系统性红斑狼疮发生、预后的统计模型研究
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摘要
目的:对系统性红斑狼疮(SLE)的临床资料和现场流行病学资料进行多维度统计模型的研究,揭示出SLE发生病因,对SLE的发病风险、临床预后进行多方位的预测,为SLE的疾病监测和高危人群的预防提供依据。
方法:(1)收集安徽医科大学第一附属医院和安徽省立医院1990年～2001年12年内SLE住院病例资料,经过资料的预处理后,在考虑住院节段为水平1、病人为水平2的情况下,主要采用MCMC参数估计方法,分别拟合总SLE病例及女性SLE病例预测住院时间长短(LOS)的两水平线性回归模型和预测疗效优劣的两水平logit回归模型、评价SLE综合治疗质量的脆弱模型、将SLE免疫物质进行分类的多反应变量两水平因子分析模型、预测总SLE和女性SLE住院病例数的时间序列模型。(2)于2004年3月～6月以家庭为单位横断面收集SLE患者及家庭其他成员的流行病学调查资料,经过资料的预处理后,考虑被调查个体为水平1、家庭为水平2,采用MCMC参数估计方法,拟合总SLE病例和女性SLE病例预测发病风险的两水平logit模型。
结果:(1)总SLE病例和女性SLE病例的LOS在病人水平上均有聚集性,前者的模型性质是两水平随机系数模型,而后者的模型性质是两水平方差成分模型;前者LOS的影响因素有药物种类、家庭所在地、入院情况、是否转科、院内感染、是否首发、抗URNP抗体、抗Sm抗体、补体C3,其中,药物种类在病人水平上有随机效应;而后者LOS的影响因素有入院情况、院内感染、住院前是否激素治疗、IgG、补体C3、流产次数;两者相同影响因素的影响效应不完全一致。对于前者,常用6种、4种、3种、2科药物者的LOS均长于单独使用激素者。(2)同一个SLE病人或女性SLE病人多次住院节段的疗效之间无相关性,总SLE病例疗效的影响因素包括药物种类、入院情况、体温、IgG,除体温之外,其它三个因素对女性SLE病例的疗效有影响,但对两者的影响效应不一致。常用6种、4种、3种、2种药物者的疗效均优于单独使用激素者。(3)非死亡SLE再发病例的综合治疗质量在病人水平上存在随机效应,而且脆弱是同质的,即脆弱服从Gamma分布的Weibull模型。非死亡SLE再发病例的综合治疗质量的影响因素有性别、是否转科、院内感染、住院前是否激素治疗、IgG、药物种类。单独使用激素者的综合治疗质量优于联合用药者。(4)IgG、IgA、IgM、C3、ESR五种正态分布变量的两水平因子分析模型发现,因子在病人水平上是存在聚集性的,而且IgG、IgA、ESR归为一类,IgM、C3归为一类。抗URNP抗体、抗Sm抗体、抗SSA抗体、抗核抗体、抗ds-DNA抗体五种二分类变量的两水平因子分析模型发现,因子在病人水平上没有聚集性,抗URNP抗体、抗Sm抗体、抗核抗体归为一类,抗SSA抗体、抗ds-DNA抗体归为一类。(5)按年份、季度将SLE病例数划分成47个序列。经过SLE病例数序列图的绘制、模型的识别、反复比较及诊断,最后确定的时间序列模型是ARIMA(1,0,2)模型,从模型中发现SLE每年每季度的住院病例数序列值之间高度自相关,自相关系数高达0.9631;某季度序列值的大小受上上个季度对数序列值的季节效应影响。总SLE病例数与女性SLE病例数的预测类似。(6)总SLE病人或女性SLE病人的发病均无家庭聚集性,前者的发病因素包括性别、年龄组别、舒张压、过敏史、职业,而后者的发病因素包括年龄、舒张压、过敏史、职业,两者共同因素的影响效应不一致。其中对于前者而言,18-25岁的发病风险最高;而仅针对女性人群,年龄增长,发病风险却下降。
结论:针对不同目的和不同研究对象范围,可以采用不同统计模型进行LOS、疗效优劣、综合治疗质量、住院病例数和发病风险的分析与预测。免疫物质的两水平因子分析模型需补充完整数据再重新拟合。所有统计预测模型必须由新的一批SLE数据反复验证才能真正应用到临床和预防的实际工作中。
Objectives:The clinical data and field epidemiological data of systemic lupus erythematosus(SLE) were studied through multidimensional statistical models to reveal the pathogen of onset,predict the risk of onset and clinical prognosis and provide the foundation for the surveillance and prevention of high risk group of SLE.
