临床试验数据分析的异方差模型中的参数估计方法
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摘要
依从性作为临床试验中的一类重要解释变量，一直是医学研究中广为关注的研究对象。本文受B.EFRON和D.FELDMAN的启发，利用他们的消胆胺对降低胆固醇水平的的双盲临床试验研究为背景，在他们提出的简单模型的基础上，探讨这类临床试验的统计分析方法，研究依从性对药物效果的真正影响，从而建立一个更符合实际的对照临床试验数据的异方差模型。根据模型的特性，我们对控制组和治疗组的模型分别用最小二乘估计、拟似然估计及两步估计等方法来估计主要参数，由此得出反映依从性对药物疗效影响的参数的一种估计。在一般的条件下，证明了参数估计的大样本性质，主要是估计的渐进正态性。然后，利用生成的随机数据对模型的估计结果进行模拟，说明这种估计方法的良好性质。
As an important explantory variable in the clinical trials,compliance is a study object concerned widely in medical study.This article is inspired by B.EFRON and D.FELDMAN.lt applies to the double-blind clinical trial as the study background that the drug cholestyramine lowers cholesterol levels.On the basis of the simple model that they gave, we put forward more concrete model and try to study the ture effect that the compliance bring to the effectiveness of the drug,so that we can reach a more suitable heteroscedastic model for the case-control clincal trial and evaluate the ture effectiveness of the prescription drug. Owning to the particularity of the model, we get the estimators for the parameters that reflects the drug effectiveness by using MLE,Pseudo-likelihood estimation and two-stage estimation in models of control group and treatment group respectively.Under regular conditions, we demonstrate that all these estimators have some good large-sample property,including the asympotical normality. Then we make some simulations to illuminate propeties of the estimation for both large smaple sizes and moderate or small sample sizes.
As an important explantory variable in the clinical trials,compliance is a study object concerned widely in medical study.This article is inspired by B.EFRON and D.FELDMAN.lt applies to the double-blind clinical trial as the study background that the drug cholestyramine lowers cholesterol levels.On the basis of the simple model that they gave, we put forward more concrete model and try to study the ture effect that the compliance bring to the effectiveness of the drug,so that we can reach a more suitable heteroscedastic model for the case-control clincal trial and evaluate the ture effectiveness of the prescription drug. Owning to the particularity of the model, we get the estimators for the parameters that reflects the drug effectiveness by using MLE,Pseudo-likelihood estimation and two-stage estimation in models of control group and treatment group respectively.Under regular conditions, we demonstrate that all these estimators have some good large-sample property,including the asympotical normality. Then we make some simulations to illuminate propeties of the estimation for both large smaple sizes and moderate or small sample sizes.
引文
1 B.Efron and D.Feldman.Compliance as an explanatory variable in clinical trials. Journal of American Statistical Association.March 1991.
2 A.H.Welsh,R.J.Carroll,and D.Ruppert.Fitting Heteroscedastic Regression Models. JASA,March 1994.
3 王松桂．线性模型的理论及其应用．安徽教育出版社，1986．
4 R.J.Carroll,D.Ruppert.Transformation and Weighting in Regression.NewYork London.1988.
5 Raymond J.Carroll,C.F.Jefe Wu,and David Ruppert.The Effect Of Estimat ing Weights in Weighted Least Squares. JASA,December 1988.
6 王松桂，陈敏，陈立萍．线性统计模型(线性回归与方差分析)．高等教育出版社．1999：164～166
7 E.T.Lee. Statistical Methods for Survival Data Analysis. John Wiley & Sons. 1992:365～404.
8 Lipid Research Clinic Program. The Lipid Research Clinics Coronary Primary Prevention Trial Results, Part Ⅰ and Ⅱ. J.Of the American Medical Association(251), 1984:351～374
9 P.Holland. Statistics and Causal Inference(with discussion). J.Of the American Statistical Association(81),1986:945～970
10 O.Ashenfelter,A.B.Krueger. Estimates of the Economic Return to Schooling From a New Sample Identical Twins. American Economics Review,1994(84): 1157～1173.
