混合效应模型在多反应变量重复测量资料分析中的应用
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摘要
重复测量数据(repeated measurement data)是医学研究中十分常见的数据类型。针对这种数据的分析方法,经过多年的发展,已经有了很大改善,尤其是通过拟合混合效应模型,应用SAS软件的MIXED过程对其进行分析,相对于用一般的多变量分析或者SAS的GLM过程分析而言,模型建立更为灵活,结果更为可信。但是,一般文献中应用MIXED过程多是针对单一反应变量重复测量的情况,数据之间的相关性也仅存在于同一个体的多次测量结果之间。
在大量的临床诊断、治疗实验和其它学科中,经常会遇到有两个甚至多个反应变量进行重复测量的情况,这些反应变量之间并非相互独立,而是也具有相关性的。例如,对高血压患者进行血压检测,每个被调查者先后三次重复测量其收缩压与舒张压水平,每位患者除收缩压或舒张压的三次测量之间有相关性外,每次测量的收缩压和舒张压之间也有相关性存在。对于这样的双反应变量重复测量数据,在一些文献中往往将两个以上的反应变量割裂开来,分别进行单变量重复测量资料或常规的单变量分析,这些方法都是不正确的。同时,对于多反应变量重复测量资料,数据之间的相关性可以分解为两部分,即某个体单反应变量重复测量值之间的相关和某个体多个反应变量之间的相关,同时其资料的随机误差仍然可以分解为个体内重复测量误差和个体间误差两部分。
本研究是在了解混合效应模型原理方法的基础上,针对多反应变量重复测量数据的特点,运用医学与环境学实例,研究混合效应模型在双反应变量重复测量资料分析中的应用,建立与完善其模型及SAS软件分析程序,并进行实例分析。结果认为该方法不仅可以更加有效、深入的挖掘该类数据中蕴藏的信息,得到固定效应和随机效应的估计值,同时可以得到反应变量本身之间的相关系数和变量多次重复测量间的相关系数,对数据间的相关性进行更加细致的分解和研究。另外,分析者也可拟合不同的混合效应模型,通过比较拟合统计量的大小和协方差参数的多少,从中选择针对该数据最切合实际解释的统计分析模型。
研究结果表明,混合效应模型完全可以应用于多反应变量重复测量数据的分析中,并且可以得到比通常单变量分析更可靠、更详尽的结果,能更充分地利用分析数据蕴藏的信息,在实际工作中有更好的应用前景。
Repeated measurement data is very common in the medical study.The analyzing method of this kind of data have been improved a lot after the development of many years,especially by fitting mixed effects models and using the MIXED procedure of SAS software to analyze,comparing to the general multivariate analysis and the GLM procedure of SAS,the model is more flexible and the result is more credible.But in many papers,the use of mixed effects model is in the single variable repeated measurement and the correlation is just between multiple repeated measure of one variable.
In many clinical diagnosis or experimental therapy and other sciences,we usually encount the repeated measures of two or more variables.The variables are not independent.For example,in the blood pressure measurement of hypertention,each patient's systolic pressure(SP) and diastolic pressure(DP) are measured three times,the three measurements of SP or DP are correlated and the two variables of each time are correlated tool In many papers,this kind of bivariate repeated measure data was dealt according single variable repeated measure or general single variable analysis,in fact,these methods are not accurate.At the same time,the correlation of multivariate repeated measure data can be cut ino two parts:between multiple measurements and between variables,and the random error also can be divided into repeated measure error in the subject and the error between subjects.
On the basis of mixed effects models,the study according to the characteristics of multiple reponses repeated measurement data,uses the mixed effects models and MIXED procedure to analyze the data,not only to mine the infomation and obtain the eastimate of fixed effect and random effect,but also to study the correlation in the data and get the correlation coefficient between variables and between multiple repeated measurement.In addition,analysts can fit different mixed effects models to select the best one by comparing fit statistics and the number of covariance parameters.
The result indicates that the mixed effects model can be applied into the analysis of multiple reponses repeated measurement data and the analyst can obtain more credible and detailed results comparing single variable analysis.It utilizes the infomation more sufficiently and could be applied in practice in future.