Methods:(1) SLE hospitalization data was collected from the first attached hospital of Anhui Medical University and the Anhui provincial hospital among twelve years from 1990 to 2001.Under the consideration with the level one of hospitalization episodes and the level two of patients after the pretreatment of the data,we mainly applied the parametric estimation method of MCMC to fit the two-level linear regression model of length of stay(LOS) and two-level logit regression model of therapeutic effectiveness according to total and female SLE patients,frailty model of synthetic evaluation of therapeutic quality,two-level factor analysis model of multiple response variables to classified the immunity substances, time series model of the number of SLE patients according to total and female SLE patients.(2) Epidemiological data of SLE patients with their family members was collected from March to June of 2004 based on the unit of family. Under the consideration with the level one of patients and the level two of families after the pretreatment of the data,we applied the parametric estimation method of MCMC to fit the two-level logit model to predict the risk of onset according to total and female SLE patients.
Results:(1) Two models of LOS of total and female SLE were all collective on the level of patients in which the former was the two-level random coefficient model and the latter was the two-level variance component model. The influence factors of the former included:types of drugs often used, family location,situation of admission,if coming from the other section offices,nosocomial infection,if occurred firstly,anti URNP antibody, anti Sm antibody and complement C3,in which the variable of types of drugs often used had the random effect on the level of patients.While the influence factors of the latter included:situation of admission, nosocomial infection,if treated with hormone before admission,IgG, complement C3 and the frequency of abortion.The affections of common factors were not all identical.According to the former,LOS of patients treated with six,four,three and two types of drugs were all longer than that of those patients treated with hormone only.(2) There had no correlation among the therapeutic effectiveness of several hospitalization episodes of a same SLE patient or female SLE patient.Influence factors of the therapeutic effectiveness of total ShE patients included:types of drugs often used,situation of admission,temperature and IgG.Except of temperature,the other three factors had effects on the therapeutic effectiveness of female SLE patients with different affections. Therapeutic effectiveness of patients treated with six,four,three and two types of drugs were all better than that of those patients treated with hormone only.(3) Synthetic therapeutic quality of those non-death SLE recurrent patients had random effect on the level of patients with a homogeneous frailty which was a Weibull model with Gamma distribution of frailty.Sex,if coming from the other section offices,nosocomial infection,if treated with hormone before admission,IgG and types of drugs often used had effects on the synthetic therapeutic quality of those non-death SLE recurrent patients.Synthetic therapeutic quality of those patients treated with hormone only was better than that of those treated with combined therapied.(4) It was found from the two-level factor analysis model of normal response variables that the factors were collected on the level of patients based on which IgG,IgA and ESR were classed as one category and IgM and C3 as the other.The two-level factor analysis model of binary response variables was fit and found that the factors were not collected on the level of patients based on which anti URNP antibody,anti Sm antibody and antinuclear antibody were classed as one category and anti SSA antibody and anti ds-DNA antibody as the other.(5) Forty-seven series of the numbers of SLE patients was divided yearly and quarterly.The lastly determined time series model of the numbers of SLE patients was ARIMA(1, 0,2) after plotting the series graph,distinguishing,comparing and diagnosing the several models.It was found from this ARIMA model that there had a high degree of auto-ccrrelation among the series values of SLE patients yearly and quarterly with the coefficient of auto-correlation of 0.9631.A certain series value was affected by the one before last. Prediction model of the numbers of total SLE patients were similar to the one of the numbers of female SLE patients.(6) The onset of SLE of female SLE patients had no congregation in families.Pathogenic factors of total SLE patients were sex,group of age,diastolic pressure,allergic history and job occupation.Age,diastolic pressure,allergic history and job occupation were pathogenic factors of female SLE patients.The affections of common factors were different.According to the former,the risk of onset of the ages from 18 to 25 was the highest.While according to the latter, the risk of onset was decreasing with the increase of age.
Conclusions:According to the different goals and different scopes of objects of studies,diverse statistical models could be applied to do analysis and prediction on the LOS,therapeutic effectiveness,synthetic therapeutic quality,the number of hospitalization patients and risk of onset.Two-level factor analysis model of the immunity substances should be re-fit after the complete data were replenished.All the statistical predictive models should be repeatedly verified by a new set of SLE data before applied in the actual work of clinics and prevention.