11 S.Greenland,J.M.Robins,J.Pearl. Confounding and Collapsibility in Causal Inference. Statistics Science,1999,14(1):29～46
12 P.Armitage,E.A.Gehan. Statistical Methods for the Identification and Use of Prognostic Factors. International Journal of Cancer,1974(13):16～35.
13 R.Simon. Restricted Randomization Design in Clinical Trials. Biometrics, 1979 (35):503～512.
14 P.Meier. Stratification in the Design of a Clinical Trial. Controlled Clinical Trials,1981(1):355～361.
15 R.McHugh,J.Matts. Post-Stratification in the Randomized Clinical Trial. Biometrics, 1983,(39):217～225.
16 陈家鼎，戴中维．生存数据的统计分析方法(第二版)．中国统计出版社．1998．
17 C.L.Cheng,Van Ness. Statistical Regression with Measurement Error. Arnold. London,1999.
18 W.A.Fuller. Measurement Error Models. Wiley,New York.1987.
19 J.P.Bull. The Historical Development of Clinical Therapeutic Trials. J.Of Chronic Diseases. 1959, (10):214～248
20 A.B.Hill. Controlled Clinical Trials. Blackwell Scientific, Oxford, England. 1960.
21 A.B.Hill. Statistical Methods in Clinical and Preventive Medicinae.Oxford University Press, Oxford. 1960b.
22 L.J.Witts. Medical Survers and Clinical Trials. Oxford University Press, London. 1964.
23 E.A.Gehan,M.A.Schneiderman. Expeimental Design of Clinical Trials,
24 李人厚，张平安．精通MATLAB综合辅导与指南．西安交通大学出版社．1999．
25 王沫然．MATLAB6.0与科学计算．电子工业出版社．2001．
26 导向科技．MATLAB6.0程序设计与实例应用．中国铁道出版社．2001．
27 茆诗松，王静龙，濮晓龙．高等数理统计．高等教育出版社，施普林格出版社．1998．
28 Lipid Research Clinic Program(1984)." The Lipid Research Clinics Coronary Primary Prevention Trial Results,Parts Ⅰ and Ⅱ."Journal of the American Medical Association. 251,351-374.
29 Holland,P.W.(1998)."Causual Inference,Path Analysis,and Recusive Structural Equations Model," Sociological Methodology,449-484.
30 Holland,P.W.,and Rubin,D.B.(1982),Test Equating,New York Academic Press.
31 Rubin,D.B.(1974)," Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,"Journal of Educational Psychology,66,688-701.
32 Rubin,D.B.(1977)," Assignment to Treatment Group on the Basis of a Covariate," Journal of Educational Statistics,2,1-26.
33 Rubin,D.B.(1978),"Bayesian Inference for Causal Effects: the Role of Randomization," The Annals of Statistics,7,34-58.
34 赵国庆．计量经济学．中国人民大学出版社．2000．
35 王维国，丛春霞，何向华．计量经济学．东北财经大学出版社．2002．
36 李子奈．计量经济学．高等教育出版社．2000．
37 高惠璇．统计计算．北京大学出版社．1999．11．
38 陈希孺．高等数理统计，中国科学技术大学出版社．，1999．2．
39 陈希孺，陈桂景，吴启光，赵林城．线性模型参数的估计理论．科学出版社．1985．
40 朱军．线性模型分析原理．科学出版社．1999．
2 A.H.Welsh,R.J.Carroll,and D.Ruppert.Fitting Heteroscedastic Regression Models. JASA,March 1994.
3 王松桂．线性模型的理论及其应用．安徽教育出版社，1986．
4 R.J.Carroll,D.Ruppert.Transformation and Weighting in Regression.NewYork London.1988.
5 Raymond J.Carroll,C.F.Jefe Wu,and David Ruppert.The Effect Of Estimat ing Weights in Weighted Least Squares. JASA,December 1988.
