随机效应模型简介ChenfengPPT学习教案

1、会计学1随机效应模型简介随机效应模型简介Chenfeng第1页/共110页配伍组配伍组A1A2A3A4B10.800.360.170.28B20.740.500.420.36B30.310.200.380.25B40.480.180.440.22B50.760.260.280.13例3.1(配伍组设计) 四种抗癌药物抑瘤效果的配伍组方差分析，测量值越大提示效果越好。第2页/共110页SourceDFSSMSF_ValuePModel 70.523170000.074738574.110.0157a 30.410840000.136946677.530.0043b 40.112330000.02

2、8082501.550.2514Error120.218110000.01817583Total190.74128000第3页/共110页配伍组配伍组A1A2A3A4MeanEffectB10.800.360.170.280.40 0.02B20.740.500.420.360.51 0.13B30.310.200.380.250.29-0.09B40.480.180.440.220.33-0.04B50.760.260.280.130.36 -0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.13第4页/共110页配伍组配伍组A1A2A3A

3、4MeanEffectB10.640.330.360.270.40 0.02B20.750.440.470.380.51 0.13B30.530.220.250.160.29-0.09B40.580.270.300.210.33-0.04B50.600.290.320.230.36 -0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.130.38+0.24+0.02第5页/共110页配伍组配伍组A1A2A3A4MeanEffectB10.160.03-0.190.010.40 0.02B2-0.010.07-0.05-0.020.51 0.1

4、3B3-0.22-0.010.130.090.29-0.09B4-0.09-0.070.150.020.33-0.04B50.16-0.02-0.04-0.100.36 -0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.13第6页/共110页20 (0,)ijiiijjjYaeeNb固定效应模型2012( (0,)0,)ijjjiiiYaeeNeeN随机效应模型第7页/共110页第8页/共110页第9页/共110页 (0,0.01818)ijiijijjYaeeNb固定效应模型 (0,0.01818)(0,0.002477)jijiijiY

5、aeNeeeN随机效应模型第10页/共110页第11页/共110页第12页/共110页xy xy5.863.265.3143.95.180.002.179.366.0319.51.937.135.7121.95.5952.54.9117.85.2950.65.535.21.9412.12.642.332.0315.72.946.535.9063.44.0722.74.9455.62.110.195.9181.22.171.485.5981.85.7748.95.5583.81.721.642.7352第13页/共110页尿中亚硝酸盐的浓度尿中亚硝酸盐的浓度胃液的胃液的pHpH值值 平均数随自变

6、量的增加而增加，方差也随自变量而增加第14页/共110页尿中亚硝酸盐的浓度尿中亚硝酸盐的浓度胃液的胃液的pHpH值值 第15页/共110页第16页/共110页第17页/共110页2 YYabXABX第18页/共110页ParameterEstimateErrorDFt ValuePr|t|beta0-12.94416.9609-1.860.1483beta110.30912.2486244.580.0001s20.000218s2z225.1143*随机系数模型随机系数模型proc mixed;class id ;model y = x /s; random x / subject = id;

7、run;第19页/共110页ParameterEstimateErrorDFt ValuePr|t|LowerUpperbeta0-12.59408.442025-1.490.1483-29.98054.7926beta110.21102.2161254.610.0001 5.646914.7750s20.7947148.50250.010.9958-305.05306.64s2z297.911638.3736252.550.017218.8797176.94*随机系数模型随机系数模型proc nlmixed data=ex_1 method=FIRO; parms beta0=-12 bet

8、a1= s2=200 s2z2=20; c2 = beta1 * x + z2 * sqrt(x); yhat = beta0 + c2;model y normal(yhat, s2); random z2 normal(0, s2z2) subject=ID; run;第20页/共110页第21页/共110页23Weight(g)Time(day)0 47 14 21354970100第22页/共110页1220 1exp()(0,)ijijjiKYbbtimeeNe1220211121322122232313132332 1 (exp( ()(0,)00 ,)0jijjjijijjjje

