Random effects meta-analysis of rare binary data in the framework of the generalized linear mixed model_Chinese Journal of Evidence-Based Medicine

Authors：

WU Min ¹ ,  ZHENG Jianqing ¹ , HUANG Bifen ² , XIAO Lihua ¹

1. The Second Affiliated Hospital of Fujian Medical University, Quanzhou, 362000, P.R.China;
2. Quanzhou Medical College People’s Hospital Affiliated, Quanzhou, 362000, P.R.China;

Corresponding author：

ZHENG Jianqing, Email: 18060108268@189.cn

Keywords：

Rare data; Generalized linear mixed effect model; Exact within-study likelihood model; Normal-normal model; Binomial-normal model; Hypergeometric normal model

DOI：

10.7507/1672-2531.201902062

Video：

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Abstract Full text Figures/Tables Video References Cited by

The meta-analysis of rare binary data is a difficulty in the field of medical research, and its methodology remains immature. The traditional meta-analysis technique is based on the normal-normal model of fixed effects analysis or random-effects analysis, however there are methodological problems in this method. Stijnen proposed an exact within-study likelihood models (EWLM) meta-analysis technique based on the generalized linear mixed model (GLMM), including the binomial-normal model (BN) and Hypergeometric-normal model (HNM), which can be used to achieve random effects meta-analysis of rare binary data. This paper introduces the model in detail and its implementation in SAS software with examples to provide relevant SAS code.

Citation： WU Min, ZHENG Jianqing, HUANG Bifen, XIAO Lihua. Random effects meta-analysis of rare binary data in the framework of the generalized linear mixed model. Chinese Journal of Evidence-Based Medicine, 2019, 19(7): 875-882. doi: 10.7507/1672-2531.201902062 Copy

1.	Vandermeer B, Bialy L, Hooton N, et al. Meta-analyses of safety data: a comparison of exact versus asymptotic methods. Stat Methods Med Res, 2009, 18(4): 421-432.
2.	Efthimiou O. Practical guide to the meta-analysis of rare events. Evid Based Ment Health, 2018, 21(2): 72-76.
3.	Bradburn MJ, Deeks JJ, Berlin JA, et al. Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Stat Med, 2007, 26(1): 53-77.
4.	Laird N. Meta-analysis in clinical trials. Control Clin Trials, 1986, 7(3): 177.
5.	Nikolakopoulou A, Mavridis D, Salanti G. Demystifying fixed and random effects meta-analysis. Evid Based Ment Health, 2014, 17(2): 53-57.
6.	Stijnen T, Hamza TH, Ozdemir P. Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Stat Med, 2010, 29(29): 3046-3067.
7.	Normand SL. Meta-analysis: formulating, evaluating, combining, and reporting. Stat Med, 1999, 18(3): 321-359.
8.	van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Stat Med, 2002, 21(4): 589-624.
9.	Rukhin AL, Biggerstaff BJ, Vangel MG. Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. J Stat Plan Infer, 2000, 83(2): 319-330.
10.	DerSimonian R, Kacker R. Random-effects model for meta-analysis of clinical trials: an update. Contemp Clin Trials, 2007, 28(2): 105-114.
11.	Kackar RN, Harville DA. Approximations for standard errors of estimators of fixed and random effect in mixed linear models. J Amer Statist Assn, 1984, 79(388): 853-862.
12.	Böhning D, Malzahn U, Dietz E, et al. Some general points in estimating heterogeneity variance with the DerSimonian-Laird estimator. Biostatistics, 2002, 3(4): 445-457.
13.	Chang BH, Waternaux C, Lipsitz S. Meta-analysis of binary data: which within study variance estimate to use? Stat Med, 2001, 20(13): 1947-1956.
14.	Hamza TH, van Houwelingen HC, Stijnen T. The binomial distribution of meta-analysis was preferred to model within-study variability. J Clin Epidemiol, 2008, 61(1): 41-51.
15.	Sweeting MJ, Sutton AJ, Lambert PC. What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Stat Med, 2004, 23(9): 1351-1375.
16.	Shuster JJ, Jones LS, Salmon DA. Fixed vs random effects meta-analysis in rare event studies: the rosiglitazone link with myocardial infarction and cardiac death. Stat Med, 2007, 26(24): 4375-4385.
17.	张天嵩, 钟文昭, 李博. 《实用循证医学方法学》(第2版). 长沙: 中南大学出版社, 2013.
18.	Brophy JM, Joseph L, Rouleau JL. Beta-blockers in congestive heart failure. A Bayesian meta-analysis. Ann Intern Med, 2001, 134(7): 550-560.
19.	Keus F, Wetterslev J, Gluud C, et al. Robustness assessments are needed to reduce bias in meta-analyses that include zero-event randomized trials. Am J Gastroenterol, 2009, 104(3): 546-551.
20.	Kuss O. Statistical methods for meta-analyses including information from studies without any events-add nothing to nothing and succeed nevertheless. Stat Med, 2015, 34(7): 1097-1116.
21.	Turner RM, Jackson D, Wei Y, et al. Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis. Stat Med, 2015, 34(6): 984-998.
22.	Chen Y, Chu H, Luo S, et al. Bayesian analysis on meta-analysis of case-control studies accounting for within-study correlation. Stat Methods Med Res, 2015, 24(6): 836-855.
23.	Tian L, Cai T, Pfeffer MA, et al. Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 x 2 tables with all available data but without artificial continuity correction. Biostatistics, 2009, 10(2): 275-281.
24.	Lu G, Ades AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med, 2004, 23(20): 3105-3124.
25.	Smith TC, Spiegelhalter DJ, Thomas A. Bayesian approaches to random-effects meta-analysis: a comparative study. Stat Med, 1995, 14(24): 2685-2699.