在大量的临床诊断、治疗实验和其它学科中,经常会遇到有两个甚至多个反应变量进行重复测量的情况,这些反应变量之间并非相互独立,而是也具有相关性的。例如,对高血压患者进行血压检测,每个被调查者先后三次重复测量其收缩压与舒张压水平,每位患者除收缩压或舒张压的三次测量之间有相关性外,每次测量的收缩压和舒张压之间也有相关性存在。对于这样的双反应变量重复测量数据,在一些文献中往往将两个以上的反应变量割裂开来,分别进行单变量重复测量资料或常规的单变量分析,这些方法都是不正确的。同时,对于多反应变量重复测量资料,数据之间的相关性可以分解为两部分,即某个体单反应变量重复测量值之间的相关和某个体多个反应变量之间的相关,同时其资料的随机误差仍然可以分解为个体内重复测量误差和个体间误差两部分。
本研究是在了解混合效应模型原理方法的基础上,针对多反应变量重复测量数据的特点,运用医学与环境学实例,研究混合效应模型在双反应变量重复测量资料分析中的应用,建立与完善其模型及SAS软件分析程序,并进行实例分析。结果认为该方法不仅可以更加有效、深入的挖掘该类数据中蕴藏的信息,得到固定效应和随机效应的估计值,同时可以得到反应变量本身之间的相关系数和变量多次重复测量间的相关系数,对数据间的相关性进行更加细致的分解和研究。另外,分析者也可拟合不同的混合效应模型,通过比较拟合统计量的大小和协方差参数的多少,从中选择针对该数据最切合实际解释的统计分析模型。
研究结果表明,混合效应模型完全可以应用于多反应变量重复测量数据的分析中,并且可以得到比通常单变量分析更可靠、更详尽的结果,能更充分地利用分析数据蕴藏的信息,在实际工作中有更好的应用前景。
Repeated measurement data is very common in the medical study.The analyzing method of this kind of data have been improved a lot after the development of many years,especially by fitting mixed effects models and using the MIXED procedure of SAS software to analyze,comparing to the general multivariate analysis and the GLM procedure of SAS,the model is more flexible and the result is more credible.But in many papers,the use of mixed effects model is in the single variable repeated measurement and the correlation is just between multiple repeated measure of one variable.
In many clinical diagnosis or experimental therapy and other sciences,we usually encount the repeated measures of two or more variables.The variables are not independent.For example,in the blood pressure measurement of hypertention,each patient's systolic pressure(SP) and diastolic pressure(DP) are measured three times,the three measurements of SP or DP are correlated and the two variables of each time are correlated tool In many papers,this kind of bivariate repeated measure data was dealt according single variable repeated measure or general single variable analysis,in fact,these methods are not accurate.At the same time,the correlation of multivariate repeated measure data can be cut ino two parts:between multiple measurements and between variables,and the random error also can be divided into repeated measure error in the subject and the error between subjects.
On the basis of mixed effects models,the study according to the characteristics of multiple reponses repeated measurement data,uses the mixed effects models and MIXED procedure to analyze the data,not only to mine the infomation and obtain the eastimate of fixed effect and random effect,but also to study the correlation in the data and get the correlation coefficient between variables and between multiple repeated measurement.In addition,analysts can fit different mixed effects models to select the best one by comparing fit statistics and the number of covariance parameters.
The result indicates that the mixed effects model can be applied into the analysis of multiple reponses repeated measurement data and the analyst can obtain more credible and detailed results comparing single variable analysis.It utilizes the infomation more sufficiently and could be applied in practice in future.
引文
[1]张岩波,何大卫,刘桂芬,等.重复测量数据的混合模型及其MIXED过程实现.中国卫生统计,2001,18(5):272-275
[2]Laird NM,Ware JH.Random effects models for longitudinal data.Biometrics,1982,38:963-974
[3]Diggle PJ,Liang KY,Zeger ST.Analysis of longitudinal data.Oxford:Clarendon Press.1995,332-336.
[4]Cnaan A,Laird NM,Slasor P.Tutorial in Biostatistics:Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data.Statistics in Medicine,1997,16:2349—2380
