Comparison of Bayesian and Frequentist Meta-Analytical Approaches for Analyzing Time to Event Data

Using meta-analysis in health care research is a common practice. Here we are interested in methods used for analysis of time-to-event data. Particularly, we are interested in their performance when there is a low event rate. We consider three methods based on the Cox proportional hazards model, including a Bayesian approach. A formal comparison of the methods is conducted using a simulation study. In our simulation we model two treatments and consider several scenarios.

[1]  M A Proschan,et al.  Statistical methods for monitoring clinical trials. , 1999, Journal of biopharmaceutical statistics.

[2]  Nicola J Cooper,et al.  Meta-analysis of rare and adverse event data , 2002, Expert review of pharmacoeconomics & outcomes research.

[3]  George A. Wells,et al.  An Assessment of Methods to Combine Published Survival Curves , 2000, Medical decision making : an international journal of the Society for Medical Decision Making.

[4]  G. Rücker,et al.  Simpson's paradox visualized: The example of the Rosiglitazone meta-analysis , 2008, BMC medical research methodology.

[5]  Christy Chuang-Stein,et al.  The Practice of Pre-Marketing Safety Assessment in Drug Development , 2013, Journal of biopharmaceutical statistics.

[6]  Jonathan J Shuster,et al.  Rebuttal to Carpenter et al. comments on ‘Fixed vs. random effects meta‐analysis in rare event studies: The rosiglitazone link with myocardial infarction and cardiac death’ , 2008, Statistics in medicine.

[7]  Jun Yan.  Survival Analysis: Techniques for Censored and Truncated Data , 2004 .

[8]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[9]  D. Spiegelhalter,et al.  Bayesian random effects meta‐analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales , 2002, Statistics in medicine.

[10]  S. Nissen,et al.  Rosiglitazone revisited: an updated meta-analysis of risk for myocardial infarction and cardiovascular mortality. , 2010, Archives of internal medicine.

[11]  D. Berry,et al.  Bayesian Survival Analysis With Nonproportional Hazards , 2004 .

[12]  Jesse A Berlin,et al.  Recommendations for safety planning, data collection, evaluation and reporting during drug, biologic and vaccine development: a report of the safety planning, evaluation, and reporting team , 2009, Clinical trials.

[13]  G A Colditz,et al.  The role of meta-analysis in the regulatory process for foods, drugs, and devices. , 1999, JAMA.

[14]  M. Pittler.  Systematic Reviews in Health Care: Meta‐analysis in Context , 2010 .

[15]  David J Spiegelhalter,et al.  Being sceptical about meta-analyses: a Bayesian perspective on magnesium trials in myocardial infarction. , 2002, International journal of epidemiology.

[16]  Gerhard Nahler,et al.  International Conference on Harmonisation (ICH) , 2009 .

[17]  M Schemper,et al.  A Solution to the Problem of Monotone Likelihood in Cox Regression , 2001, Biometrics.

[18]  Lu Tian,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. , 2009, Biostatistics.

[19]  W. Haenszel,et al.  Statistical aspects of the analysis of data from retrospective studies of disease. , 1959, Journal of the National Cancer Institute.

[20]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[21]  Douglas G Altman,et al.  Bayesian random effects meta‐analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales by D. E. Warn, S. G. Thompson and D. J. Spiegelhalter, Statistics in Medicine 2002; 21: 1601–1623 , 2005, Statistics in medicine.

[22]  Alex J. Sutton,et al.  Bayesian methods in meta-analysis and evidence synthesis , 2001 .

[23]  Alexander J Sutton,et al.  What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. , 2004, Statistics in medicine.

[24]  M. D. O'Connell,et al.  Correction , 2013, Nature.

[25]  R. Kay.  Statistical Principles for Clinical Trials , 1998, The Journal of international medical research.

[26]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[27]  Jonathan J Deeks,et al.  Much ado about nothing: a comparison of the performance of meta‐analytical methods with rare events , 2007, Statistics in medicine.

[28]  Douglas G. Altman,et al.  Systematic Reviews in Health Care , 2001 .

[29]  S. Sharp,et al.  Explaining heterogeneity in meta-analysis: a comparison of methods. , 1997, Statistics in medicine.

[30]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[31]  Ralf Bender,et al.  Generating survival times to simulate Cox proportional hazards models , 2005, Statistics in medicine.

[32]  Georg Heinze,et al.  SAS and SPLUS programs to perform Cox regression without convergence problems , 2002, Comput. Methods Programs Biomed..

[33]  D. Firth.  Bias reduction of maximum likelihood estimates , 1993 .