Skip to main content
Top
Published in: BMC Medical Research Methodology 1/2011

Open Access 01-12-2011 | Research article

Quantifying, displaying and accounting for heterogeneity in the meta-analysis of RCTs using standard and generalised Qstatistics

Authors: Jack Bowden, Jayne F Tierney, Andrew J Copas, Sarah Burdett

Published in: BMC Medical Research Methodology | Issue 1/2011

Login to get access

Abstract

Background

Clinical researchers have often preferred to use a fixed effects model for the primary interpretation of a meta-analysis. Heterogeneity is usually assessed via the well known Q and I 2 statistics, along with the random effects estimate they imply. In recent years, alternative methods for quantifying heterogeneity have been proposed, that are based on a 'generalised' Q statistic.

Methods

We review 18 IPD meta-analyses of RCTs into treatments for cancer, in order to quantify the amount of heterogeneity present and also to discuss practical methods for explaining heterogeneity.

Results

Differing results were obtained when the standard Q and I 2 statistics were used to test for the presence of heterogeneity. The two meta-analyses with the largest amount of heterogeneity were investigated further, and on inspection the straightforward application of a random effects model was not deemed appropriate. Compared to the standard Q statistic, the generalised Q statistic provided a more accurate platform for estimating the amount of heterogeneity in the 18 meta-analyses.

