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BMC Med Res Methodol. 2012; 12: 34.
Published online Mar 23, 2012. doi:  10.1186/1471-2288-12-34
PMCID: PMC3398853
Individual patient data meta-analysis of survival data using Poisson regression models
Michael J Crowther,1 Richard D Riley,corresponding author2 Jan A Staessen,3,4 Jiguang Wang,5 Francois Gueyffier,6 and Paul C Lambert1,7
1Centre for Biostatistics and Genetic Epidemiology, Department of Health Sciences, University of Leicester, Adrian Building, University Road, Leicester LE1 7RH, UK
2School of Health and Population Sciences, University of Birmingham, Birmingham B15 2TT, UK
3The Studies Coordinating Centre, Division of Hypertension and Cardiovascular Rehabilitation, Department of Cardiovascular Research, University of Leuven, Campus Sint Rafaël, Kapucijnenvoer 35, Block D, Box 7001, Leuven BE-3000, Belgium
4Department of Epidemiology, Maastricht University, Peter Debyeplein 1, Box 616, Maastricht, MD NL-6200, The Netherlands
5Centre for Epidemiological Studies and Clinical Trials, Ruijin Hospital, Shanghai Jiaotong University School of Medicine, Ruijin 2nd Road 197, Shanghai 200025, China
6INSERM, CIC201, Lyon F-69000, France
7Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Box 281, Stockholm S-171 77, Sweden
corresponding authorCorresponding author.
Michael J Crowther: michael.crowther/at/le.ac.uk; Richard D Riley: r.d.riley/at/bham.ac.uk; Jan A Staessen: jan.staessen/at/med.kuleuven.be; Jiguang Wang: jiguangwang/at/netscape.net; Francois Gueyffier: francois.gueyffier/at/chu-lyon.fr; Paul C Lambert: paul.lambert/at/le.ac.uk
Received June 27, 2011; Accepted March 23, 2012.
Abstract
Background
An Individual Patient Data (IPD) meta-analysis is often considered the gold-standard for synthesising survival data from clinical trials. An IPD meta-analysis can be achieved by either a two-stage or a one-stage approach, depending on whether the trials are analysed separately or simultaneously. A range of one-stage hierarchical Cox models have been previously proposed, but these are known to be computationally intensive and are not currently available in all standard statistical software. We describe an alternative approach using Poisson based Generalised Linear Models (GLMs).
Methods
We illustrate, through application and simulation, the Poisson approach both classically and in a Bayesian framework, in two-stage and one-stage approaches. We outline the benefits of our one-stage approach through extension to modelling treatment-covariate interactions and non-proportional hazards. Ten trials of hypertension treatment, with all-cause death the outcome of interest, are used to apply and assess the approach.
Results
We show that the Poisson approach obtains almost identical estimates to the Cox model, is additionally computationally efficient and directly estimates the baseline hazard. Some downward bias is observed in classical estimates of the heterogeneity in the treatment effect, with improved performance from the Bayesian approach.
Conclusion
Our approach provides a highly flexible and computationally efficient framework, available in all standard statistical software, to the investigation of not only heterogeneity, but the presence of non-proportional hazards and treatment effect modifiers.
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