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Martín Andrés, A.; Herranz Tejedor, I.; Álvarez Hernández, M.

Two-tailed asymptotic inferences for the odds ratio in prospective and retrospective studies: evaluation of methods of inference. (English) Zbl 07194277

J. Stat. Comput. Simulation 90, No. 1, 138-156 (2020).
Summary: Various asymptotic methods have been proposed for obtaining a two-tailed confidence interval (CI) for the odds ratio (OR) based on two independent samples. This paper evaluates 22 different methods, including 14 new methods or modifications of old methods. Because the CI is obtained by inversion in \(\theta\) of the two-tailed test for \(H_0: OR = \theta\), this paper evaluates the tests for various values of \(\theta\), rather than the CIs that are obtained. The paper concludes that none of the classic methods were selected as a top method, although the Agresti logit method is an acceptable option when the sample imbalance and the true value of OR are moderate; however the CI so obtained is very wide. The best methods are based on the likelihood-ratio test and on the inverse sine transformation – which is a new method – after adding 0.5 to all the data; the likelihood-ratio test method has one disadvantage, which is that the CI is obtained iteratively. The paper also selects the best methods for ensuring compatibility between the conclusions for the CI and the independence test.

Cited in 1 Document

MSC:

62-XX Statistics

Keywords:

comparison of methods; asymptotic confidence intervals; chi-squared method; likelihood-ratio method; Sterne method; odds ratio; logit and inverse sine transformations
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References:

