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1、第十章 方差分析（三）：重复测量资料的方差分析医学医学统计学1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。医学医学统计学1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。医学医学统计学1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
2、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1234567家兔号891011121314处理组对照组实验前0.7450.9040.3581.0780.5840.9851.0515周后2.0132.0541.1381.9491.6681.9261.639实验前0.3760.9950.5990.7200.1570.8610.87210周后2.6211.6282.1972.2390.9852.9161.2265周后0.6680.5840.9561.3540.2460.8830.55510周后0.5700.4610.5991.0320.6130.757
3、0.540医学医学统计学1图1 两组家兔血清胆固醇的对数随时间的变化医学医学统计学1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1234567编号8910111213141516旧剂型新剂型4小时142.12163.17144.75126.33138.96126.33121.068小时65.5448.9586.0648.9570.0275.0178.950小时70.5368.4357.37105.8080.0156.3253.6985.27
4、66.3212小时73.2871.7780.0139.5460.8983.6670.244小时97.3895.2778.43120.54104.7575.27110.02110.01115.278小时112.12133.1783.16136.33114.7596.33138.96126.33129.060小时90.5388.43100.0146.3273.69105.2786.3212小时58.5056.9048.3484.0365.6147.5245.4469.4755.29医学医学统计学1图2 某药新旧剂型血药浓度随时间的变化医学医学统计学1重复测量数据统计分析常见的误用情况1.忽略个体曲
5、线变化特征；2.重复进行各时间点的t检验；医学医学统计学1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
6、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&CP Matrix TIME.N represents the contrast between th
7、e nth level of TIME and the last TIME.1 TIME.2 TIME.3 TIME.4 TIME.1 3681.522100 -264.735800 1608.338100 953.425925 TIME.2 -264.735800 7626.346875 -171.707550 -811.039413 TIME.3 1608.338100 -171.707550 3251.096500 795.731175 TIME.4 953.425925 -811.039413 795.731175 931.841687 医学医学统计学1 Analysis of Var
8、iance 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 -0.049962 0.464888 0.514757 0.0001 0.8596 0.0808 0.0496 TIME.2 -
9、0.049962 1.000000 -0.034484 -0.304237 0.8596 0.0001 0.9029 0.2703 TIME.3 0.464888 -0.034484 1.000000 0.457173 0.0808 0.9029 0.0001 0.0867 TIME.4 0.514757 -0.304237 0.457173 1.000000 0.0496 0.2703 0.0867 0.0001 医学医学统计学1Test for Sphericity: Mauchlys Criterion = 0.1769156 Chisquare Approximation = 21.5
10、06692 with 9 df Prob Chisquare = 0.0106 Applied to Orthogonal Components: Test for Sphericity: Mauchlys Criterion = 0.1145431 Chisquare Approximation = 26.904488 with 9 df Prob Chisquare = 0.0015 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME Effect H = Anova SS&CP Matrix
11、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 0.03837936 68.9031 4 11 0.0001 Pillais Trace 0.96162064 68.9031 4 11 0.0001 Hotelling-Lawley Trace 25.05567469 68.9031 4 11 0.0001 Roys Greatest Root 25.05567469 68.9031 4 11 0.0001 Manova Test Criteria a
12、nd 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 0.63813116 1.5595 4 11 0.2528 Pillais Trace 0.36186884 1.5595 4 11 0.2528 Hotelling-Lawley Trace 0.56707596 1.55
13、95 4 11 0.2528 Roys Greatest Root 0.56707596 1.5595 4 11 0.2528 医学医学统计学1 Analysis of Variance Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects EffectsSource DF Anova SS Mean Square F Value Pr FTYPE 1 2635.80800000 2635.80800000 4.03 0.0645Error 14 9163.545820
14、00 654.53898714 医学医学统计学1 Analysis of Variance Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject EffectsSource: TIME Adj Pr F DF Anova SS Mean Square F Value Pr F G - G H - F 4 41880.78808000 10470.19702000 50.77 0.0001 0.0001 0.0001Source: TIME*TYPE A
15、dj Pr F DF Anova SS Mean Square F Value Pr F G - G H - F 4 951.18912500 237.79728125 1.15 0.3413 0.3312 0.3366Source: Error(TIME) DF Anova SS Mean Square 56 11548.64075500 206.22572777 Greenhouse-Geisser Epsilon = 0.5172 Huynh-Feldt Epsilon = 0.6517 医学医学统计学1 Analysis of Variance ProcedureLevel of -T
16、IME1- -TIME2- -TIME3-TYPE N Mean SD Mean SD Mean SD1 8 5.57125000 3.07648425 46.5475000 39.0852408 78.4512500 15.12015732 8 3.85250000 4.68717018 32.7487500 15.5025947 55.7175000 14.1827931 Level of -TIME4- -TIME5- TYPE N Mean SD Mean SD 1 8 69.3437500 15.4693032 60.5137500 14.5504236 2 8 58.4987500
17、 8.4132131 52.2100000 14.4185951医学医学统计学1第四节 趋势分析医学医学统计学1例10-3 趋势比较data samp10_3;input type $ subj time1 time2 time3 time4 time5;cards;1 1 4.865 32.170 110.52 102.72 94.371 2 2.750 28.185 130.77 142.27 117.401 3 3.980 15.695 87.53 120.10 101.151 4 1.185 10.510 91.75 149.15 136.851 5 1.185 28.805 148.
