zbMATH — the first resource for mathematics

Comparison between Bayesian approach and frequentist methods for estimating relative risk in randomized controlled trials: a simulation study. (English) Zbl 07191961
Summary: Relative risks (RRs) are often considered as preferred measures of association in randomized controlled trials especially when the binary outcome of interest is common. To directly estimate RRs, log-binomial regression has been recommended. Although log-binomial regression is a special case of generalized linear models, it does not respect the natural parameter constraints, and maximum likelihood estimation is often subject to numerical instability that leads to convergence problems. Alternative methods for solving log-binomial regression convergence problems have been proposed. A Bayesian approach also was introduced, but the comparison between this method and frequentist methods has not been fully explored. We compared five frequentist and one Bayesian methods for estimating RRs under a variety of scenario. Based on our simulation study, there is not a method that can perform well based on different statistical properties, but COPY 1000 and modified log-Poisson regression can be considered in practice.
62 Statistics
Full Text: DOI
[1] Sackett DL, Rosenberg WM, Gray JA, Haynes RB, Richardson WS. Evidence based medicine: what it is and what it isn’t. Brit Med J. 1996;312(7023):71-72. doi: 10.1136/bmj.312.7023.71[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[2] Yelland LN, Salter AB, Ryan P. Relative risk estimation in randomized controlled trials: a comparison of methods for independent observations. Int J Biostat. 2011;7:1-31. [Crossref], [Google Scholar]
[3] Lumley T, Kronmal R, Ma S. Relative risk regression in medical research: models, contrasts, estimators, and algorithms. UW Biostatistics working paper series, Working paper 293; 2006. [Google Scholar]
[4] Lee J. Odds ratio or relative risk for cross-sectional data? Int J Epidemiol. 1994;23(1):201-203. doi: 10.1093/ije/23.1.201[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[5] Sinclair JC, Bracken MB. Clinically useful measures of effect in binary analyses of randomized trials. J Clin Epidemiol. 1994;47(8):881-889. doi: 10.1016/0895-4356(94)90191-0[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[6] Walter SD. Choice of effect measure for epidemiological data. J Clin Epidemiol. 2000;53(9):931-939. doi: 10.1016/S0895-4356(00)00210-9[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[7] Miettinen OS, Cook EF. Confounding: essence and detection. Am J Epidemiol. 1981;114(4):593-603. [PubMed], [Web of Science ®], [Google Scholar]
[8] Cummings P. The relative merits of risk ratios and odds ratios. Arch Pediat Adol Med. 2009;163(5):438-445. doi: 10.1001/archpediatrics.2009.31[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[9] Wacholder S. Binomial regression in GLIM: estimating risk ratios and risk differences. Am J Epidemiol. 1986;123(1):174-184. [PubMed], [Web of Science ®], [Google Scholar]
[10] Greenland S. Interpretation and choice of effect measures in epidemiologic analyses. Am J Epidemiol. 1987;125(5):761-768. [PubMed], [Web of Science ®], [Google Scholar]
[11] McNutt L-A, Wu C, Xue X, Hafner JP. Estimating the relative risk in cohort studies and clinical trials of common outcomes. Am J Epidemiol. 2003;157(10):940-943. doi: 10.1093/aje/kwg074[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[12] Fitzmaurice GM, Lipsitz SR, Arriaga A, Sinha D, Greenberg C, Gawande AA. Almost efficient estimation of relative risk regression. Biostatistics. 2014;15(4):745-756. doi: 10.1093/biostatistics/kxu012[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[13] Schwartz LM, Woloshin S, Welch HG. Misunderstandings about the effects of race and sex on physicians’ referrals for cardiac catheterization. New Engl J Med. 1999;341(4):279-283. doi: 10.1056/NEJM199907223410411[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[14] Deddens J, Petersen MR, Endahl L. Prevalence proportion ratios: estimation and hypothesis testing. Int J Epidemiol. 1998;27(1):91-95. doi: 10.1093/ije/27.1.91[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[15] Wallenstein S, Bodian C. Inferences on odds ratios, relative risks, and risk differences based on standard regression programs. Am J Epidemiol. 1987;126(2):346-355. doi: 10.1093/aje/126.2.346[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[16] Zhou R, Sivaganesan S, Longla M. An objective Bayesian estimation of parameters in a log-binomial model. J Statist Plann Inference. 2014;146:113-121. doi: 10.1016/j.jspi.2013.09.006[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1279.62067
[17] Flanders WD, Rhodes PH. Large sample confidence intervals for regression standardized risks, risk ratios, and risk differences. J Chronic Dis. 1987;40(7):697-704. doi: 10.1016/0021-9681(87)90106-8[Crossref], [PubMed], [Google Scholar]
[18] Schouten EG, Dekker JM, Kok FJ, et al. Risk ratio and rate ratio estimation in case-cohort designs: Hypertension and cardiovascular mortality. Stat Med. 1993;12(18):1733-1745. doi: 10.1002/sim.4780121808[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[19] Deddens JA, Petersen MR, Lei X. Estimation of prevalence ratios when PROC GENMOD does not converge. In Proceedings of the 28th Annual SAS Users Group International Conference. Cary, NC: SAS Institute Inc. Paper 270-28; 2003. [Google Scholar]