[1] Agresti A.On logit confidence intervals for the odds ratio with small samples. Biometrics. 1999;55(2):597-602. doi:10.1111/j.0006-341X.1999.00597.x. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1059.62532 · doi:10.1111/j.0006-341X.1999.00597.x
[2] Kraemer HC.Reconsidering the odds ratio as a measure of 2×2 association in a population. Stat Med. 2004;23:257-270. doi:10.1002/sim.1714. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1002/sim.1714
[3] Lui KJ, Lin CHD.A revisit on comparing the asymptotic interval estimators of odds ratio in a single 2×2 table. Biom J. 2003;45:226-237. doi:10.1002/ bimj.200390008. doi: 10.1002/bimj.200390008[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1441.62429 · doi:10.1002/
[4] Lin CY, Yang MC.Improved exact confidence intervals for the odds ratio in two independent binomial samples. Biom J. 2006;48(6):1008-1019. doi:10.1002/bimj.200510222. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1442.62496 · doi:10.1002/bimj.200510222
[5] Fagerland MW, Lydersen S, Laake P.Recommended confidence intervals for two independent binomial proportions. Stat Methods Med Res. 2015;24(2):224-254. doi:10.1177/0962280211415469. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1177/0962280211415469
[6] Wang W.On exact interval estimation for the odds ratio in subject-specific table. Stati Probabil Lett. 2017;129:360-366. doi:10.1016/j.spl.2017.06.016. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1380.62119 · doi:10.1016/j.spl.2017.06.016
[7] Chan ISF.Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods. Stat Methods Med Res. 2003;12:37-58. doi:10.1191=0962280203sm314ra. doi: 10.1191/0962280203sm314ra[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1121.62584 · doi:10.1191=0962280203sm314ra
[8] Agresti A, Min Y.Unconditional small-sample confidence intervals for the odds ratio. Biostatistics. 2002;3(3):379-386. doi:10.1093/biostatistics/3.3.379. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1135.62320 · doi:10.1093/biostatistics/3.3.379
[9] Martín Andrés A, Álvarez Hernández M, Herranz Tejedor I.Asymptotic two-tailed confidence intervals for the difference of proportions. J Appl Stat. 2012;39(7):1423-1435. doi:10.1080/02664763.2011.650686. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1250.62017 · doi:10.1080/02664763.2011.650686
[10] Cornfield J.A statistical problem arising from retrospective studies. In: Proceedings of third Berkeley symposium on mathematical statistics and probability. Berkeley: University of California Press; 1956. p. 135-148. [Google Scholar] · Zbl 0070.14707
[11] Wang W, Shan G.Exact confidence intervals for the relative risk and the odds ratio. Biometrics. 2015;71:985-995. doi:10.1111/biom.12360. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1419.62056 · doi:10.1111/biom.12360
[12] Reiczigel J, Abonyi-Tóth Z, Singer J.An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions. Comput Stat Data Anal. 2008;52:5046-5053. doi:10.1016/j.csda.2008.04.032. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1452.62237 · doi:10.1016/j.csda.2008.04.032
[13] Agresti A.Dealing with discreteness: making ‘exact’ confidence intervals for proportions, differences of proportions, and odds ratios more exact. Stat Methods Med Res. 2003;12:3-21. doi:10.1191/0962280203sm311ra. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1121.62564 · doi:10.1191/0962280203sm311ra
[14] Gart JJ, Thomas DG.The performance of three approximate confidence limit methods for the odds ratio. Am J Epidemiol. 1982;115(3):453-470. doi:10.1093/oxfordjournals.aje.a113323. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1093/oxfordjournals.aje.a113323
[15] Lawson R.Small sample confidence intervals for the odds ratio. Commun Stat-Simul C. 2004;33(4):1095-1113. doi:10.1081/SAC-200040691. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1101.62334 · doi:10.1081/SAC-200040691
[16] Siqueira AL, Whitehead A, Todd S.Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio. Stat Med. 2008;27:353-370. doi:10.1002/sim.2975. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1002/sim.2975
[17] Fagerland MW, Newcombe RG.Confidence intervals for odds ratio and relative risk based on the inverse hyperbolic sine transformation. Stat Med. 2013;32:2833-2836. doi:10.1002/sim.5714. [Crossref], [Web of Science ®], [Google Scholar] · doi:10.1002/sim.5714
[18] Miettinen O, Nurminen M.Comparative analysis of two rates. Stat Med. 1985;4:213-226. doi:10.1002/sim.4780040211. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1002/sim.4780040211
[19] Newcombe RG.Interval estimation for the difference between independent proportions: comparison of eleven methods. Stat Med. 1998;17:873-890. doi:10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E. doi: 10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E
[20] Woolf B.On estimating the relation between blood group and disease. Ann Hum Genet. 1955;19(4):251-253. doi:10.1111/j.1469-1809.1955.tb01348.x. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1111/j.1469-1809.1955.tb01348.x
[21] Martín Andrés A, Álvarez Hernández M.Two-tailed approximate confidence intervals for the ratio of proportions. Stat Comput. 2014;24:65-75. doi:10.1007/s11222-012-9353-5. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1325.62061 · doi:10.1007/s11222-012-9353-5
[22] Álvarez Hernández M, Martín Andrés A.New asymptotic inferences about the difference, ratio and linear combination of two independent proportions. Commun Stat-Simul C. 2017;46(2):1557-1568. doi:10.1080/03610918. 2015.1005231. doi: 10.1080/03610918.2015.1005231[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1362.62042 · doi:10.1080/03610918.
[23] Sterne TE.Some remarks on confidence of fiducial limits. Biometrika. 1954;41(1/2):275-278. doi:10.1093/biomet/41.1-2.275. doi: 10.2307/2333026[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0055.12807 · doi:10.1093/biomet/41.1-2.275
[24] Li Y, Koval JJ, Donner A, et al. Interval estimation for the area under the receiver operating characteristic curve when data are subject to error. Stat Med. 2010;29:2521-2531. doi:10.1002/sim.4015. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1002/sim.4015
[25] Gart JJ, Zweifel JR.On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika. 1967;54:181-187. doi:10.2307/2333861. doi: 10.1093/biomet/54.1-2.181[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 0163.14601 · doi:10.2307/2333861
[26] Agresti A, Caffo B.Simple and effective confidence intervals for proportions and difference of proportions result from adding two successes and two failures. Am Stat. 2000;54(4):280-288. doi:10.2307/2685779. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1250.62016 · doi:10.2307/2685779
[27] Price RM, Bonett DG.An improved confidence interval for a linear function of binomial proportions. Comput Stat Data Anal. 2004;45(3):449-456. doi:10.1016/s0167-9473(03)00007-0. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1429.62102 · doi:10.1016/s0167-9473(03)00007-0
[28] Upton GJG.A comparison of alternative test for the 2×2 comparative trial. J R Stat Soc A. 1982;145(1):86-105. doi:10.2307/2981423. [Crossref], [Web of Science ®], [Google Scholar] · doi:10.2307/2981423
[29] Martín Andrés A, Silva Mato A.Choosing the optimal unconditioned test for comparing two independent proportions. Comput Stat Data Anal. 1994;17:555-574. doi:10.1016/0167-9473(94)90148-1. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 0937.62534 · doi:10.1016/0167-9473(94)90148-1
[30] Chen LA, Hung HN, Chen CR.Maximum average-power (MAP) tests. Commun Stat-Theor M. 2007;36:2237-2249. doi:10.1080/ 03610920701215480. doi: 10.1080/03610920701215480[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1124.62007 · doi:10.1080/
[31] Martín Andrés A, Álvarez Hernández M.Comments on ‘active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio. Stat Med. 2008;27(27):5799-5800. doi:10.1080/ 10629360601026386. doi: 10.1002/sim.3373[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · doi:10.1080/
[32] Barnard GA.Significance tests for 2×2 tables. Biometrika. 1947;34:123-138. doi:10.2307/2332517. doi: 10.1093/biomet/34.1-2.179[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 0029.15603 · doi:10.2307/2332517
[33] Munk A, Skipka G, Stratmann B.Testing general hypotheses under binomial sampling: the two sample case—asymptotic theory and exact procedures. Comput Stat Data Anal. 2005;49:723-739. doi:10.1016/j.csda.2004.05.035. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1429.62575 · doi:10.1016/j.csda.2004.05.035
[34] Essenberg JM.Cigarette smoke and the incidence of primary neoplasm of the lung in the albino mouse. Science. 1952;116:561-562. doi: 10.1126/science.116.3021.561[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
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