[5]任仕泉.非独立数据统计分析方法及其医学应用:[博士学位论文].四川:华西医科大学,1999
[6]赵晋芳,刘桂芬.重复测量线性混合模型中方差—协方差结构的选择.现代预防医学,2004,31(1):11-12
[7]许汝福,沈渝菊,肖瑞卿.单样本重复测量资料的混合线性模型及其应用.第三军医大学学报,2006,28(7):732-733
[8]董英,赵耐清.重复测量资料方差分析中主效应意义的探讨.复旦学报(医学版),2005,32(6):682-686
[9]Littell RC,Henry PR,Ammerman CB.Statistical Analysis of Repeated Measures Data Using SAS Procedures.J.Anim.Sci,1998,76:1215-1231
[10]Lindstorm ML,Bates TM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46:673-687
[11]Moser EB.Repeated measure modeling with PROC MIXED.SUGI,Statistics and Data Analysis,Paper 188-29,1-19
[12]陈华,陈冠民.重复测量数据的方差分析与SAS程序实现.数理医约学杂志,2001,14(4):325—326
[13]徐天和,柳青,余松林,等.中国卫生统计百科全书—多元统计分册.北京:人民卫生出版社,2004,100-120
[14]Bland JM,Altman DG.Correlation,regression,and repeated data.British Medical Journal,1994,308:896
[15]Bland JM,Altman DG.Calculating correlation coefficients with repeated observation:Part1-correlation within subjects.British Medical Journal,1995,310:446
[16]Bland JM,Altman DG.Calculating correlation coefficients with repeated observation:Part1-correlation between subjects.British Medical Journal,1995,310:663
[17]Lam M,Webb KA,O' Donnell DE,Correlation between two variables in repeated measures.American Statistical Association,Proceeding of the Biometric Section 213-218
[18]Hamlett A,Ryan L,Serranno-Trespalacios P,et al.Mixed models for assessing correlation in the presence of replication.Journal of the Air&Waste Management Association.2003,53:442-450
[19]Hamlett A,Ryan L,Wolfinger R.On the use of PROC MIXED to estimate correlation in the presence of repeated measure.SUGI,Statistics and Data Analysis,Paper 198-29,1-7
[20]Roy A.Estimating correlation coefficient between two variables with repeated observation using mixed effects model.Biometrical Journal,2006,48(2):286-301
[21]罗天娥,刘桂芬.重复测量资料非线性混合效应模型应用与实现.中国卫生统计,2006,23(2):104-107
[22]赵晋芳.重复测量线性混合模型在医学研究中的应用:[硕士学位论文].山西:山西医科大学,2002
[23]任仕泉,陈峰,杨树勤,等.多反应变量重复测量的混合效应模型及其应用.生物数学学报,1999,14(2):229-234
[24]余松林.混合线性模型的应用.中国医院统计,2006,13(1):70-75
[25]余松林,向惠云.重复测量资料分析方法与SAS程序.北京:科学出版社,2004,136-163
[26]任仕泉,陈峰.非独立数据及其协方差结构表达.中国卫生统计,1998,15(4):4-8
[27]陈长生,徐勇勇,袁天峰,等.医学多变量重复观测资料的随机系数模型.第四军医大学学报.2004,25(23):2182-2185
[28]陈峰,任仕泉,陆守曾.非独立计量资料的内部相关性研究.现代预防医学.1998,25(3):269-277
[29]陈峰,姚晨,孙高,等.新药临床试验中重复测量资料的混合效应模型.中国卫生统计,2000,17(6):372-376
[30]Roy A,Khattree,R.Testing the hypothesis of a Kroneckar Product covariance matrix in multivariate repeated measures data.SUGI,Statistics and Data Analysis,Paper 199-30,1-11
[31]The MIXED procedure.SAS/STAT User's Guide,Version 8,Vol.2,Chap.41.SAS Institute Inc,1999
[32]张海敏.多水平模型理论研究及其医学应用:[硕士学位论文].山西:山西医科大学,1999
[33]唐守正,李勇.生物数学模型的统计学基础.北京:科学出版社,2002,179-186
[34]薛富波,张文彤,田晓燕.SAS 8.2统计应用教程.北京:北京希望电子出版社,2004,130-137
[35]高惠璇.SAS系统SAS/STAT软件使用手册.北京:中国统计出版社,1997,339-363
[36]刘桂芬,孟海英,张岩波.Bayes线性混合效应模型多中心临床试验应用.中国卫生统计,2005,22(4):200-203
[37]孟海英.多中心临床试验重复测量设计与Bayes分析:[硕士学位论文].山西:山西医科大学,2004
[38]黄坤,倪宗瓒,程薇波.混合线性模型在临床试验中重复测量资料的应用.现代预防医学,2005,32(11):1584-1585
[39]张精文,许漂致,王永林.山西城市大气硫酸盐化速率与二氧化硫的相关性研究.华北地质矿产杂志.1996,11(2):171-176
[40]Yutaka Matsuyama,Yasuo Ohashi.Mixed models for bivariate response repeated measures data using gibbs sampling.Statistics In Medicine,1997,16:1587-1601
[41]娄冬华.重复测量数据的两变量的独立性.中国卫生统计,2001,18(5):285
[2]Laird NM,Ware JH.Random effects models for longitudinal data.Biometrics,1982,38:963-974
[3]Diggle PJ,Liang KY,Zeger ST.Analysis of longitudinal data.Oxford:Clarendon Press.1995,332-336.