9、eKYbbtimeeNeMNeeee 第23页/共110页conctime02468101214161820222426024681012第24页/共110页23232212123202111222122 ()(0,)0,0bjjjjbijbetimeetimeijijjjbeeYDose eeeeeeNbMNbe 第25页/共110页proc nlmixed data=theoph; parms beta1=- beta2= beta3=- s2b1= cb12=0 s2b2= s2=; cl = exp(beta1 + b1); ka = exp(beta2 + b2); ke = exp

10、(beta3); pred = dose*ke*ka*(exp(-ke*time)-exp(-ka*time)/cl/(ka-ke); model conc normal(pred,s2); random b1 b2 normal(0,0,s2b1,cb12,s2b2) subject=subject; run;第26页/共110页第27页/共110页Subject specific effects of X on Pr(Death), OR = 20 per 1 unit increase in X Population average effect of X on Pr(Death), O

11、R = 2.7 per 1 unit increase in X 第28页/共110页第29页/共110页第30页/共110页32第31页/共110页33第32页/共110页3412个试验单元T1T2T3T4AXXXXBXXXXCXXXX第33页/共110页35完全随机区组设计n112个动物随机分配到12个试验单元T1T2T3T4A81311B2479C126105重复测量n13个动物随机分配到3个组T1T2T3T4A1111B2222C3333第34页/共110页36第35页/共110页37第36页/共110页38第37页/共110页39第38页/共110页1111R第39页/共110页12

12、12232334341001001001R第40页/共110页1001001001R第41页/共110页2322321111R第42页/共110页3121413221423132434341421111ttttttttttttttttttttttttR第43页/共110页1213141223241323341424341111R第44页/共110页10.20560.42120.42120.205610.42920.42920.42120.429210.56220.42120.42920.56221R12213323423241 111_11_ 2 FMCCFatherMotherRChildC

13、hild第45页/共110页22220000( )00Cov yI121 nnyyyY)1(1212111111 mnmnnmmxxxxxxX1)1(10 mm 121 nneeeE47第46页/共110页2111112113121121( )1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111Cov y22324313212mm48第47页/共110页120000( )00mCov yRRR第48页/共110页50第

14、49页/共110页51iNk第50页/共110页1/21/2iiiVARA()ijijh110, , niiiiiiiiDVEDEy第51页/共110页第52页/共110页-1 = (X X) X y111()XXVX =VyV111= (XX)XVVy第53页/共110页第54页/共110页56第55页/共110页第56页/共110页5820uexp()(1)1 exp()exp()(1)1 exp()jijijjjjaxP yeaxaxP yeaxrrr第57页/共110页591 1exp()ijijkijkijjjiyxxer20u1 1exp()ijijkijkijjjiyrxxe第5

15、8页/共110页第59页/共110页proc mixed data=ex_5_1 ;class id;model x = group /s;random intercept / subject = ID;run;proc genmod data=ex_5_1 ;class id;model x = group ;repeated subject = ID / type=CS CORRW V6CORR;run;第60页/共110页第61页/共110页第62页/共110页21221089.30950.7471256.9048*55.619089.30950.571589.309566.9524Co

16、rrICC第63页/共110页表 30名急性脑梗塞患者治疗不同时期神经系统体症总分idtreatage观察时间01234567810271071061061081081121121121122021107106106106106112112114116302110010010010610910811411611640361071061061071061111121171095017110111112112113113113116116602210510810810610810810810911070291021011041009410610610510680159797979999991011

17、011039021108108108110116116120128120100271081081081141161181181241281113498981021211201241241321401213710098114118126126134138138131311041231271291301301361401401412810812011511913412612612714015132106108108108112112112114116161181031021021041141141161281431711510110310410811311311812212618131919092

18、938995102105108191399494969911612413513814520134104104105105122128131129138212361071111121271271281381411412224510911412013013113213914214323240103103108112116118123125135242441101141201241331351421441442522295103115113119122126134136262259210211010811611611612212727232981061121121201241261361412823

