医学]医学统计学 第10章.ppt

第十章 方差分析（三）： 重复测量资料的方差分析 第一节 重复测量资料的概念 对同一研究对象（如人、动物、仪器等 ）的同一测量指标在不同时间点的多次 测量结果称为重复测量资料。 重复测量试验通常需要考虑处理的分组与重复 测量的时间点两个因素。 设计时一般应遵循以下原则： 不同的受试对象按随机化原则分配至各组； 研究中可设置两个以上的处理分组，其中一 个最好是平行对照组； 明确规定重复测量的时间点，每个受试对象 按规定的时间点接受测试。 例 为研究某食物对血清胆固醇浓度的影响，各取7只兔子，分别 以正常食物和待研究食物喂养，在实验前、喂养5星期、10星期后 ，各取血测量其中胆固醇浓度，其自然对数转换后的数据见下表 。 表1 家兔血清胆固醇浓度（mmol/L）的自然对数 家兔 号 1 2 3 4 5 6 7 家兔 号 8 9 10 11 12 13 14 处理组对照组 实验前 0.745 0.904 0.358 1.078 0.584 0.985 1.051 5周后 2.013 2.054 1.138 1.949 1.668 1.926 1.639 实验前 0.376 0.995 0.599 0.720 0.157 0.861 0.872 10周后 2.621 1.628 2.197 2.239 0.985 2.916 1.226 5周后 0.668 0.584 0.956 1.354 0.246 0.883 0.555 10周后 0.570 0.461 0.599 1.032 0.613 0.757 0.540 图1 两组家兔血清胆固醇的对数随时间的变化 例 某药物有新、旧两种剂型。为比较这两种剂型的代谢情况，对 16例某病病人服药后0、4、8、12小时的血药浓度（mol/L）作了 测量，结果见下表。 表2 4个时点的某药新旧剂型血药浓度（mol/L） 编号 1 2 3 4 5 6 7 编号 8 9 10 11 12 13 14 15 16 旧剂型新剂型 4小时 142.12 163.17 144.75 126.33 138.96 126.33 121.06 8小时 65.54 48.95 86.06 48.95 70.02 75.01 78.95 0小时 70.53 68.43 57.37 105.80 80.01 56.32 53.69 85.27 66.32 12小时 73.28 71.77 80.01 39.54 60.89 83.66 70.24 4小时 97.38 95.27 78.43 120.54 104.75 75.27 110.02 110.01 115.27 8小时 112.12 133.17 83.16 136.33 114.75 96.33 138.96 126.33 129.06 0小时 90.53 88.43 100.01 46.32 73.69 105.27 86.32 12小时 58.50 56.90 48.34 84.03 65.61 47.52 45.44 69.47 55.29 图2 某药新旧剂型血药浓度随时间的变化 重复测量数据统计分析常见的误用情况 1.忽略个体曲线变化特征； 2.重复进行各时间点的t检验； 图3 各组家兔血清胆固醇浓度对数的均数与标准差 （*表示P |r| DF = 14 TIME1 TIME2 TIME3 TIME4 TIME5 TIME1 1.000000 0.229851 -0.299593 -0.228551 -0.326024 0.0001 0.4099 0.2780 0.4126 0.2357 TIME2 0.229851 1.000000 0.341167 0.421210 0.637466 0.4099 0.0001 0.2133 0.1179 0.0106 TIME3 -0.299593 0.341167 1.000000 0.506284 0.453232 0.2780 0.2133 0.0001 0.0541 0.0898 TIME4 -0.228551 0.421210 0.506284 1.000000 0.826936 0.4126 0.1179 0.0541 0.0001 0.0001 TIME5 -0.326024 0.637466 0.453232 0.826936 1.000000 0.2357 0.0106 0.0898 0.0001 0.0001 E = Error SS input type $ subj time1 time2 time3 time4 time5; cards; 1 1 4.865 32.170 110.52 102.72 94.37 1 2 2.750 28.185 130.77 142.27 117.40 1 3 3.980 15.695 87.53 120.10 101.15 1 4 1.185 10.510 91.75 149.15 136.85 1 5 1.185 28.805 148.59 127.84 158.82 1 6 3.250 19.290 105.53 149.72 136.50 1 7 4.170 70.220 234.10 199.83 190.60 1 8 0.900 3.600 91.20 159.75 134.09 2 1 7.330 21.830 77.880 101.120 83.890 2 2 0.420 12.920 78.800 98.050 76.630 2 3 0.340 9.010 81.900 126.160 117.400 2 4 1.070 8.120 83.870 136.420 121.080 2 5 1.150 27.850 127.230 135.830 119.310 2 6 3.085 16.010 71.650 99.050 101.200 2 7 1.225 27.880 112.100 116.600 128.900 2 8 0.790 22.790 74.300 100.500 137.260 ; proc anova data=samp10_3; class type; model time1 time2 time3 time4 time5=type/nouni; repeated time 5(1 2 3 4 5) polynomial/summary printe; means type; run; Analysis of Variance Procedure Class Level Information Class Levels Values TYPE 2 1 2 Number of observations in data set = 16 Analysis of Variance Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable TIME1 TIME2 TIME3 TIME4 TIME5 Level of TIME 1 2 3 4 5 Analysis of Variance Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix / Prob |r| DF = 14 TIME1 TIME2 TIME3 TIME4 TIME5 TIME1 1.000000 0.349618 0.065358 -0.229122 -0.350287 0.0001 0.2015 0.8170 0.4114 0.2006 TIME2 0.349618 1.000000 0.903208 0.359015 0.499624 0.2015 0.0001 0.0001 0.1888 0.0579 TIME3 0.065358 0.903208 