方法:(1)收集安徽医科大学第一附属医院和安徽省立医院1990年～2001年12年内SLE住院病例资料,经过资料的预处理后,在考虑住院节段为水平1、病人为水平2的情况下,主要采用MCMC参数估计方法,分别拟合总SLE病例及女性SLE病例预测住院时间长短(LOS)的两水平线性回归模型和预测疗效优劣的两水平logit回归模型、评价SLE综合治疗质量的脆弱模型、将SLE免疫物质进行分类的多反应变量两水平因子分析模型、预测总SLE和女性SLE住院病例数的时间序列模型。(2)于2004年3月～6月以家庭为单位横断面收集SLE患者及家庭其他成员的流行病学调查资料,经过资料的预处理后,考虑被调查个体为水平1、家庭为水平2,采用MCMC参数估计方法,拟合总SLE病例和女性SLE病例预测发病风险的两水平logit模型。
结果:(1)总SLE病例和女性SLE病例的LOS在病人水平上均有聚集性,前者的模型性质是两水平随机系数模型,而后者的模型性质是两水平方差成分模型;前者LOS的影响因素有药物种类、家庭所在地、入院情况、是否转科、院内感染、是否首发、抗URNP抗体、抗Sm抗体、补体C3,其中,药物种类在病人水平上有随机效应;而后者LOS的影响因素有入院情况、院内感染、住院前是否激素治疗、IgG、补体C3、流产次数;两者相同影响因素的影响效应不完全一致。对于前者,常用6种、4种、3种、2科药物者的LOS均长于单独使用激素者。(2)同一个SLE病人或女性SLE病人多次住院节段的疗效之间无相关性,总SLE病例疗效的影响因素包括药物种类、入院情况、体温、IgG,除体温之外,其它三个因素对女性SLE病例的疗效有影响,但对两者的影响效应不一致。常用6种、4种、3种、2种药物者的疗效均优于单独使用激素者。(3)非死亡SLE再发病例的综合治疗质量在病人水平上存在随机效应,而且脆弱是同质的,即脆弱服从Gamma分布的Weibull模型。非死亡SLE再发病例的综合治疗质量的影响因素有性别、是否转科、院内感染、住院前是否激素治疗、IgG、药物种类。单独使用激素者的综合治疗质量优于联合用药者。(4)IgG、IgA、IgM、C3、ESR五种正态分布变量的两水平因子分析模型发现,因子在病人水平上是存在聚集性的,而且IgG、IgA、ESR归为一类,IgM、C3归为一类。抗URNP抗体、抗Sm抗体、抗SSA抗体、抗核抗体、抗ds-DNA抗体五种二分类变量的两水平因子分析模型发现,因子在病人水平上没有聚集性,抗URNP抗体、抗Sm抗体、抗核抗体归为一类,抗SSA抗体、抗ds-DNA抗体归为一类。(5)按年份、季度将SLE病例数划分成47个序列。经过SLE病例数序列图的绘制、模型的识别、反复比较及诊断,最后确定的时间序列模型是ARIMA(1,0,2)模型,从模型中发现SLE每年每季度的住院病例数序列值之间高度自相关,自相关系数高达0.9631;某季度序列值的大小受上上个季度对数序列值的季节效应影响。总SLE病例数与女性SLE病例数的预测类似。(6)总SLE病人或女性SLE病人的发病均无家庭聚集性,前者的发病因素包括性别、年龄组别、舒张压、过敏史、职业,而后者的发病因素包括年龄、舒张压、过敏史、职业,两者共同因素的影响效应不一致。其中对于前者而言,18-25岁的发病风险最高;而仅针对女性人群,年龄增长,发病风险却下降。
结论:针对不同目的和不同研究对象范围,可以采用不同统计模型进行LOS、疗效优劣、综合治疗质量、住院病例数和发病风险的分析与预测。免疫物质的两水平因子分析模型需补充完整数据再重新拟合。所有统计预测模型必须由新的一批SLE数据反复验证才能真正应用到临床和预防的实际工作中。
Objectives:The clinical data and field epidemiological data of systemic lupus erythematosus(SLE) were studied through multidimensional statistical models to reveal the pathogen of onset,predict the risk of onset and clinical prognosis and provide the foundation for the surveillance and prevention of high risk group of SLE.