1. Vandermeer B, Bialy L, Hooton N, et al. Meta-analyses of safety data: a comparison of exact versus asymptotic methods. Stat Methods Med Res, 2009, 18(4): 421-432.
2. Efthimiou O. Practical guide to the meta-analysis of rare events. Evid Based Ment Health, 2018, 21(2): 72-76.
3. Bradburn MJ, Deeks JJ, Berlin JA, et al. Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Stat Med, 2007, 26(1): 53-77.
4. Laird N. Meta-analysis in clinical trials. Control Clin Trials, 1986, 7(3): 177.
5. Nikolakopoulou A, Mavridis D, Salanti G. Demystifying fixed and random effects meta-analysis. Evid Based Ment Health, 2014, 17(2): 53-57.
6. Stijnen T, Hamza TH, Ozdemir P. Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Stat Med, 2010, 29(29): 3046-3067.
7. Normand SL. Meta-analysis: formulating, evaluating, combining, and reporting. Stat Med, 1999, 18(3): 321-359.
8. van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Stat Med, 2002, 21(4): 589-624.
9. Rukhin AL, Biggerstaff BJ, Vangel MG. Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. J Stat Plan Infer, 2000, 83(2): 319-330.
10. DerSimonian R, Kacker R. Random-effects model for meta-analysis of clinical trials: an update. Contemp Clin Trials, 2007, 28(2): 105-114.
11. Kackar RN, Harville DA. Approximations for standard errors of estimators of fixed and random effect in mixed linear models. J Amer Statist Assn, 1984, 79(388): 853-862.
12. Böhning D, Malzahn U, Dietz E, et al. Some general points in estimating heterogeneity variance with the DerSimonian-Laird estimator. Biostatistics, 2002, 3(4): 445-457.
13. Chang BH, Waternaux C, Lipsitz S. Meta-analysis of binary data: which within study variance estimate to use? Stat Med, 2001, 20(13): 1947-1956.
14. Hamza TH, van Houwelingen HC, Stijnen T. The binomial distribution of meta-analysis was preferred to model within-study variability. J Clin Epidemiol, 2008, 61(1): 41-51.
15. Sweeting MJ, Sutton AJ, Lambert PC. What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Stat Med, 2004, 23(9): 1351-1375.
16. Shuster JJ, Jones LS, Salmon DA. Fixed vs random effects meta-analysis in rare event studies: the rosiglitazone link with myocardial infarction and cardiac death. Stat Med, 2007, 26(24): 4375-4385.
17. 张天嵩, 钟文昭, 李博. 《实用循证医学方法学》(第2版). 长沙: 中南大学出版社, 2013.
18. Brophy JM, Joseph L, Rouleau JL. Beta-blockers in congestive heart failure. A Bayesian meta-analysis. Ann Intern Med, 2001, 134(7): 550-560.
19. Keus F, Wetterslev J, Gluud C, et al. Robustness assessments are needed to reduce bias in meta-analyses that include zero-event randomized trials. Am J Gastroenterol, 2009, 104(3): 546-551.
20. Kuss O. Statistical methods for meta-analyses including information from studies without any events-add nothing to nothing and succeed nevertheless. Stat Med, 2015, 34(7): 1097-1116.
21. Turner RM, Jackson D, Wei Y, et al. Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis. Stat Med, 2015, 34(6): 984-998.
22. Chen Y, Chu H, Luo S, et al. Bayesian analysis on meta-analysis of case-control studies accounting for within-study correlation. Stat Methods Med Res, 2015, 24(6): 836-855.
23. Tian L, Cai T, Pfeffer MA, et al. Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 x 2 tables with all available data but without artificial continuity correction. Biostatistics, 2009, 10(2): 275-281.
24. Lu G, Ades AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med, 2004, 23(20): 3105-3124.
25. Smith TC, Spiegelhalter DJ, Thomas A. Bayesian approaches to random-effects meta-analysis: a comparative study. Stat Med, 1995, 14(24): 2685-2699.

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