醫(yī)學(xué)]醫(yī)學(xué)統(tǒng)計(jì)學(xué)[2]

1、醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2第十章 方差分析（三）：重復(fù)測(cè)量資料的方差分析醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2第一節(jié) 重復(fù)測(cè)量資料的概念 對(duì)同一研究對(duì)象（如人、動(dòng)物、儀器等）的同一測(cè)量指標(biāo)在不同時(shí)間點(diǎn)的多次測(cè)量結(jié)果稱(chēng)為重復(fù)測(cè)量資料。醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 重復(fù)測(cè)量試驗(yàn)通常需要考慮處理的分組與重復(fù)測(cè)量的時(shí)間點(diǎn)兩個(gè)因素。 設(shè)計(jì)時(shí)一般應(yīng)遵循以下原則： 不同的受試對(duì)象按隨機(jī)化原則分配至各組； 研究中可設(shè)置兩個(gè)以上的處理分組，其中一個(gè)最好是平行對(duì)照組； 明確規(guī)定重復(fù)測(cè)量的時(shí)間點(diǎn)，每個(gè)受試對(duì)象按規(guī)定的時(shí)間點(diǎn)接受測(cè)試。醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2例 為研究某食物對(duì)血清膽固醇濃度的影響，各取7只兔子，分別以正常食物和待研究食物喂養(yǎng)，在實(shí)驗(yàn)前、喂養(yǎng)5星期、10

2、星期后，各取血測(cè)量其中膽固醇濃度，其自然對(duì)數(shù)轉(zhuǎn)換后的數(shù)據(jù)見(jiàn)下表。 表1 家兔血清膽固醇濃度（mmol/L）的自然對(duì)數(shù)家兔號(hào)1234567家兔號(hào)891011121314處理組對(duì)照組實(shí)驗(yàn)前0.7450.9040.3581.0780.5840.9851.0515周后2.0132.0541.1381.9491.6681.9261.639實(shí)驗(yàn)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

3、.0320.6130.7570.540醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2圖1 兩組家兔血清膽固醇的對(duì)數(shù)隨時(shí)間的變化醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2例 某藥物有新、舊兩種劑型。為比較這兩種劑型的代謝情況，對(duì)16例某病病人服藥后0、4、8、12小時(shí)的血藥濃度（mol/L）作了測(cè)量，結(jié)果見(jiàn)下表。 表2 4個(gè)時(shí)點(diǎn)的某藥新舊劑型血藥濃度（mol/L）編號(hào)1234567編號(hào)8910111213141516舊劑型新劑型4小時(shí)142.12163.17144.75126.33138.96126.33121.068小時(shí)65.5448.9586.0648.9570.0275.0178.950小時(shí)70.5368.4357.37105.8080.015

4、6.3253.6985.2766.3212小時(shí)73.2871.7780.0139.5460.8983.6670.244小時(shí)97.3895.2778.43120.54104.7575.27110.02110.01115.278小時(shí)112.12133.1783.16136.33114.7596.33138.96126.33129.060小時(shí)90.5388.43100.0146.3273.69105.2786.3212小時(shí)58.5056.9048.3484.0365.6147.5245.4469.4755.29醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2圖2 某藥新舊劑型血藥濃度隨時(shí)間的變化醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2重復(fù)測(cè)量數(shù)據(jù)統(tǒng)計(jì)分析

5、常見(jiàn)的誤用情況 1.忽略個(gè)體曲線變化特征； 2.重復(fù)進(jìn)行各時(shí)間點(diǎn)的t檢驗(yàn)；醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2圖3 各組家兔血清膽固醇濃度對(duì)數(shù)的均數(shù)與標(biāo)準(zhǔn)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.

6、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&CP Matrix TIME.N represents the con

7、trast between the 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 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2

8、 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 -0.049962 0.464888 0.514757 0.0001 0.8596 0.0808

9、 0.0496 TIME.2 -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 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2Test for Sphericity: Mauchlys Criterion = 0.1769156 Chisquare Appr

10、oximation = 21.506692 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 = Ano

11、va 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 0.03837936 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

12、 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 0.63813116 1.5595 4 11 0.2528 Pillais Trace 0.36186884 1.5595 4 11 0.2528 Hotelling-Lawley Trace

13、 0.56707596 1.5595 4 11 0.2528 Roys Greatest Root 0.56707596 1.5595 4 11 0.2528 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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 0.0645Erro

14、r 14 9163.54582000 654.53898714 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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 0.0001Sou

15、rce: TIME*TYPE Adj 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 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 Analysis of Variance Proc

16、edureLevel of -TIME1- -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 14.550423

17、6 2 8 58.4987500 8.4132131 52.2100000 14.4185951醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2第四節(jié) 趨勢(shì)分析醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2例10-3 趨勢(shì)比較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

18、.185 28.805 148.59 127.84 158.821 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醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2

19、2 5 1.150 27.850 127.230 135.830 119.3102 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

20、type;run;醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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 L

21、evel of TIME 1 2 3 4 5 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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

22、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 0.72610

23、0 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 -835.9073

24、34 2533.807437 1970.919422 TIME.4 1706.649023 -3671.618316 1970.919422 3784.378970 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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 T

25、IME.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.

26、0004 0.0107 0.0001 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2Test 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.

27、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 Tr

28、ace 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 0.6

29、3000835 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 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 Analysis of Variance Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects Effects

30、Source DF Anova SS Mean Square F Value Pr FTYPE 1 7662.82952000 7662.82952000 4.79 0.0460Error 14 22380.92114500 1598.63722464 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 Analysis of Variance Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject EffectsSource: TIME Adj Pr F DF Anova SS Mea

31、n Square F Value 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 Greenho

32、use-Geisser Epsilon = 0.6052 Huynh-Feldt Epsilon = 0.7930 醫(yī)學(xué)醫(yī)學(xué)統(tǒng)計(jì)學(xué)2 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 192219.85431391 192219.85