[4]Cnaan A,Laird NM,Slasor P.Tutorial in Biostatistics:Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data.Statistics in Medicine,1997,16:2349—2380
[5]任仕泉.非独立数据统计分析方法及其医学应用:[博士学位论文].四川:华西医科大学,1999
[6]赵晋芳,刘桂芬.重复测量线性混合模型中方差—协方差结构的选择.现代预防医学,2004,31(1):11-12
[7]许汝福,沈渝菊,肖瑞卿.单样本重复测量资料的混合线性模型及其应用.第三军医大学学报,2006,28(7):732-733
[8]董英,赵耐清.重复测量资料方差分析中主效应意义的探讨.复旦学报(医学版),2005,32(6):682-686
[9]Littell RC,Henry PR,Ammerman CB.Statistical Analysis of Repeated Measures Data Using SAS Procedures.J.Anim.Sci,1998,76:1215-1231
[10]Lindstorm ML,Bates TM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46:673-687
[11]Moser EB.Repeated measure modeling with PROC MIXED.SUGI,Statistics and Data Analysis,Paper 188-29,1-19
[12]陈华,陈冠民.重复测量数据的方差分析与SAS程序实现.数理医约学杂志,2001,14(4):325—326
[13]徐天和,柳青,余松林,等.中国卫生统计百科全书—多元统计分册.北京:人民卫生出版社,2004,100-120
[14]Bland JM,Altman DG.Correlation,regression,and repeated data.British Medical Journal,1994,308:896
[15]Bland JM,Altman DG.Calculating correlation coefficients with repeated observation:Part1-correlation within subjects.British Medical Journal,1995,310:446
[16]Bland JM,Altman DG.Calculating correlation coefficients with repeated observation:Part1-correlation between subjects.British Medical Journal,1995,310:663
[17]Lam M,Webb KA,O' Donnell DE,Correlation between two variables in repeated measures.American Statistical Association,Proceeding of the Biometric Section 213-218
[18]Hamlett A,Ryan L,Serranno-Trespalacios P,et al.Mixed models for assessing correlation in the presence of replication.Journal of the Air&Waste Management Association.2003,53:442-450
[19]Hamlett A,Ryan L,Wolfinger R.On the use of PROC MIXED to estimate correlation in the presence of repeated measure.SUGI,Statistics and Data Analysis,Paper 198-29,1-7
[20]Roy A.Estimating correlation coefficient between two variables with repeated observation using mixed effects model.Biometrical Journal,2006,48(2):286-301
[21]罗天娥,刘桂芬.重复测量资料非线性混合效应模型应用与实现.中国卫生统计,2006,23(2):104-107
[22]赵晋芳.重复测量线性混合模型在医学研究中的应用:[硕士学位论文].山西:山西医科大学,2002
[23]任仕泉,陈峰,杨树勤,等.多反应变量重复测量的混合效应模型及其应用.生物数学学报,1999,14(2):229-234
[24]余松林.混合线性模型的应用.中国医院统计,2006,13(1):70-75
[25]余松林,向惠云.重复测量资料分析方法与SAS程序.北京:科学出版社,2004,136-163
[26]任仕泉,陈峰.非独立数据及其协方差结构表达.中国卫生统计,1998,15(4):4-8
[27]陈长生,徐勇勇,袁天峰,等.医学多变量重复观测资料的随机系数模型.第四军医大学学报.2004,25(23):2182-2185
[28]陈峰,任仕泉,陆守曾.非独立计量资料的内部相关性研究.现代预防医学.1998,25(3):269-277
[29]陈峰,姚晨,孙高,等.新药临床试验中重复测量资料的混合效应模型.中国卫生统计,2000,17(6):372-376
[30]Roy A,Khattree,R.Testing the hypothesis of a Kroneckar Product covariance matrix in multivariate repeated measures data.SUGI,Statistics and Data Analysis,Paper 199-30,1-11
[31]The MIXED procedure.SAS/STAT User's Guide,Version 8,Vol.2,Chap.41.SAS Institute Inc,1999
[32]张海敏.多水平模型理论研究及其医学应用:[硕士学位论文].山西:山西医科大学,1999
[33]唐守正,李勇.生物数学模型的统计学基础.北京:科学出版社,2002,179-186
[34]薛富波,张文彤,田晓燕.SAS 8.2统计应用教程.北京:北京希望电子出版社,2004,130-137
[35]高惠璇.SAS系统SAS/STAT软件使用手册.北京:中国统计出版社,1997,339-363
[36]刘桂芬,孟海英,张岩波.Bayes线性混合效应模型多中心临床试验应用.中国卫生统计,2005,22(4):200-203
[37]孟海英.多中心临床试验重复测量设计与Bayes分析:[硕士学位论文].山西:山西医科大学,2004
[38]黄坤,倪宗瓒,程薇波.混合线性模型在临床试验中重复测量资料的应用.现代预防医学,2005,32(11):1584-1585
[39]张精文,许漂致,王永林.山西城市大气硫酸盐化速率与二氧化硫的相关性研究.华北地质矿产杂志.1996,11(2):171-176
[40]Yutaka Matsuyama,Yasuo Ohashi.Mixed models for bivariate response repeated measures data using gibbs sampling.Statistics In Medicine,1997,16:1587-1601
[41]娄冬华.重复测量数据的两变量的独立性.中国卫生统计,2001,18(5):285