Conclusions

Explaining heterogeneity via the pre-specification of trial subgroups, graphical diagnostic tools and sensitivity analyses produced a more desirable outcome than an automatic application of the random effects model. Generalised Q statistic methods for quantifying and adjusting for heterogeneity should be incorporated as standard into statistical software. Software is provided to help achieve this aim.
Appendix
Available only for authorised users
Literature
1.
go back to reference Simmonds M, Higgins J, Stewart L, Tierney J, Clarke M, Thompson S: Meta analysis of individual patient data from randomized trials: a review of methods used in practice. Clinical Trials. 2005, 2: 209-217. 10.1191/1740774505cn087oa.CrossRefPubMed Simmonds M, Higgins J, Stewart L, Tierney J, Clarke M, Thompson S: Meta analysis of individual patient data from randomized trials: a review of methods used in practice. Clinical Trials. 2005, 2: 209-217. 10.1191/1740774505cn087oa.CrossRefPubMed
2.
go back to reference Stewart L, Parmar M: Bias in the analysis and reporting of randomized controlled trials. International Journal of Technology Assessment in Health Care. 1996, 12: 264-275. 10.1017/S0266462300009612.CrossRefPubMed Stewart L, Parmar M: Bias in the analysis and reporting of randomized controlled trials. International Journal of Technology Assessment in Health Care. 1996, 12: 264-275. 10.1017/S0266462300009612.CrossRefPubMed
3.
go back to reference DerSimonian R, Laird N: Meta-analysis in clinical trials. Controlled Clinical Trials. 1986, 7: 177-188. 10.1016/0197-2456(86)90046-2.CrossRefPubMed DerSimonian R, Laird N: Meta-analysis in clinical trials. Controlled Clinical Trials. 1986, 7: 177-188. 10.1016/0197-2456(86)90046-2.CrossRefPubMed
4.
go back to reference Higgins J, Thompson S: Quantifying heterogeneity in a meta-analysis. Statistics in Medicine. 2002, 21: 1539-1558. 10.1002/sim.1186.CrossRefPubMed Higgins J, Thompson S: Quantifying heterogeneity in a meta-analysis. Statistics in Medicine. 2002, 21: 1539-1558. 10.1002/sim.1186.CrossRefPubMed
7.
go back to reference AOCTG: Chemotherapy in advanced ovarian cancer: an overview of randomised clinical trials. Advanced Ovarian Cancer Trials Group. British Medical Journal. 1991, 303: 884-893. 10.1136/bmj.303.6807.884.CrossRef AOCTG: Chemotherapy in advanced ovarian cancer: an overview of randomised clinical trials. Advanced Ovarian Cancer Trials Group. British Medical Journal. 1991, 303: 884-893. 10.1136/bmj.303.6807.884.CrossRef
8.
go back to reference NSCLC: Chemotherapy in non-small cell lung cancer: a meta-analysis using updated data on individual patients from 52 randomised trials. Non-Small cell Lung cancer Collaborative group. British Medical Journal. 1995, 311: 899-909.CrossRef NSCLC: Chemotherapy in non-small cell lung cancer: a meta-analysis using updated data on individual patients from 52 randomised trials. Non-Small cell Lung cancer Collaborative group. British Medical Journal. 1995, 311: 899-909.CrossRef
9.
go back to reference SMC: Adjuvant chemotherapy for localised resectable soft tissue sarcoma of adults: meta-analysis of individual data. Sarcoma Meta-analysis Collaboration. Lancet. 1997, 350: 1647-1654. 10.1016/S0140-6736(97)08165-8.CrossRef SMC: Adjuvant chemotherapy for localised resectable soft tissue sarcoma of adults: meta-analysis of individual data. Sarcoma Meta-analysis Collaboration. Lancet. 1997, 350: 1647-1654. 10.1016/S0140-6736(97)08165-8.CrossRef
10.
go back to reference AOCTG: Chemotherapy in advanced ovarian cancer: for systematic meta-analyses of individual patient data from 37 randomized trials. Advanced Ovarian Cancer Trials Group. British Journal of Cancer. 1998, 78: 1479-1487. 10.1038/bjc.1998.710.CrossRef AOCTG: Chemotherapy in advanced ovarian cancer: for systematic meta-analyses of individual patient data from 37 randomized trials. Advanced Ovarian Cancer Trials Group. British Journal of Cancer. 1998, 78: 1479-1487. 10.1038/bjc.1998.710.CrossRef
11.
go back to reference PMTG: Postoperative radiotherapy in non-small-cell lung cancer: systematic review and meta-analysis of individual patient data from nine-randomised controlled trials. PORT Meta-analysis Trialists Group. Lancet. 1998, 352: 257-263. 10.1016/S0140-6736(98)06341-7.CrossRef PMTG: Postoperative radiotherapy in non-small-cell lung cancer: systematic review and meta-analysis of individual patient data from nine-randomised controlled trials. PORT Meta-analysis Trialists Group. Lancet. 1998, 352: 257-263. 10.1016/S0140-6736(98)06341-7.CrossRef
12.