Methods:(1) SLE hospitalization data was collected from the first attached hospital of Anhui Medical University and the Anhui provincial hospital among twelve years from 1990 to 2001.Under the consideration with the level one of hospitalization episodes and the level two of patients after the pretreatment of the data,we mainly applied the parametric estimation method of MCMC to fit the two-level linear regression model of length of stay(LOS) and two-level logit regression model of therapeutic effectiveness according to total and female SLE patients,frailty model of synthetic evaluation of therapeutic quality,two-level factor analysis model of multiple response variables to classified the immunity substances, time series model of the number of SLE patients according to total and female SLE patients.(2) Epidemiological data of SLE patients with their family members was collected from March to June of 2004 based on the unit of family. Under the consideration with the level one of patients and the level two of families after the pretreatment of the data,we applied the parametric estimation method of MCMC to fit the two-level logit model to predict the risk of onset according to total and female SLE patients.
Results:(1) Two models of LOS of total and female SLE were all collective on the level of patients in which the former was the two-level random coefficient model and the latter was the two-level variance component model. The influence factors of the former included:types of drugs often used, family location,situation of admission,if coming from the other section offices,nosocomial infection,if occurred firstly,anti URNP antibody, anti Sm antibody and complement C3,in which the variable of types of drugs often used had the random effect on the level of patients.While the influence factors of the latter included:situation of admission, nosocomial infection,if treated with hormone before admission,IgG, complement C3 and the frequency of abortion.The affections of common factors were not all identical.According to the former,LOS of patients treated with six,four,three and two types of drugs were all longer than that of those patients treated with hormone only.(2) There had no correlation among the therapeutic effectiveness of several hospitalization episodes of a same SLE patient or female SLE patient.Influence factors of the therapeutic effectiveness of total ShE patients included:types of drugs often used,situation of admission,temperature and IgG.Except of temperature,the other three factors had effects on the therapeutic effectiveness of female SLE patients with different affections. Therapeutic effectiveness of patients treated with six,four,three and two types of drugs were all better than that of those patients treated with hormone only.(3) Synthetic therapeutic quality of those non-death SLE recurrent patients had random effect on the level of patients with a homogeneous frailty which was a Weibull model with Gamma distribution of frailty.Sex,if coming from the other section offices,nosocomial infection,if treated with hormone before admission,IgG and types of drugs often used had effects on the synthetic therapeutic quality of those non-death SLE recurrent patients.Synthetic therapeutic quality of those patients treated with hormone only was better than that of those treated with combined therapied.(4) It was found from the two-level factor analysis model of normal response variables that the factors were collected on the level of patients based on which IgG,IgA and ESR were classed as one category and IgM and C3 as the other.The two-level factor analysis model of binary response variables was fit and found that the factors were not collected on the level of patients based on which anti URNP antibody,anti Sm antibody and antinuclear antibody were classed as one category and anti SSA antibody and anti ds-DNA antibody as the other.(5) Forty-seven series of the numbers of SLE patients was divided yearly and quarterly.The lastly determined time series model of the numbers of SLE patients was ARIMA(1, 0,2) after plotting the series graph,distinguishing,comparing and diagnosing the several models.It was found from this ARIMA model that there had a high degree of auto-ccrrelation among the series values of SLE patients yearly and quarterly with the coefficient of auto-correlation of 0.9631.A certain series value was affected by the one before last. Prediction model of the numbers of total SLE patients were similar to the one of the numbers of female SLE patients.(6) The onset of SLE of female SLE patients had no congregation in families.Pathogenic factors of total SLE patients were sex,group of age,diastolic pressure,allergic history and job occupation.Age,diastolic pressure,allergic history and job occupation were pathogenic factors of female SLE patients.The affections of common factors were different.According to the former,the risk of onset of the ages from 18 to 25 was the highest.While according to the latter, the risk of onset was decreasing with the increase of age.
Conclusions:According to the different goals and different scopes of objects of studies,diverse statistical models could be applied to do analysis and prediction on the LOS,therapeutic effectiveness,synthetic therapeutic quality,the number of hospitalization patients and risk of onset.Two-level factor analysis model of the immunity substances should be re-fit after the complete data were replenished.All the statistical predictive models should be repeatedly verified by a new set of SLE data before applied in the actual work of clinics and prevention.
