Statistical methods for meta-analyses including information from studies without any events—add nothing to nothing and succeed nevertheless

Statistics in Medicine

Volumn 34, Issue 7, 2015, Pages 1097-1116

  Kuss, O ^a  

^a HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

continuity correction; meta analysis; rare events; safety; sparse data

Indexed keywords

ATTRIBUTABLE RISK; CORONARY ARTERY BYPASS GRAFT; HUMAN; LIFE; META ANALYSIS; ODDS RATIO; OFF PUMP SURGERY; RISK FACTOR; SAFETY; SCIENTIST; STATISTICAL MODEL;

EID: 85006341153     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6383     Document Type: Article

References (57)

1. Sutton AJ, Cooper NJ, Lambert PC, Jones DR, Abrams KR, Sweeting MJ. Meta-analysis of rare and adverse event data. Expert Review of Pharmacoeconomics & Outcomes Research 2002; 2(4):367–379.
2. Huang HY, Andrews E, Jones J, Skovron ML, Tilson H. Pitfalls in meta-analyses on adverse events reported from clinical trials. Pharmacoepidemioly & Drug Safety 2011; 20(10):1014–1020.
3. Vandermeer B, Bialy L, Hooton N, Hartling L, Klassen TP, Johnston BC, Wiebe N. Meta-analyses of safety data: a comparison of exact versus asymptotic methods. Statistical Methods in Medical Research 2009; 18(4):421–432.
4. Kuss O, Wandrey M, Kunze M. How frequent are meta-analyses with “double-zero” studies in systematic reviews? 2009. Available from: http://www.egms.de/static/de/meetings/gmds2009/09gmds155.shtml [Accessed 7 November 2014].
5. Salpeter SR, Greyber E, Pasternak GA, Salpeter EE. Risk of fatal and nonfatal lactic acidosis with metformin use in type 2 diabetes mellitus. Cochrane Database Syst Reviews 2010; 4:CD002967. DOI: 10.1002/14651858.
6. Brookes G, Ahmed AG. Pharmacological treatments for psychosis-related polydipsia. Cochrane Database of Systematic Reviews 2006; 4:CD003544. DOI: 10.1002/14651858.CD003544.pub2.
7. Nietert PJ, Wahlquist AE, Herbert TL. Characteristics of recent biostatistical methods adopted by researchers publishing in general/internal medicine journals. Statistics in Medicine 2013; 32(1):1–10.
8. Sweeting MJ, Sutton AJ, Lambert PC. What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Statistics in Medicine 2004; 23(9):1351–1375.
9. Bradburn MJ, Deeks JJ, Berlin JA, Russell Localio A. Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Statistics in Medicine 2007; 26(1):53–77.
10. Friedrich JO, Adhikari NK, Beyene J. Inclusion of zero total event trials in meta-analyses maintains analytic consistency and incorporates all available data. BMC Medical Research Methodology 2007; 7:5. DOI: 10.1186/1471-2288-7-5.
11. Liu D. Combining information for heterogeneous studies and rare events studies: a confidence distribution approach, 2012. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/37435/ [Accessed 7 November 2014].
12. Keus F, Wetterslev J, Gluud C, Gooszen HG, van Laarhoven CJ. Robustness assessments are needed to reduce bias in meta-analyses that include zero-event randomized trials. The American Journal of Gastroenterology 2009; 104(3):546–551.
13. Agresti A, Hartzel J. Strategies for comparing treatments on a binary response with multi-centre data. Statistics in Medicine 2000; 19(8):1115–1139.
14. Hirji KF. Exact Analysis of Discrete Data. Chapman & Hall/ CRC: Boca Raton, FL, USA, 2006.
15. Kuss O, Gummert JF, Borgermann J. Meta-analyses with rare events should use adequate methods. The Journal of Thoracic and Cardiovascular Surgery 2008; 136(1):241.
16. Eaton S, Hall NJ, Pierro A. Zero-total event trials and incomplete pyloromyotomy. The Journal of Pediatric Surgery 2009; 44(12):2434–2435.
17. Greenland S. Simpson's paradox from adding constants in contingency tables as an example of Bayesian noncollapsibility. The American Statistician 2010; 64(4):340–344.
18. Breslow N. Odds ratio estimators when the data are sparse. Biometrika 1981; 68(1):73–84.
19. O'Gorman TW, Woolson RF, Jones MP, Lemke JH. A Monte Carlo study of three odds ratio estimators and four tests of association in several 2 × 2 tables when the data are sparse. Communication in Statistics - Simulation and Computation 1988; 17(3):813–835.
20. Sankey SS, Weissfeld LA, Fine MJ, Kapoor W. An assessment of the use of the continuity correction for sparse data in meta-analysis. Communication in Statistics - Simulation and Computation 1996; 25(4):1031–1056.
21. Lui KJ. A Monte Carlo evaluation of five interval estimators for the relative risk in sparse data. Biometrical Journal 2006; 48(1):131–143.
22. Kuss O, Gromann C. An exact test for meta-analysis with binary endpoints. Methods of Information in Medicine 2007; 46(6):662–668.
23. Higgins JPT, Green S (eds). Cochrane Handbook for Systematic Reviews of Interventions Version 5.1.0 [updated March 2011]. The Cochrane Collaboration, 2011. Available from: www.cochrane-handbook.org [Accessed on 26 November 2014].
24. Tian L, Cai T, Pfeffer MA, Piankov N, Cremieux PY, Wei LJ. Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 × 2 tables with all available data but without artificial continuity correction. Biostatistics 2009; 10(2):275–281.