[20] Zou G. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol. 2004;159(7):702-706. doi: 10.1093/aje/kwh090[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[21] Localio AR, Margolis DJ, Berlin JA. Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression. J Clin Epidemiol. 2007;60(9):874-882. doi: 10.1016/j.jclinepi.2006.12.001[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[22] Gelfand AE, Smith AF, Lee T-M. Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J Am Statist Assoc. 1992;87(418):523-532. doi: 10.1080/01621459.1992.10475235[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[23] Smith AF, Roberts GO. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J R Statist Soc B (Methodol.). 1993;55(1):3-23. [Web of Science ®], [Google Scholar] · Zbl 0779.62030
[24] Gelfand AE, Smith AF. Sampling-based approaches to calculating marginal densities. J Am Statist Assoc. 1990;85(410):398-409. doi: 10.1080/01621459.1990.10476213[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0702.62020
[25] Ashby D. Bayesian statistics in medicine: a 25 year review. Stat Med. 2006;25(21):3589-3631. doi: 10.1002/sim.2672[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[26] Greenland S. Bayesian perspectives for epidemiological research: I. Foundations and basic methods. Int J Epidemiol. 2006;35(3):765-775. doi: 10.1093/ije/dyi312[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[27] Greenland S. Bayesian perspectives for epidemiological research. II. Regression analysis. Int J Epidemiol. 2007;36(1):195-202. doi: 10.1093/ije/dyl289[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[28] Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. Texts in Statistical Science. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC; 2004. [Google Scholar]
[29] Chu H, Cole SR. Estimation of risk ratios in cohort studies with common outcomes: a Bayesian approach. Epidemiology. 2010;21(6):855-862. doi: 10.1097/EDE.0b013e3181f2012b[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[30] Barros AJ, Hirakata VN. Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio. BMC Med Res Methodol. 2003;3(1). Available from: https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-3-21 doi: 10.1186/1471-2288-3-21[Crossref], [PubMed], [Google Scholar]
[31] Savu A, Liu Q, Yasui Y. Estimation of relative risk and prevalence ratio. Stat Med. 2010;29(22):2269-2281. doi: 10.1002/sim.3989[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[32] Carter RE, Lipsitz SR, Tilley BC. Quasi-likelihood estimation for relative risk regression models. Biostatistics. 2005;6(1):39-44. doi: 10.1093/biostatistics/kxh016[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1069.62088
[33] Spiegelhalter D, Thomas A, Best NG, Lunn D. WinBUGS Version 1.4 User Manual. Cambridge: Medical Research Council Biostatistics Unit; 2004. [Google Scholar]
[34] R Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2014. [Google Scholar]
[35] Halekoh U, Højsgaard S, Yan J. The R package geepack for generalized estimating equations. J Statist Softw. 2006;15(2):1-11. doi: 10.18637/jss.v015.i02[Crossref], [Web of Science ®], [Google Scholar]
[36] Yan J, Fine J. Estimating equations for association structures. Stat Med. 2004;23(6):859-874. doi: 10.1002/sim.1650[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[37] Yan J. Geepack: yet another package for generalized estimating equations. R News. 2002;2(3):12-14. [Google Scholar]
[38] Sturtz S, Ligges U, Gelman AE. R2WinBUGS: a package for running WinBUGS from R. J Statist Softw. 2005;12(3):1-16. doi: 10.18637/jss.v012.i03[Crossref], [Web of Science ®], [Google Scholar]
[39] Green BB, Cook AJ, Ralston JD, et al. Effectiveness of home blood pressure monitoring, Web communication, and pharmacist care on hypertension control: a randomized controlled trial. J Am Med Assoc. 2008;299(24):2857-2867. doi: 10.1001/jama.299.24.2857[Crossref], [Web of Science ®], [Google Scholar]
[40] Gilks WR, Best N, Tan K. Adaptive rejection Metropolis sampling within Gibbs sampling. J Appl Stat. 1995;44(4):455-472. doi: 10.2307/2986138[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0893.62110
[41] Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087-1092. doi: 10.1063/1.1699114[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1431.65006
[42] Gelfand AE, Hills SE, Racine-Poon A, Smith AFM, et al. Illustration of Bayesian inference in normal data models using Gibbs sampling. J Am Statist Assoc. 1990;85(412):972-985. doi: 10.1080/01621459.1990.10474968[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[43] Neal RM. Slice sampling. Ann Stat. 2003;31(3):705-767. doi: 10.1214/aos/1056562461[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1051.65007
[44] Lipsitz SR, Fitzmaurice GM, Arriaga A, Sinha D, Gawande AA. Using the jackknife for estimation in log link Bernoulli regression models. Stat Med. 2014;34(3):444-453. doi: 10.1002/sim.6348[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.