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37.Tan EM,Cohen AS,Fries JF,Masi AT,McShane DJ,Rothfield NF,et al.Special article:The 1982 revised criteria for the classification of systemic lupus erythematosus.Arthritis Rheum.1982,25:1271-1277;
38.Hochberg MC.Updating the American College of Rheumatology revised criteria for the classifiction of systemic lupus erythemtosus(letter).Arthritis Rheum.1997,40:1725;
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40.洪毅,贺德华,昌志华。经济数学模型。广州:华南理工大学出版社,2002;
41.Albert,J.H.and Chib,S.Bayesian Analysis of binary and Polychotomous Response Data.Journal of the American Statistical Association. 1993,88:669-679;
42. Box-Steffensmeier, JM, Jones BS. Event History Modeling: Aguide for Social Scientists. 2004. Cambridge: Cambridge University Press;
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44. Gutierrez RG. Parametric frailty and shared frailty survival models. Stata Journal. 2004, 2: 180-190;
45. Kalbflersch JD, Prentice RL. The Statistical Analysis of Failure Time Data. 2002, 2nd ed. New York: Wiley;
46. Lee ET, Wang JW. Statistical Methods for Survival Data Analysis. 2003, 3~(rd) ed. New York: Wiley;
47. Asim Ansari, Kamel Jedidi. Bayesian factor analysis for multilevel binary observations. Psychometrika. 2000, 65(4):475-496;
48. Reise SP, Ventura J, Nuechterlein KH, Kim KH. An illustration of multilevel factor analysis. J Pers Assess. 2005, 84(2):126-136;
49. Michael G. Dodds, Paolo Vicini. Assessing convergence of Markov Chain Monte Carlo simulations in hierarchical Bayesian models for population pharmacokinetics. Annals of Biomedical Engineering. 2004, 32(9) : 1300-1313;
50. Jonathan J. Forster, John W. McDonald, Peter W. F. Smith. Markov Chain Monte Carlo exact inference for binomial and multinomial logistic regression models. Statistics and computing. 2003, 13(2):169-177;
51. Austin PC, Rothwell DM, TuJV. A comparison of statistical modeling strategies for analyzing length of stay after CABF surgery. Health Services & Outcomes Research Methodology. 2002,3:107-133;
52. Yau KKW, Lee AH, Gracey M. Multilevel modeling of hospitalizations for recurrent diarrhoeal disease in Aboriginal and non-Aboriginal infants and young children in Western Australia. Paediatric and Perinatal Epidemiology. 2005,19:165-172;
53. AnandKJS, Hopkins SE, Wright JA, Richetts RR, Flanders WD. Statistical models to predict the need for postoperative intensive care and hospitalization in pediatric surgical patients. Intensive Care Med. 2001,27:873-883;
54. Krishnan E. Hospitalization and mortality of patients with systemic lupus erythematosus. J Rheumatol. 2006 Sep;33(9):1770-4;
55. Alzeer AH, Al-Arfaj A, Basha SJ, Alballa S, Al-Wakeel J, Al-Arfaj H, et al. Outcome of patients with systemic lupus erythematosus in intensive care unit. Lupus. 2004;13(7):537-542;
56. Ward MM, Pajevic S, Dreyfuss J, Malley JD. Short-term prediction of mortality in patients with systemic lupus erythematosus:classification of outcomes using random forests. Arthritis Rheum. 2006,55:74-80;
57. Bertoli AM, Alarcon GS, McGwin GJ, et al. Systemic lupus erythematosus in a multithnic U. S. cohort (LUMINA) X XVII:factors predictive of a decline to low levels of disease activity. Lupus. 2006, 15:13-18;
58. Alarcon GS, Calvo-Alen J, McGwin GJ, et al. Systemic lupus erythematosus in a multithnic U. S. cohort(LUMINA) X X X V. Predictive factors of high disease activity over time. Ann Rheum Dis. Published online 31 Jan 2006;doi:10. 1136/ard. 2005. 046896;
59. Hitchon CA, Peschken CA. Sm antibodies increase risk of death in systemic lupus erythemaosus. Lupus. 2007,16(3):186-194;
60. Funauchi M, Shimadzu H, Tamaki C, Yamagata T, Nozaki Y, Sugiyama M, et al. Survival study by organ disorders in 306 Japanese patients with systemic lupus erythematosus: results from a single center. Rheumatol Int. 2007, 27 (3):243-249;
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63.Kasitanon N,Magder LS,Petri M.Predictors of survival in systemic lupus erythemaosus.Medicine(Baltimore).2006,85(3):147-156;