25. 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. Statistics in Medicine 2010; 29(29):3046–3067.
26. Møller CH, Penninga L, Wetterslev J, Steinbrüchel DA, Gluud C. Off-pump versus on-pump coronary artery bypass grafting for ischaemic heart disease. Cochrane Database Systematic Reviews 2012; 3:CD007224. DOI: 10.1002/14651858.CD007224.pub2.
27. Altman DG, Deeks JJ. Meta-analysis, Simpson's paradox, and the number needed to treat. BMC Medical Research Methodology 2002; 2:3. DOI: 10.1186/1471-2288-2-3.
28. Lièvre M, Cucherat M, Leizorovicz A. Pooling, meta-analysis, and the evaluation of drug safety. Current Controlled Trials in Cardiovascular Medicine 2002; 3(1):6.
29. Platt RW, Leroux BG, Breslow N. Generalized linear mixed models for meta-analysis. Statistics in Medicine 1999; 18(6):643–654.
30. McCulloch CE, Searle SR, Neuhaus JM. Generalized, Linear, and Mixed Models. John Wiley & Sons, Inc.: Hoboken, New Jersey, USA, 2008.
31. Gao S. Combining binomial data using the logistic normal model. Journal of Statistical Computation and Simulation 2006; 74(4):293–306.
32. Agresti A. Categorical Data Analysis. John Wiley & Sons, Inc.: Hoboken, New Jersey, USA, 2002.
33. Molenberghs G, Verbeke G. Models for Discrete Longitudinal Data, Springer Series in Statistics. Springer: New York, USA, 2005.
34. Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions. John Wiley & Sons, Inc.: Hoboken, New Jersey, USA, 2003.
35. Lin DY, Wei LJ. The robust inference for the proportional hazards model. Journal of the American Statistical Association 1989; 84(408):1074–1078.
36. Firth D. Bias reduction of maximum likelihood estimates. Biometrika 1993; 80(1):27–38.
37. Heinze G. A comparative investigation of methods for logistic regression with separated or nearly separated data. Statistics in Medicine 2006; 25(24):4216–4226.
38. Cai T, Parast L, Ryan L. Meta-analysis for rare events. Statistics in Medicine 2010; 29(20):2078–2089.
39. Greenland S, Robins JM. Estimation of a common effect parameter from sparse follow-up data. Biometrics 1985; 41(1):55–68.
40. Sato T. On the variance estimator for the Mantel–Haenszel risk difference (letter). Biometrics 1989; 45(4):1323–1324.
41. Kuhnert R, Böhning D. The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference. Statistical Papers 2005; 46(4):541–554.
42. Newman SC. Biostatistical Methods in Epidemiology. John Wiley & Sons, Inc.: Hoboken, New Jersey, USA, 2001.
43. Rücker G, Schwarzer G, Carpenter J, Olkin I. Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells. Statistics in Medicine 2009; 28(5):721–738.
44. Kuss O, Hoyer A, Solms A. Meta-analysis for diagnostic accuracy studies: a new statistical model using beta-binomial distributions and bivariate copulas. Statistics in Medicine 2014; 33(1):17–30.
45. Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JP. Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews. International Journal of Epidemiology 2012; 41(3):818–827.
46. Moher D, Tetzlaff J, Tricco AC, Sampson M, Altman DG. Epidemiology and reporting characteristics of systematic reviews. PLoS Medicine 2007; 4(3):e78. DOI: 10.1371/journal.pmed.0040078.
47. Fleishman AI. A method for simulating non-normal distributions. Psychometrika 1978; 43(4):521–532.
48. Fan X, Felsövályi A, Sivo SA, Kennan SC. SAS for Monte Carlo Studies: A Guide for Quantitative Researchers. SAS Institute: Cary, NC, USA, 2002.
49. Sato T. Bias in the Peto one-step estimator for the common odds ratio. Bulletin of Informatics and Cybernetics 2005; 37:13–18.
50. Lambert PC, Sutton AJ, Burton PR, Abrams KR, Jones DR. How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS. Statistics in Medicine 2005; 24(15):2401–2428.
51. Hall DB, Berenhaut KS. Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. The Canadian Journal of Statistics 2002; 30(3):415–430.
52. Morel JG, Neerchal NK. Clustered binary logistic regression in teratology data using a finite mixture distribution. Statistics in Medicine 1997; 16(24):2843–2853.
53. Fu R, Gartlehner G, Grant M, Shamliyan T, Sedrakyan A, Wilt TJ, Griffith L, Oremus M, Raina P, Ismaila A, Santaguida P, Lau J, Trikalinos TA. Conducting quantitative synthesis when comparing medical interventions: AHRQ and the Effective Health Care Program. Journal of Clinical Epidemiology 2011; 64(11):1187–1197.
54. Parzen M, Lipsitz S, Ibrahim J, Klar N. An estimate of the odds ratio that always exists. Journal of Computational and Graphical Statistics 2002; 11(2):420–436.
55. Carter RE, Lin Y, Lipsitz SR, Newcombe RG, Hermayer KL. Relative risk estimated from the ratio of two median unbiased estimates. Applied Statistics 2010; 59(4):657–671.
56. Lin Y, Newcombe RG, Lipsitz S, Carter RE. Fully specified bootstrap confidence intervals for the difference of two independent binomial proportions based on the median unbiased estimator. Statistics in Medicine 2009; 28(23):2876–2890.
57. Salpeter S, Ormiston T, Salpeter E. Cardioselective beta-blockers for chronic obstructive pulmonary disease. Cochrane Database Syst Reviews 2005; 4:CD003566. DOI: 10.1002/14651858.CD003566.pub2.