go back to reference OCCG: Preoperative radiotherapy in esophageal carcinoma: A meta-analysis using individual patient data. Oesophageal Cancer Collaborative Group. Int J Radiation Oncology Biol Phys. 1998, 41: 579-583. 10.1016/S0360-3016(97)00569-5.CrossRef OCCG: Preoperative radiotherapy in esophageal carcinoma: A meta-analysis using individual patient data. Oesophageal Cancer Collaborative Group. Int J Radiation Oncology Biol Phys. 1998, 41: 579-583. 10.1016/S0360-3016(97)00569-5.CrossRef
13.
go back to reference GMTG: Chemotherapy in adult high-grade glioma: a systematic review and meta-analysis of individual patient data from 12 randomised trials. Glioma Meta-analysis Trialists Group. Lancet. 2002, 359: 1011-1018. 10.1016/S0140-6736(02)08091-1.CrossRef GMTG: Chemotherapy in adult high-grade glioma: a systematic review and meta-analysis of individual patient data from 12 randomised trials. Glioma Meta-analysis Trialists Group. Lancet. 2002, 359: 1011-1018. 10.1016/S0140-6736(02)08091-1.CrossRef
14.
go back to reference ABCMC: Neoadjuvant chemotherapy in invasive bladder cancer: a systematic review and meta-analysis. Advanced Bladder Cancer Meta-analysis Collaboration. Lancet. 2003, 361: 1927-1934. 10.1016/S0140-6736(03)13580-5.CrossRef ABCMC: Neoadjuvant chemotherapy in invasive bladder cancer: a systematic review and meta-analysis. Advanced Bladder Cancer Meta-analysis Collaboration. Lancet. 2003, 361: 1927-1934. 10.1016/S0140-6736(03)13580-5.CrossRef
15.
go back to reference NACCCMA: Neoadjuvant chemotherapy for locally advanced cervical cancer: A systematic review and meta-analysis of individual patient data from 21 randomised trials. Neoadjuvant Chemotherapy for Cervix Cancer Meta-analysis Collaboration. European Journal of Cancer. 2003, 39: 2470-2486. 10.1016/S0959-8049(03)00425-8.CrossRef NACCCMA: Neoadjuvant chemotherapy for locally advanced cervical cancer: A systematic review and meta-analysis of individual patient data from 21 randomised trials. Neoadjuvant Chemotherapy for Cervix Cancer Meta-analysis Collaboration. European Journal of Cancer. 2003, 39: 2470-2486. 10.1016/S0959-8049(03)00425-8.CrossRef
16.
go back to reference ABCMC: Adjuvant chemotherapy in invasive bladder cancer: a systematic review and meta-analysis of individual patient data. Advanced Bladder Cancer Meta-analysis Collaboration. European Urology. 2005, 48: 189-201. 10.1016/j.eururo.2005.04.005.CrossRef ABCMC: Adjuvant chemotherapy in invasive bladder cancer: a systematic review and meta-analysis of individual patient data. Advanced Bladder Cancer Meta-analysis Collaboration. European Urology. 2005, 48: 189-201. 10.1016/j.eururo.2005.04.005.CrossRef
17.
go back to reference CCCMC: Reducing uncertainties about the effects of chemoradiotherapy for cervical cancer: a systematic review and meta-analysis of individual patient data from 18 randomized trials. Chemoradiotherapy for Cervical Cancer Meta-analysis Collaboration. Journal of Clinical Oncology. 2008, 26: 5802-5812. 10.1200/JCO.2008.16.4368.CrossRef CCCMC: Reducing uncertainties about the effects of chemoradiotherapy for cervical cancer: a systematic review and meta-analysis of individual patient data from 18 randomized trials. Chemoradiotherapy for Cervical Cancer Meta-analysis Collaboration. Journal of Clinical Oncology. 2008, 26: 5802-5812. 10.1200/JCO.2008.16.4368.CrossRef
18.
go back to reference Yusef S, Peto R: Beta blockade during and after myocardial infarction: an overview of the randomised trials. Prog Cardio Dis. 1985, 27: 335-371. 10.1016/S0033-0620(85)80003-7.CrossRef Yusef S, Peto R: Beta blockade during and after myocardial infarction: an overview of the randomised trials. Prog Cardio Dis. 1985, 27: 335-371. 10.1016/S0033-0620(85)80003-7.CrossRef
19.
go back to reference Higgins J, Thompson S, Spiegelhalter D: A re-evaluation of random-effects meta-analysis. J Royal Statistical Soc Series A. 2009, 172: 137-159.CrossRef Higgins J, Thompson S, Spiegelhalter D: A re-evaluation of random-effects meta-analysis. J Royal Statistical Soc Series A. 2009, 172: 137-159.CrossRef
20.
go back to reference Hardy R, Thompson S: A likelihood approach to meta-analysis with random effects. Statistics in Medicine. 1999, 15: 619-629. 10.1002/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A.CrossRef Hardy R, Thompson S: A likelihood approach to meta-analysis with random effects. Statistics in Medicine. 1999, 15: 619-629. 10.1002/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A.CrossRef
21.