19、81061211271261281301321381402922210211211011911912312513314230219109109124127128132133144147第64页/共110页yGraphs by grouptimegroup=080100120140160group=102468group=20246880100120140160第65页/共110页1223320 (0,)ijijjiYTimeGroupGroupeeN1221312203332 (0,)ijijijTime GroupTime GroupYTimeGroupGroupeNe12221312233

20、2013 (0,)(0,)ijiijjiiTime GroupTime GrYTimeGroupoupGroupeeeeNN第66页/共110页第67页/共110页第68页/共110页proc mixed;class id group;model y = time group time*group ; random intercept / subject = id;run;第69页/共110页71第70页/共110页72o 4水平：医院o 3水平：个体o 2水平：时期o 1水平：重复测量第71页/共110页73变量名含义取值缺失情况Vomit呕吐次数0,1,2缺20个数据ID患者1,2,112

21、无24和42号repeat重复测量次数1,2,12treat组别A1，B=0sequence顺序AB1，BA0period试验阶段第1阶段1，第2阶段2age年龄95号年龄缺失gender性别男1，女0height身高(m)weight体重(kg)BMI体质指数MBI体重(kg)/身高(m)2hospital医院编号1,2,5第72页/共110页74Poisson0123456()log()var(|)ijijijijjjjjijijijvomittreatsequenceperiodgenderagebmivomit 第73页/共110页75第74页/共110页76第75页/共110页770

22、12345600020021011log()( ,), var(|)ijjijjjjjjjjjuuujuuijijijtreatsequenceperiodgenderagebmiuuNuvomit0 22220(0,),2()uuutreatu treattreattreat第76页/共110页78第77页/共110页79效应参数系数(估计误差)模型A模型B模型C模型D固定效应 0(常数项)-0.42652(0.25229) -1.84120(1.42945) -1.31793(1.04845) -1.60242(1.39406) 1 (treat)-0.07071(0.06682) -0.

23、06607(0.07225) -0.06659(0.06666) -0.32444(0.16520) 2 (sequence)-0.20121(0.06789) -0.31956(0.40336) -0.05945(0.28112) -0.26090(0.40152) 3 (period)0.15327(0.06682)0.14863(0.07225)0.14916(0.06666)0.09386(0.16513) 4 (age)-0.01472(0.00251) -0.01990(0.01506) -0.01849(0.01066) -0.05045(0.01468) 5 (gender)0

24、.99880(0.07400)1.61931(0.40359)0.993230.28834)1.59512(0.39394) 6 (bmi)0.00577(0.00953)0.01851(0.05751)0.04955(0.04088)0.01477(0.05573)随机效应3水平0.06204(0.10277)0.01599(0.12841)2水平2.91438(0.52678)1.90950(0.28888)2.56729(0.51850)-0.13005(0.29402)1.19838(0.32152) 1水平 var(vomitij|ij)= ij111120u01u21u20v第78

25、页/共110页80第79页/共110页81第80页/共110页第81页/共110页指标变量变量取值医院编号hosp115患者编号no1456观察时间time13周组别group试验组1，对照组0患者年龄age1875岁患者性别gender女性0，男性1疗前ESS评分ess04080 (评分高病情轻)疗前ADL评分adl0095 (评分高病情轻)疗后ESS评分ess0100疗后ADL评分adl0100第82页/共110页医院编号患者编号组别 年龄性别疗前疗后1周疗后2周疗后3周ESS0 ADL0 ESS1 ADL1 ESS2 ADL2 ESS3 ADL311160069 50 73 50 86

26、90 85 10012043176 75 82 75 84 100 90 10013161140 30 42 35 55 35 72 4514171178 80 90 95 92 100 93 10015071172 75 75 75 82 82 16167180 80 93 85 100 95 第83页/共110页医院编号患者编号时间组别年龄性别疗前疗前疗后疗后ESS0 ADL0 ESS1 ADL111116006950501121600695086901131600695085100121043176758275122043176758410012304317675861611671808