1.000000 0.629656 0.672019 0.8170 0.0001 0.0001 0.0119 0.0061 TIME4 -0.229122 0.359015 0.629656 1.000000 0.726100 0.4114 0.1888 0.0119 0.0001 0.0022 TIME5 -0.350287 0.499624 0.672019 0.726100 1.000000 0.2006 0.0579 0.0061 0.0022 0.0001 E = Error SS&CP Matrix TIME.N represents the nth degree polynomial contrast for TIME TIME.1 TIME.2 TIME.3 TIME.4 TIME.1 6533.720660 -1298.188663 -563.290146 1706.649023 TIME.2 -1298.188663 5623.602757 -835.907334 -3671.618316 TIME.3 -563.290146 -835.907334 2533.807437 1970.919422 TIME.4 1706.649023 -3671.618316 1970.919422 3784.378970 Analysis of Variance Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix of the Variables Defined by the Specified Transformation / Prob |r| DF = 14 TIME.1 TIME.2 TIME.3 TIME.4 TIME.1 1.000000 -0.214166 -0.138441 0.343215 0.0001 0.4434 0.6227 0.2104 TIME.2 -0.214166 1.000000 -0.221444 -0.795890 0.4434 0.0001 0.4277 0.0004 TIME.3 -0.138441 -0.221444 1.000000 0.636480 0.6227 0.4277 0.0001 0.0107 TIME.4 0.343215 -0.795890 0.636480 1.000000 0.2104 0.0004 0.0107 0.0001 Test for Sphericity: Mauchlys Criterion = 0.0463618 Chisquare Approximation = 38.135046 with 9 df Prob Chisquare = 0.0000 Applied to Orthogonal Components: Test for Sphericity: Mauchlys Criterion = 0.0463618 Chisquare Approximation = 38.135046 with 9 df Prob Chisquare = 0.0000 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME Effect H = Anova SS&CP Matrix for TIME E = Error SS&CP Matrix S=1 M=1 N=4.5 Statistic Value F Num DF Den DF Pr F Wilks Lambda 0.02941195 90.7494 4 11 0.0001 Pillais Trace 0.97058805 90.7494 4 11 0.0001 Hotelling-Lawley Trace 32.99978789 90.7494 4 11 0.0001 Roys Greatest Root 32.99978789 90.7494 4 11 0.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME*TYPE Effect H = Anova SS&CP Matrix for TIME*TYPE E = Error SS&CP Matrix S=1 M=1 N=4.5 Statistic Value F Num DF Den DF Pr F Wilks Lambda 0.63000835 1.6150 4 11 0.2391 Pillais Trace 0.36999165 1.6150 4 11 0.2391 Hotelling-Lawley Trace 0.58728055 1.6150 4 11 0.2391 Roys Greatest Root 0.58728055 1.6150 4 11 0.2391 Analysis of Variance Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects Effects Source DF Anova SS Mean Square F Value Pr F TYPE 1 7662.82952000 7662.82952000 4.79 0.0460 Error 14 22380.92114500 1598.63722464 Analysis of Variance Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject Effects Source: TIME Adj Pr F DF Anova SS Mean Square F Value Pr F G - G H - F 4 227446.9038331 56861.7259583 172.35 0.0001 0.0001 0.0001 Source: TIME*TYPE Adj Pr F DF Anova SS Mean Square F Value Pr F G - G H - F 4 3567.7487331 891.9371833 2.70 0.0394 0.0718 0.0539 Source: Error(TIME) DF Anova SS Mean Square 56 18475.5098238 329.9198183 Greenhouse-Geisser Epsilon = 0.6052 Huynh-Feldt Epsilon = 0.7930 Analysis of Variance Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables TIME.N represents the nth degree polynomial contrast for TIME Contrast Variable: TIME.1 Source DF Anova SS Mean Square F Value Pr F MEAN 1 192219.85431391 192219.85431391 411.88 0.0001 TYPE 1 1755.98939391 1755.98939391 3.76 0.0728 Error 14 6533.72065969 466.69433283 Contrast Variable: TIME.2 Source DF Anova SS Mean Square F Value Pr F MEAN 1 15264.89835279 15264.89835279 38.00 0.0001 TYPE 1 1126.20593850 1126.20593850 2.80 0.1162 Error 14 5623.60275692 401.68591121 Contrast V