go back to reference Tweedie R, Scott D, Biggerstaff B, Mengersen K: Bayesian meta-analysis, with application to studies of ETS and lung cancer. Lung Cancer. 1996, 14: S171-S194. 10.1016/S0169-5002(96)90222-6.CrossRefPubMed Tweedie R, Scott D, Biggerstaff B, Mengersen K: Bayesian meta-analysis, with application to studies of ETS and lung cancer. Lung Cancer. 1996, 14: S171-S194. 10.1016/S0169-5002(96)90222-6.CrossRefPubMed
22.
go back to reference DerSimonian R, Kacker R: Random-effects models for meta-analysis of clinical trials: An update. Contemporary Clinical Trials. 2007, 28: 105-114. 10.1016/j.cct.2006.04.004.CrossRefPubMed DerSimonian R, Kacker R: Random-effects models for meta-analysis of clinical trials: An update. Contemporary Clinical Trials. 2007, 28: 105-114. 10.1016/j.cct.2006.04.004.CrossRefPubMed
23.
go back to reference Paule R, Mandel J: Consensus values and weighting factors. J Res Natl Bur Stand. 1982, 87: 377-385.CrossRef Paule R, Mandel J: Consensus values and weighting factors. J Res Natl Bur Stand. 1982, 87: 377-385.CrossRef
24.
go back to reference Ruhkin A, Biggerstaff B, Vangel M: Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. Journal of Statistical Planning and Inference. 2000, 83: 319-330. 10.1016/S0378-3758(99)00098-1.CrossRef Ruhkin A, Biggerstaff B, Vangel M: Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. Journal of Statistical Planning and Inference. 2000, 83: 319-330. 10.1016/S0378-3758(99)00098-1.CrossRef
25.
go back to reference Viechtbauer W: Confidence intervals for the amount of heterogeneity in meta-analysis. Statistics in Medicine. 2007, 26: 37-52. 10.1002/sim.2514.CrossRefPubMed Viechtbauer W: Confidence intervals for the amount of heterogeneity in meta-analysis. Statistics in Medicine. 2007, 26: 37-52. 10.1002/sim.2514.CrossRefPubMed
26.
go back to reference Biggerstaff B, Tweedie R: Incorporating variability in estimates of heterogeneity in the random effect smodel in meta-analysis. Statistics in Medicine. 1997, 16: 753-768. 10.1002/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G.CrossRefPubMed Biggerstaff B, Tweedie R: Incorporating variability in estimates of heterogeneity in the random effect smodel in meta-analysis. Statistics in Medicine. 1997, 16: 753-768. 10.1002/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G.CrossRefPubMed
27.
go back to reference Sidik K, Jonkman J: Simple heterogeneity variance estimation for meta-analysis. J Royal Statistical Soc Series C. 2005, 54: 367-384. 10.1111/j.1467-9876.2005.00489.x.CrossRef Sidik K, Jonkman J: Simple heterogeneity variance estimation for meta-analysis. J Royal Statistical Soc Series C. 2005, 54: 367-384. 10.1111/j.1467-9876.2005.00489.x.CrossRef
28.
go back to reference Huedo-Medina T, Sanchez-Meca J, Marin-Martinez F, Botella J: Assessing Heterogeneity in Meta-Analysis: Q Statistic or I 2 Index?. Psychological Methods. 2006, 11: 193-206. 10.1037/1082-989X.11.2.193.CrossRefPubMed Huedo-Medina T, Sanchez-Meca J, Marin-Martinez F, Botella J: Assessing Heterogeneity in Meta-Analysis: Q Statistic or I 2 Index?. Psychological Methods. 2006, 11: 193-206. 10.1037/1082-989X.11.2.193.CrossRefPubMed
29.
go back to reference Light R, Pillemer D: Summing up: The Science of Reviewing Research. 1984, Cambridge: Harvard University Press Light R, Pillemer D: Summing up: The Science of Reviewing Research. 1984, Cambridge: Harvard University Press
30.
31.
go back to reference Copas J, Malley P: A robust P-value for treatment effect in meta-analysis with publication bias. Statistics in Medicine. 2008, 27: 4267-4278. 10.1002/sim.3284.CrossRefPubMed Copas J, Malley P: A robust P-value for treatment effect in meta-analysis with publication bias. Statistics in Medicine. 2008, 27: 4267-4278. 10.1002/sim.3284.CrossRefPubMed
32.
go back to reference Baujat B, Mahe C, Pignon J, Hill C: A graphical method for exploring heterogeneity in meta-analyses: application to a meta-analysis of 65 trials. Statistics in Medicine. 2002, 21: 2641-2652. 10.1002/sim.1221.CrossRefPubMed Baujat B, Mahe C, Pignon J, Hill C: A graphical method for exploring heterogeneity in meta-analyses: application to a meta-analysis of 65 trials. Statistics in Medicine. 2002, 21: 2641-2652. 10.1002/sim.1221.CrossRefPubMed
33.
go back to reference Anzures-Cabrera J, Higgins J: Graphical displays for meta-analysis: An overview with suggestions for practice. Research Synthesis Methods. 2010, 1: 66-80. 10.1002/jrsm.6.CrossRefPubMed Anzures-Cabrera J, Higgins J: Graphical displays for meta-analysis: An overview with suggestions for practice. Research Synthesis Methods. 2010, 1: 66-80. 10.1002/jrsm.6.CrossRefPubMed
34.