27、09385162167180801009516316718080第84页/共110页(,)ijkYN XB 01 02345ijkijkjkjkjkjkijkYYagegendergrouptime00000ijkkjkijkvue200(0,)kvvN200(0,)jkuuN200(0,)ijkeeN第85页/共110页效应参数单因变量模型单因变量模型ESS(模型A)ADL(模型B)固定效应0 (常数项)20.017(4.270)15.271(5.983)1 (疗前观察值) 0.772(0.044) 0.770(0.044)2 (age)-0.123(0.049)-0.172(0.078)3

28、 (gender) 1.661(1.009) 2.905(1.592)4 (group) 4.189(1.111) 8.156(1.746)5 (time) 6.010(0.159)10.152(0.312)随机效应3水平 9.612(5.006) 34.820(16.617)2水平96.431(7.090)228.786(17.627)1水平21.521(1.042)83.361(4.036)-2loglikelihood8864.60210429.30020v20u20e第86页/共110页(1)96.4310.81796.431 21.521ID(1)9.6120.07549.612 9

29、6.431 21.521Hospital(2)228.7860.7329228.786 83.361ID(2)34.8200.100434.820 228.786 83.361Hospital第87页/共110页医院编号患者编号时间变量标识组别年龄性别疗前疗前疗后疗后111116006973111216005050112116006986112216005090113116006985113216005010012110431768212120431757512210431768412220431751001231043176901232043175100第88页/共110页医院编号Hosp患

30、者编号ID观察时间Time指标ID1常数项cons疗前年龄Age性别Gender组别Group时间Time结果Y 0(1) 0(2) 1(1) 1(2) 2(1) 2(2) 3(1) 3(2) 4(1) 4(2) 5(1) 5(2)111ESS1069060000101073111ADL0105006000010150112ESS1069060000102068112ADL0105006000010290113ESS1069060000103085113ADL01050060000103100121ESS1076043010001082121ADL0107504301000175122ESS1

31、076043010002084122ADL01075043010002100123ESS1076043010003090123ADL01075043010003100第89页/共110页(1)(2)(1)(2)(1)(2)(1)(2)0010102233(1)(2)(1)(2)4455 YESSADLageagegendergendergroupgrouptimetime(1)(1)(1)(1)(1)(1) 010 2345(2)(2)(2)(2)(2)(2)0102345jkljklijklijklijklijklijkljkljklijklijklijklijklijklESSESSage

32、gendergrouptimeADLADLagegendergrouptime第90页/共110页(1)(1)(1)(1)(1)(1) 010 2345(2)(2)(2)(2)(2)(2)0102345jkljklijklijklijklijklijkljkljklijklijklijklijklijklESSESSagegendergrouptimeADLADLagegendergrouptime(1)(1)(1)(1)(1)00000(2)(2)(2)(2)(2)00000jkllkljkljkllkljklfvufvu2(1)12(2)1220,flfflfMNf(1)21(2)2122

33、0,klvklvvvMNv(1)21(2)21220,jklujkluuuMNu第91页/共110页效应参数多因变量模型多因变量模型ESSADL固定效应0 (常数项)36.490(3.998)28.176(5.879)1 (疗前观察值)0.483(0.029)0.529(0.029)2 (age)-0.120(0.051)-0.220(0.080)3 (gender)2.120(1.049)3.694(1.837)4 (group)4.864(1.155)8.847(1.800)5 (time)6.012(0.159)10.137(0.312)随机效应3水平 2水平1水平21.534(1.043)29.690(1.771)83.393(4.036)u 105.335(7.692)145.159(11.327)245.609(18.757)v 15.095(7.195)23.956(11.287)38.156(18.110)f 第92页/共110页(1)105.3350.8303105.335 29.690ID(1)15.0950.106315.09