64.方积乾,万崇华,郝元涛。与健康有关的生存质量的研究概况。中国康复医学杂志。2000,1:40-43;
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66.Metcalfe C,Thompson SG.The importance of varying the event generation process in simulation studies of statistical methods for recurrent events.Stat Med.2006,25:165-179;
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68.Wienke A,Arbeev KG,Locatelli I,Yashin AI.A comparison of different bivariate correlated frailty models and estimation strategies.Math Biosci.2005,198:1-13;
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72.Zhang NJ,Wan TTH.The measurement of nursing home quality:Multilevel confirmatory factor analysis of panel data.Journal of Medical Systems.2005,29:401-411;
73.Kuhlemeier H,Van den Bergh H,Rijlaarsdam G.The dimensionality of speaking and writing:a multilevel factor analysis of situational,task and school effects.Br J Educ Psychol.2002,72(Pt 4):467-482;
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4.叶冬青,陆伟,李向培,等。系统性红斑狼疮HLA-DM基因与环境危险因素研究。中国卫生统计 2004,5:300-302,281;
5.Hardy CJ,Palmer BP,Muir KR,Sutton AJ,Powell RJ.Smoking history,alcohol consumption and systemic lupus erythematosus:a case-control study.Ann Rheum Dis 1998,57:451-455;
6.Sanchez-Guerrero J,Karlson EW,Liang MH,Hunter DJ,Speizer FE,Colditz GA.Past use of oral contraceptives and the risk of developing systemic lupus erythematosus,Arthritis Rheum 1997,40:804-808;
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11.Seligman VA,Suarez C,Lum R,et al.The Fc γ receptor ⅢA-158F allele is a major risk factor for the development of lupus nephritis among Caucasians but not non-Caucasians.Arthritis Rheum 2001,44:618-625:
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48. Reise SP, Ventura J, Nuechterlein KH, Kim KH. An illustration of multilevel factor analysis. J Pers Assess. 2005, 84(2):126-136;
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54. Krishnan E. Hospitalization and mortality of patients with systemic lupus erythematosus. J Rheumatol. 2006 Sep;33(9):1770-4;
55. Alzeer AH, Al-Arfaj A, Basha SJ, Alballa S, Al-Wakeel J, Al-Arfaj H, et al. Outcome of patients with systemic lupus erythematosus in intensive care unit. Lupus. 2004;13(7):537-542;
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59. Hitchon CA, Peschken CA. Sm antibodies increase risk of death in systemic lupus erythemaosus. Lupus. 2007,16(3):186-194;
60. Funauchi M, Shimadzu H, Tamaki C, Yamagata T, Nozaki Y, Sugiyama M, et al. Survival study by organ disorders in 306 Japanese patients with systemic lupus erythematosus: results from a single center. Rheumatol Int. 2007, 27 (3):243-249;
61 . Doria A, Iaccarino L, Ghirardello A, Zampieri S, Arienti S, Sarzi-Puttini P,et al.Long-term prognosis and causes of death in systemic lupus erythemaosus.Am J Med.2006,119(8):700-706;
62.Bernatsky S,Boivin JF,Joseph L,Manzi S,Ginzler E,Gladman DD,et al.Mortality in systemic lupus erythemaosus.Arthritis Rheum.2006,54(8):2550-2557;
63.Kasitanon N,Magder LS,Petri M.Predictors of survival in systemic lupus erythemaosus.Medicine(Baltimore).2006,85(3):147-156;
64.方积乾,万崇华,郝元涛。与健康有关的生存质量的研究概况。中国康复医学杂志。2000,1:40-43;
65.Fung KY,Khan S,Krewski D,Ramsay T.A comparison of methods for the analysis of recurrent health outcome data with environmental covariates.Star Med.2006,online;
66.Metcalfe C,Thompson SG.The importance of varying the event generation process in simulation studies of statistical methods for recurrent events.Stat Med.2006,25:165-179;
67.Box-Steffensmeier JM,De Boef S.Repeated events survival models:the conditional frailty model.Star Med.2005,online;
68.Wienke A,Arbeev KG,Locatelli I,Yashin AI.A comparison of different bivariate correlated frailty models and estimation strategies.Math Biosci.2005,198:1-13;
69.Maengseok Noh,Il Do Ha,Youngjo Lee.Dispersion frailty models and HGLMs.Star Med.2006,25:1341-1354;
70.宁自军。因子分析在居民消费结构的变动分析中的应用。数理统计与管理。2004,23:11-14;
71.Toland MD,DeAyala RJ.A multilevel factor analysis of students'evaluations of teaching.Educational and Psychological Measurement.2005,65:272-296;
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