There are several user written programs for performing meta-analysis in Stata. These include metan (univariate meta-analysis), metareg (meta-regression), mvmeta (multivariate meta-analysis), midas and metandi for diagnostic tests and glst (dose-response models). However, there are several cases for which these programs do not suffice. For instance, there is no software for performing univariate meta-analysis with correlated estimates, for performing a multilevel or hierarchical meta-analysis, or for meta-analysis of longitudinal and repeated measurements data. In this work, we are going to show with practical applications, that many seemingly unrelated models, including but not limited to the ones mentioned above, can be fit using gllamm. The software is very versatile and can handle a wide variety of models with applications in a wide range of disciplines. The method presented here, takes advantage of these modelling capabilities and makes use of appropriate transformations (based on the Cholesky decomposition of the inverse of the covariance matrix) known as generalised least squares (GLS), in order to handle correlated data. Most of the models described above can be thought as special instances of a general linear mixed model formulation, but to the author’s knowledge a general exposition in order to incorporate all the available models for meta-analysis as special cases, and the instructions to fit them in a single statistical package has not been presented so far.
Three general classes of models are covered:
If you use this software, please cite:
Bagos PG. Meta-analysis in Stata using gllamm. 2015, Research Synthesis Methods (in press) [PDF][Pubmed] [Google Scholar]
With the software provided here, the user can fit the models for:
Univariate meta-analysis and meta-regression (univariate.do, my-meta.do and bcg.dta)
Normand SL. Meta-analysis: formulating, evaluating, combining, and reporting.Stat Med. 1999;18(3):321-59. [PDF]
Higgins JP, Thompson SG (2004) Controlling the risk of spurious findings from meta-regression. Stat Med 23(11): 1663-1682
Thompson SG, Higgins JP (2002) How should meta-regression analyses be undertaken and interpreted? Stat Med 21(11): 1559-1573
Multivariate meta-analysis with and without within-studies correlation (bivariate.do, my-bivariate.do, periodontitis.do, sclerotherapy.do, periodontitis.dta and sclerotherapy.dta)
Mavridis D, Salanti G (2012) A practical introduction to multivariate meta-analysis. Stat Methods Med Res
van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Stat Med. 2002;21(4):589-624.[PDF]
Jackson D, Riley R, White IR.Multivariate meta-analysis: Potential and promise. Stat Med. 2011 Jan 26. doi: 10.1002/sim.4172
Berkey CS, Hoaglin DC, Antczak-Bouckoms A, Mosteller F, Colditz GA (1998) Meta-analysis of multiple outcomes by regression with random effects. Stat Med 17(22): 2537-2550
Thompson SG, Smith TC, Sharp SJ (1997) Investigating underlying risk as a source of heterogeneity in meta-analysis. Stat Med 16: 2741-2758
Daniels MJ, Hughes MD (1997) Meta-analysis for the evaluation of potential surrogate markers. Stat Med 16(17): 1965-1982
Harbord RM, Deeks JJ, Egger M, Whiting P, Sterne JA (2007) A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics 8(2): 239-251 [PDF]
Arends LR, Hamza TH, van Houwelingen JC, Heijenbrok-Kal MH, Hunink MG, Stijnen T. Bivariate random effects meta-analysis of ROC curves. Med Decis Making 2008, 28(5):621-638.
Higgins JP, Whitehead A (1996) Borrowing strength from external trials in a meta-analysis. Stat Med 15(24): 2733-2749
Trikalinos TA, Olkin I (2008) A method for the meta-analysis of mutually exclusive binary outcomes. Stat Med
Bagos PG.A unification of multivariate methods for meta-analysis of genetic association studies. 2008, Statistical Applications in Genetics and Molecular Biology, 7(1), Article 13 [PDF]
Thompson JR, Minelli C, Abrams KR, Tobin MD, Riley RD (2005) Meta-analysis of genetic studies using Mendelian randomization--a multivariate approach. Stat Med 24(14): 2241-2254
Arends LR, Voko Z, Stijnen T (2003) Combining multiple outcome measures in a meta-analysis: an application. Stat Med 22: 1335-1353
Hierarchical meta-analysis and meta-analysis of correlated estimates (multilevel.do, dose_response.do, bmi-dose.dta and multilevel.dta)
Gleser LJ, Olkin I (1994) Stochastically dependent effect sizes. In The Handbook of Research Synthesis Cooper HM, Hedges LV (eds), pp 339-355. New York: Russell Sage Foundation
Lin D, Sullivan PF: Meta-Analysis of Genome-wide Association Studies with Overlapping Subjects. Am J Hum Genet 2009, 85:862-872. [PDF]
Greenland S, Longnecker MP (1992) Methods for trend estimation from summarized dose-response data, with applications to meta-analysis. Am J Epidemiol 135(11): 1301-1309
Peters JL, Mengersen KL: Meta-analysis of repeated measures study designs. J Eval Clin Pract 2008, 14:941-950.
Platt RW, Leroux BG, Breslow N. Generalized linear mixed models for meta-analysis. Stat Med 1999, 18(6):643-654.
Arends LR, Hunink MG, Stijnen T (2008) Meta-analysis of summary survival curve data. Stat Med 27: 4381-4396
Thompson SG, Turner RM, Warn DE (2001) Multilevel models for meta-analysis, and their application to absolute risk differences. Stat Methods Med Res 10(6): 375-392
Bagos PG, Dimou NL, Liakopoulos TD, Nikolopoulos GK (2011) Meta-Analysis of Family-Based and Case-Control Genetic Association Studies that Use the Same Cases. Stat Appl Genet Mol Biol 10
Hemming K, Bowater RJ, Lilford RJ (2012) Pooling systematic reviews of systematic reviews: a Bayesian panoramic meta-analysis. Stat Med 31: 201-216
Ishak KJ, Platt RW, Joseph L, Hanley JA, Caro JJ (2007) Meta-analysis of longitudinal studies. Clin Trials 4: 525-539
Laird NM, Ware JH (1982) Random-Effects Models for Longitudinal Data. Biometrics 38: 963-974
Stevens JR, Taylor AM (2009) Hierarchical Dependence in Meta-Analysis. Journal of Educational and Behavioral Statistics 34: 46-73