39-65.
Not in our library10.1002/jrsm.5 (opens in a new tab)
46.
Berlin JA, Santanna J, Schmid CH, Szczech LA, Feldman HI. Individual patient- versus group-level data meta-regressions for the investigation of treatment effect modifiers: ecological bias rears its ugly head. Statistics in Medicine. 2002;21(3):371-387.
Not in our library10.1002/sim.1023 (opens in a new tab)
47.
Lambert PC, Sutton AJ, Abrams KR, Jones DR. A comparison of summary patient-level covariates in meta-regression with individual patient data meta-analysis. Journal of Clinical Epidemiology. 2002;55(1):86-94.
Not in our library10.1016/s0895-4356(01)00414-0 (opens in a new tab)
48.
Olkin I, Sampson A. Comparison of meta-analysis versus analysis of variance of individual patient data. Biometrics. 1998;54(1):317-322.
Not in our library
49.
Mathew T, Nordstrom K. Comparison of one-step and two-step meta-analysis models using individual patient data. Biometrical Journal. 2010;52(2):271-287.
Not in our library10.1002/bimj.200900143 (opens in a new tab)
50.
Riley RD, Thompson JR, Abrams KR. An alternative model for bivariate random-effects meta-analysis when the within-study correlations are unknown. Biostatistics. 2008;9(1):172.
Not in our library10.1093/biostatistics/kxm023 (opens in a new tab)
51.
Riley RD. Multivariate meta-analysis: the effect of ignoring within-study correlation. Journal of the Royal Statistical Society: Series A. 2009;172(4):789-811.
Not in our library
52.
Sauerbrei W, Royston P. A new strategy for meta-analysis of continuous covariates in observational studies. Statistics in Medicine. 2011;30(28):3341-3360.
Not in our library10.1002/sim.4333 (opens in a new tab)
53.
Schwartz J, Zanobetti A. Using meta-smoothing to estimate dose–response trends across multiple studies, with application to air pollution and daily death. Epidemiology. 2000;11(6):666-672.
Not in our library10.1097/00001648-200011000-00009 (opens in a new tab)
54.
Dominici F, Daniels MJ, Zeger SL, Samet JM. Air pollution and mortality: estimating regional and national dose–response relationships. Journal of the American Statistical Association. 2002;97:100-111.
Not in our library
55.
Estimating the Exposure–Response Relationships between Particulate Matter and Mortality within the APHEA Multicity Project · 2004
No notice
56.
Greenland S, Longnecker MP. Methods for trend estimation from summarized dose–response data, with applications to meta-analysis. American Journal of Epidemiology. 1992;135(11):1301-1309.
Not in our library10.1093/oxfordjournals.aje.a116237 (opens in a new tab)
57.
Berlin JA, Longnecker MP, Greenland S. Meta-analysis of epidemiologic dose–response data. Epidemiology. 1993;4(3):218-228.
Not in our library10.1097/00001648-199305000-00005 (opens in a new tab)
58.
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(11):1077-1086.
Not in our library10.1093/aje/kwh142 (opens in a new tab)
59.
Hartemink N, Boshuizen HC, Nagelkerke NJ, Jacobs MA, van Houwelingen HC. Combining risk estimates from observational studies with different exposure cutpoints: a meta-analysis on body mass index and diabetes type 2. American Journal of Epidemiology. 2006;163(11):1042-1052.
Not in our library10.1093/aje/kwj141 (opens in a new tab)
60.
Vlaanderen J, Portengen L, Rothman N, Lan Q, Kromhout H, Vermeulen R. Flexible meta-regression to assess the shape of the benzene-leukemia exposure–response curve. Environmental Health Perspectives. 2010;118(4):526-532.
Not in our library10.1289/ehp.0901127 (opens in a new tab)
61.
Shi JQ, Copas JB. Meta-analysis for trend estimation. Statistics in Medicine. 2004;23(1):3-19.
Not in our library10.1002/sim.1595 (opens in a new tab)
62.
Orsini N. Meta-analysis for linear and nonlinear dose–response relations: examples, an evaluation of approximations, and software. American Journal of Epidemiology. 2012;175(1):66-73.
Not in our library10.1093/aje/kwr265 (opens in a new tab)
63.
Liu Q, Cook NR, Bergstrom A, Hsieh CC. A two-stage hierarchical regression model for meta-analysis of epidemiologic nonlinear dose–response data. Computational Statistics and Data Analysis. 2009;53(12):4157-4167.
Not in our library
64.
Rota M, Bellocco R, Scotti L, Tramacere I, Jenab M, Corrao G, La Vecchia C, Boffetta P, Bagnardi V. Random-effects meta-regression models for studying nonlinear dose–response relationship, with an application to alcohol and esophageal squamous cell carcinoma. Statistics in Medicine. 2010;29:2679-2687.
Not in our library10.1002/sim.4041 (opens in a new tab)
65.
Arends LR, Hunink MG, Stijnen T. Meta-analysis of summary survival curve data. Statistics in Medicine. 2008;27(22):4381-4396.
Not in our library10.1002/sim.3311 (opens in a new tab)
66.
Ishak KJ, Platt RW, Joseph L, Hanley JA, Caro JJ. Meta-analysis of longitudinal studies. Clinical Trials. 2007;4(5):525-539.
Not in our library10.1177/1740774507083567 (opens in a new tab)
67.
Arends LR, Hamza TH, Van Houwelingen JC, Heijenbrok-Kal MH, Hunink MGM, Stijnen T. Bivariate random effects meta-analysis of ROC curves. Medical Decision Making. 2008;28(5):621-638.
Not in our library10.1177/0272989x08319957 (opens in a new tab)
68.
Gasparrini A, Armstrong B. The impact of heat waves on mortality. Epidemiology. 2011;22(1):68-73.
Not in our library10.1097/ede.0b013e3181fdcd99 (opens in a new tab)
69.
Zanobetti A, Schwartz J, Samoli E, Gryparis A, Touloumi G, Atkinson R, Le Tertre A, Bobros J, Celko M, Goren A, Forsberg B, Michelozzi P, Rabczenko D, Aranguez Ruiz E, Katsouyanni K. The temporal pattern of mortality responses to air pollution: a multicity assessment of mortality displacement. Epidemiology. 2002;13(1):87-93.
Not in our library10.1097/00001648-200201000-00014 (opens in a new tab)
70.
Zanobetti A, Schwartz J. Mortality displacement in the association of ozone with mortality: an analysis of 48 cities in the United States. American Journal of Respiratory and Critical Care Medicine. 2008;177(2):184-189.
Not in our library10.1164/rccm.200706-823oc (opens in a new tab)
71.
Samoli E, Zanobetti A, Schwartz J, Atkinson R, Le Tertre A, Schindler C, Perez L, Cadum E, Pekkanen J, Paldy A, Touloumi G, Katsouyanni K. The temporal pattern of mortality responses to ambient ozone in the APHEA project. Journal of Epidemiology and Community Health. 2009;63:960-966.
Not in our library10.1136/jech.2008.084012 (opens in a new tab)
72.
Analitis A, Katsouyanni K, Biggeri A, Baccini M, Forsberg B, Bisanti L, Kirchmayer U, Ballester F, Cadum E, Goodman PG, Hojs A, Sunyer J, Tiittanen P, Michelozzi P. Effects of cold weather on mortality: results from 15 European cities within the PHEWE Project. American Journal of Epidemiology. 2008;168(12):1397.
Not in our library10.1093/aje/kwn266 (opens in a new tab)
73.
Zanobetti A, Schwartz J. Temperature and mortality in nine US cities. Epidemiology. 2008;19(4):563-570.
Not in our library10.1097/ede.0b013e31816d652d (opens in a new tab)
74.
Gasparrini A. Distributed lag linear and non-linear models in R: the package dlnm. Journal of Statistical Software. 2011;43(8):1-20.
Not in our library
75.
van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Statistics in Medicine. 2002;21(4):589-624.
Not in our library10.1002/sim.1040 (opens in a new tab)