6 王松桂，陈敏，陈立萍．线性统计模型(线性回归与方差分析)．高等教育出版社．1999：164～166
7 E.T.Lee. Statistical Methods for Survival Data Analysis. John Wiley & Sons. 1992:365～404.
8 Lipid Research Clinic Program. The Lipid Research Clinics Coronary Primary Prevention Trial Results, Part Ⅰ and Ⅱ. J.Of the American Medical Association(251), 1984:351～374
9 P.Holland. Statistics and Causal Inference(with discussion). J.Of the American Statistical Association(81),1986:945～970
10 O.Ashenfelter,A.B.Krueger. Estimates of the Economic Return to Schooling From a New Sample Identical Twins. American Economics Review,1994(84): 1157～1173.
11 S.Greenland,J.M.Robins,J.Pearl. Confounding and Collapsibility in Causal Inference. Statistics Science,1999,14(1):29～46
12 P.Armitage,E.A.Gehan. Statistical Methods for the Identification and Use of Prognostic Factors. International Journal of Cancer,1974(13):16～35.
13 R.Simon. Restricted Randomization Design in Clinical Trials. Biometrics, 1979 (35):503～512.
14 P.Meier. Stratification in the Design of a Clinical Trial. Controlled Clinical Trials,1981(1):355～361.
15 R.McHugh,J.Matts. Post-Stratification in the Randomized Clinical Trial. Biometrics, 1983,(39):217～225.
16 陈家鼎，戴中维．生存数据的统计分析方法(第二版)．中国统计出版社．1998．
17 C.L.Cheng,Van Ness. Statistical Regression with Measurement Error. Arnold. London,1999.
18 W.A.Fuller. Measurement Error Models. Wiley,New York.1987.
19 J.P.Bull. The Historical Development of Clinical Therapeutic Trials. J.Of Chronic Diseases. 1959, (10):214～248
20 A.B.Hill. Controlled Clinical Trials. Blackwell Scientific, Oxford, England. 1960.
21 A.B.Hill. Statistical Methods in Clinical and Preventive Medicinae.Oxford University Press, Oxford. 1960b.
22 L.J.Witts. Medical Survers and Clinical Trials. Oxford University Press, London. 1964.
23 E.A.Gehan,M.A.Schneiderman. Expeimental Design of Clinical Trials,
24 李人厚，张平安．精通MATLAB综合辅导与指南．西安交通大学出版社．1999．
25 王沫然．MATLAB6.0与科学计算．电子工业出版社．2001．
26 导向科技．MATLAB6.0程序设计与实例应用．中国铁道出版社．2001．
27 茆诗松，王静龙，濮晓龙．高等数理统计．高等教育出版社，施普林格出版社．1998．
28 Lipid Research Clinic Program(1984)." The Lipid Research Clinics Coronary Primary Prevention Trial Results,Parts Ⅰ and Ⅱ."Journal of the American Medical Association. 251,351-374.
29 Holland,P.W.(1998)."Causual Inference,Path Analysis,and Recusive Structural Equations Model," Sociological Methodology,449-484.
30 Holland,P.W.,and Rubin,D.B.(1982),Test Equating,New York Academic Press.
31 Rubin,D.B.(1974)," Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,"Journal of Educational Psychology,66,688-701.
32 Rubin,D.B.(1977)," Assignment to Treatment Group on the Basis of a Covariate," Journal of Educational Statistics,2,1-26.
33 Rubin,D.B.(1978),"Bayesian Inference for Causal Effects: the Role of Randomization," The Annals of Statistics,7,34-58.
34 赵国庆．计量经济学．中国人民大学出版社．2000．
35 王维国，丛春霞，何向华．计量经济学．东北财经大学出版社．2002．
36 李子奈．计量经济学．高等教育出版社．2000．
37 高惠璇．统计计算．北京大学出版社．1999．11．
38 陈希孺．高等数理统计，中国科学技术大学出版社．，1999．2．
39 陈希孺，陈桂景，吴启光，赵林城．线性模型参数的估计理论．科学出版社．1985．
40 朱军．线性模型分析原理．科学出版社．1999．