18、59 127.84 158.821 6 3.250 19.290 105.53 149.72 136.501 7 4.170 70.220 234.10 199.83 190.601 8 0.900 3.600 91.20 159.75 134.092 1 7.330 21.830 77.880 101.120 83.8902 2 0.420 12.920 78.800 98.050 76.6302 3 0.340 9.010 81.900 126.160 117.4002 4 1.070 8.120 83.870 136.420 121.080医学医学统计学12 5 1.150 27.850
19、 127.230 135.830 119.3102 6 3.085 16.010 71.650 99.050 101.2002 7 1.225 27.880 112.100 116.600 128.9002 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;医学医学统计学
20、1 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
21、 3 4 5 医学医学统计学1 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
22、.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 0.200
23、6 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 1
24、970.919422 TIME.4 1706.649023 -3671.618316 1970.919422 3784.378970 医学医学统计学1 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 TIM
25、E.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 0.00
26、01 医学医学统计学1Test 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
27、 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
28、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
29、 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 医学医学统计学1 Analysis of Variance Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects EffectsSource DF Anova
30、SS Mean Square F Value Pr FTYPE 1 7662.82952000 7662.82952000 4.79 0.0460Error 14 22380.92114500 1598.63722464 医学医学统计学1 Analysis of Variance Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject EffectsSource: TIME Adj Pr F DF Anova SS Mean Square F Value
31、 Pr F G - G H - F 4 227446.9038331 56861.7259583 172.35 0.0001 0.0001 0.0001Source: 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 0.0539Source: Error(TIME) DF Anova SS Mean Square 56 18475.5098238 329.9198183 Greenhouse-Geisser Epsi
32、lon = 0.6052 Huynh-Feldt Epsilon = 0.7930 医学医学统计学1 Analysis of Variance Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables TIME.N represents the nth degree polynomial contrast for TIMEContrast Variable: TIME.1Source DF Anova SS Mean Square F Value Pr FMEAN 1
33、192219.85431391 192219.85431391 411.88 0.0001TYPE 1 1755.98939391 1755.98939391 3.76 0.0728Error 14 6533.72065969 466.69433283Contrast Variable: TIME.2Source DF Anova SS Mean Square F Value Pr FMEAN 1 15264.89835279 15264.89835279 38.00 0.0001TYPE 1 1126.20593850 1126.20593850 2.80 0.1162Error 14 56
34、23.60275692 401.68591121Contrast Variable: TIME.3Source DF Anova SS Mean Square F Value Pr FMEAN 1 14113.07664391 14113.07664391 77.98 0.0001TYPE 1 189.08365141 189.08365141 1.04 0.3241Error 14 2533.80743719 180.98624551Contrast Variable: TIME.4Source DF Anova SS Mean Square F Value Pr FMEAN 1 5849.
35、07452252 5849.07452252 21.64 0.0004TYPE 1 496.46974931 496.46974931 1.84 0.1968Error 14 3784.37896996 270.31278357 医学医学统计学1 Analysis of Variance ProcedureLevel of -TIME1- -TIME2- -TIME3-TYPE N Mean SD Mean SD Mean SD1 8 2.78562500 1.53824213 26.0593750 20.3505303 124.998750 48.89251432 8 1.92625000 2.34358509 18.3012500 7.9257707 88.466250 20.0513540 Level of -TIME4- -TIME5- TYPE N Mean SD Mean SD 1 8 143.922500 29.1881364 133.722500 31.0726714 2 8 114.216250 16.7310925 110.708750 21.4916279医学医学统计学1
