Fiducial Hypothesis Testing for the Ratio of the Parameters of Two Independent Binomials
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摘要: 两个独立二项分布参数之间的风险比的非劣效性检验在医学统计研究中是一个非常有意义的问题. 常用的限制性极大估计方法在大多数情况下都不能控制第一类错误. 本文提出用基于信仰推断法来解决基于两个独立二项分布参数之间的风险比的非劣效性检验问题. 模拟结果显示: 在小样本的研究情况下,这种基于信仰推断法的MF检验方法能很好地控制第一类错误, 检验功效也不差.
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关键词:
- 功效.
Abstract: In medical statistics study, non-inferiority test for two independent binomial distribution parameters is a very important problem. The constrained maximum likelihood test statistic cannot control the type I error rates for some cases be investigated. In this article, we use the fiducial inference methodology in order to develop more powerful tests for Non-inferiority based on the ratio between two independent binomial distributions. We present a broad Monte Carlo comparison between different tests for non-inferiority, confirming the preference of the proposed method from a power perspective. Simulation studies suggest that our MF test can control the type I error rates and its empirical type I error rate are much closer to the prespecified nominal significance level than those of other tests well with competitive powers.-
Keywords:
- Power study.
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[1] Almendra-Arao, F , Sotres-Ramos, D. .Comparison of some non-inferiority asymptotic tests for two independent proportions.[J].Agrociencia, 2009, 43:163 -172 [2]Chan, I. S. F..Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies.[J].Statist Med., 1998, 17:1403-1413 [3] Chan, I.S. F. .Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods. [J].Stat. Methods Med. Res., 2003, 12:37-58 [4] Fisher, R.A. .Inverse probability. [J].Math. Proc. Cambridge Philos. Soc., 1930, 26:528-535 [5] Grundy, P.M. .Fiducial distributions and prior distributions: an example in which the former cannot be associated with the latter. [J].J.Roy. Statist. Soc. Ser. B., 1956,, 18:217-221 [6]. [7]. [8] Hannig, J..On generalized fiducial inference. 19 :491-544.[J].Statist. Sinica., 2009, 19:491-544 [9] Hannig, J.Generalized fiducial inference via discretization.[J].Statist. Sinica, 2013, 23:489-514 [10] Hannig, J,Lai, R. C. S., Lee, T.C.M, .Computational Issues of Generalized Fiducial Inference.[J].Computational Statistics and Data Analysis., 2014, 71:849-858 [11] Hua Jin, Xiaobo Feng, Mingming Chen, Chenling Zhang.Two new methods for non-inferiority testing of the ratio in matched-pair setting.[J].TEST, 2014, 23:691-707 [12]. [13]Lusher, J.M., Roberts, H. R., Davignon, G., Joist, J. H., Smith, H.,Shapiro, A., Laurian, Y., Kasper, C. K., Mannucci, .A randomized, double-blind comparison of two dosage levels of recombinant factor VIIa in the treatment of joint, muscle and mucocutaneous haemorrhages in persons with haemophilia A and B, with and without inhibitors.[J].Haemophilia., 1998, 4:790-798 [14]. [15]. [16] Miettinen, O, Nurminen, M. .Comparative analysis of two rates. [J].Statist. Med., 1985, 4:213-226 [17] Sotres-Ramos, D, Almendra-Arao, F.,Ramírez-Figueroa, C. .Exact critical values for Farrington-Manning noninferiority exact test. [J].Drug Information Journal, 2010, 44:159-164 [18] Taraldsen, G, Lindqvist, B. H. .Fiducial theory and optimal inference. [J].Ann. Statist., 2013, 41:323-341 [19] Zaslavsky, B,G. .Bayesian hypothesis testing in two-arm trials with dichotomous outcomes. [J].Biometrics., 2013, 69:157-163
[1] Almendra-Arao, F , Sotres-Ramos, D. .Comparison of some non-inferiority asymptotic tests for two independent proportions.[J].Agrociencia, 2009, 43:163 -172 [2]Chan, I. S. F..Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies.[J].Statist Med., 1998, 17:1403-1413 [3] Chan, I.S. F. .Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods. [J].Stat. Methods Med. Res., 2003, 12:37-58 [4] Fisher, R.A. .Inverse probability. [J].Math. Proc. Cambridge Philos. Soc., 1930, 26:528-535 [5] Grundy, P.M. .Fiducial distributions and prior distributions: an example in which the former cannot be associated with the latter. [J].J.Roy. Statist. Soc. Ser. B., 1956,, 18:217-221 [6]. [7]. [8] Hannig, J..On generalized fiducial inference. 19 :491-544.[J].Statist. Sinica., 2009, 19:491-544 [9] Hannig, J.Generalized fiducial inference via discretization.[J].Statist. Sinica, 2013, 23:489-514 [10] Hannig, J,Lai, R. C. S., Lee, T.C.M, .Computational Issues of Generalized Fiducial Inference.[J].Computational Statistics and Data Analysis., 2014, 71:849-858 [11] Hua Jin, Xiaobo Feng, Mingming Chen, Chenling Zhang.Two new methods for non-inferiority testing of the ratio in matched-pair setting.[J].TEST, 2014, 23:691-707 [12]. [13]Lusher, J.M., Roberts, H. R., Davignon, G., Joist, J. H., Smith, H.,Shapiro, A., Laurian, Y., Kasper, C. K., Mannucci, .A randomized, double-blind comparison of two dosage levels of recombinant factor VIIa in the treatment of joint, muscle and mucocutaneous haemorrhages in persons with haemophilia A and B, with and without inhibitors.[J].Haemophilia., 1998, 4:790-798 [14]. [15]. [16] Miettinen, O, Nurminen, M. .Comparative analysis of two rates. [J].Statist. Med., 1985, 4:213-226 [17] Sotres-Ramos, D, Almendra-Arao, F.,Ramírez-Figueroa, C. .Exact critical values for Farrington-Manning noninferiority exact test. [J].Drug Information Journal, 2010, 44:159-164 [18] Taraldsen, G, Lindqvist, B. H. .Fiducial theory and optimal inference. [J].Ann. Statist., 2013, 41:323-341 [19] Zaslavsky, B,G. .Bayesian hypothesis testing in two-arm trials with dichotomous outcomes. [J].Biometrics., 2013, 69:157-163
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