Cited by papers we hold 18

Heat-related mortality in Europe during the summer of 2022 · 2023
Corrected
Non-occupational physical activity and risk of cardiovascular disease, cancer and mortality outcomes: a dose–response meta-analysis of large prospective studies · 2023
No notice
Comparison of weather station and climate reanalysis data for modelling temperature-related mortality · 2022
Not checked
Cardiac dyspnea risk zones in the South of France identified by geo-pollution trends study · 2022
Not checked
Association Between Physical Activity and Risk of Depression · 2022
No notice
Joint association between accelerometry-measured daily combination of time spent in physical activity, sedentary behaviour and sleep and all-cause mortality: a pooled analysis of six prospective cohorts using compositional analysis · 2021
No notice
Excess mortality during the COVID-19 outbreak in Italy: a two-stage interrupted time-series analysis · 2020
No notice
Individual participant data meta‐analysis to examine interactions between treatment effect and participant‐level covariates: Statistical recommendations for conduct and planning · 2020
No notice
Short term association between ozone and mortality: global two stage time series study in 406 locations in 20 countries · 2020
No notice
Performance of the Framingham risk models and pooled cohort equations for predicting 10-year risk of cardiovascular disease: a systematic review and meta-analysis · 2019
No notice
Multivariate and network meta-analysis of multiple outcomes and multiple treatments: rationale, concepts, and examples · 2017
No notice
Temperature Variability and Mortality: A Multi-Country Study · 2016
No notice
Dose-response meta-analysis of differences in means · 2016
No notice
Mortality risk attributable to high and low ambient temperature: a multicountry observational study · 2015
No notice
Temporal Variation in Heat–Mortality Associations: A Multicountry Study · 2015
No notice
Heat, Heat Waves, and Hospital Admissions among the Elderly in the United States, 1992–2006 · 2014
No notice
A graphical tool for locating inconsistency in network meta-analyses · 2013
No notice
Reducing and meta-analysing estimates from distributed lag non-linear models · 2013
No notice

Questions about this paper

We email you if it is retracted, withdrawn, corrected or flagged.

Reads

Read by people on this page

None yet.

Checked or read by AI through naulon

None yet.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.

Are you an author?

Is this your paper?

Claim it to add your note and be paid when agents cite it. Free.