go back to reference Greenland S: Invited Commentary: A Critical Look at Some Popular Meta-Analytic Methods. American Journal of Epidemiology. 1994, 140: 291-296. Greenland S: Invited Commentary: A Critical Look at Some Popular Meta-Analytic Methods. American Journal of Epidemiology. 1994, 140: 291-296.
35.
go back to reference Stanley T: Meta-regression methods for detecting and estimating empirical effects in the presence of publication selection. Oxford Bulletin of Economics and Statistics. 2008, 70: 103-127. Stanley T: Meta-regression methods for detecting and estimating empirical effects in the presence of publication selection. Oxford Bulletin of Economics and Statistics. 2008, 70: 103-127.
36.
go back to reference Moreno S, Sutton A, Ades A, Stanley T, Abrams K, Peters J, Cooper N: Assessment of regression-based methods to adjust for publication bias through a comprehensive simulation study. BMC Medical Research Methodology. 2009, 9: 2-10.1186/1471-2288-9-2.CrossRefPubMedPubMedCentral Moreno S, Sutton A, Ades A, Stanley T, Abrams K, Peters J, Cooper N: Assessment of regression-based methods to adjust for publication bias through a comprehensive simulation study. BMC Medical Research Methodology. 2009, 9: 2-10.1186/1471-2288-9-2.CrossRefPubMedPubMedCentral
37.
go back to reference Rücker G, Schwarzer G, Carpenter J, Binder H, Shumacher M: Treatment-effect estimates adjusted for small study effects via a limit meta-analysis. Biostatistics. 2011, 12: 122-142. 10.1093/biostatistics/kxq046.CrossRefPubMed Rücker G, Schwarzer G, Carpenter J, Binder H, Shumacher M: Treatment-effect estimates adjusted for small study effects via a limit meta-analysis. Biostatistics. 2011, 12: 122-142. 10.1093/biostatistics/kxq046.CrossRefPubMed
38.
go back to reference Henmi M, Copas J: Confidence intervals for random effects meta-analysis and robustness to publication bias. Statistics in Medicine. 2010, 29: 2969-2983. 10.1002/sim.4029.CrossRefPubMed Henmi M, Copas J: Confidence intervals for random effects meta-analysis and robustness to publication bias. Statistics in Medicine. 2010, 29: 2969-2983. 10.1002/sim.4029.CrossRefPubMed
39.
go back to reference Baker R, Jackson D: A new approach to outliers in meta-analysis. Health Care Management Science. 2008, 11: 121-131. 10.1007/s10729-007-9041-8.CrossRefPubMed Baker R, Jackson D: A new approach to outliers in meta-analysis. Health Care Management Science. 2008, 11: 121-131. 10.1007/s10729-007-9041-8.CrossRefPubMed
40.
go back to reference Jackson D, Bowden J, Baker R: How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts. Journal of Statistical Planning and Inference. 2010, 140: 961-970. 10.1016/j.jspi.2009.09.017.CrossRef Jackson D, Bowden J, Baker R: How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts. Journal of Statistical Planning and Inference. 2010, 140: 961-970. 10.1016/j.jspi.2009.09.017.CrossRef
41.
go back to reference Rücker G, Schwarzer G, Carpenter J, Shumacher M: Undue reliance on I 2 in assessing heterogeneity may mislead. BMC Medical Research Methodology. 2008, 8: 79-10.1186/1471-2288-8-79.CrossRefPubMedPubMedCentral Rücker G, Schwarzer G, Carpenter J, Shumacher M: Undue reliance on I 2 in assessing heterogeneity may mislead. BMC Medical Research Methodology. 2008, 8: 79-10.1186/1471-2288-8-79.CrossRefPubMedPubMedCentral
42.
go back to reference Van der Tweel I, Bollen C: Sequential meta-analysis: an efficient decision-making tool. Clinical Trials. 2010, 7: 136-146. 10.1177/1740774509360994.CrossRefPubMed Van der Tweel I, Bollen C: Sequential meta-analysis: an efficient decision-making tool. Clinical Trials. 2010, 7: 136-146. 10.1177/1740774509360994.CrossRefPubMed
44.
go back to reference Rücker G, Schwarzer G, Carpenter J, Shumacher M: Comments on "Empirical vs natural weighting in random effects meta-analysis" by JJ Shuster, Statistics in Medicine 2009. Statistics in Medicine. 2010, 29: 2963-2965. 10.1002/sim.3957.CrossRefPubMed Rücker G, Schwarzer G, Carpenter J, Shumacher M: Comments on "Empirical vs natural weighting in random effects meta-analysis" by JJ Shuster, Statistics in Medicine 2009. Statistics in Medicine. 2010, 29: 2963-2965. 10.1002/sim.3957.CrossRefPubMed
Metadata
Title
Quantifying, displaying and accounting for heterogeneity in the meta-analysis of RCTs using standard and generalised Qstatistics
Authors
Jack Bowden
Jayne F Tierney
Andrew J Copas
Sarah Burdett
Publication date
01-12-2011
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2011
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-11-41

Other articles of this Issue 1/2011

BMC Medical Research Methodology 1/2011 Go to the issue