OPTIONS NOCENTER; FILENAME IN1 'C:\DATA\ROBIN2.dat'; DATA one; infile in1; INPUT id quit int time helmert1 helmert2 helmert3 h1time h2time h3time racew tv manual; /* categorical version of time */ timec = time+1; /* have time so that post-int = 0, 6 mo = 1, 12 mo = 2, 24 mo = 4 */ if time=3 then time=4; PROC GENMOD DESCENDING; CLASS id timec; MODEL quit = time time*time helmert1 helmert2 helmert3 racew / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=id / WITHIN=timec CORRW TYPE=UN; TITLE 'main effects model'; PROC GENMOD DESCENDING; CLASS id timec; MODEL quit = time time*time helmert1 helmert2 helmert3 racew helmert1*time helmert2*time helmert3*time / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=id / WITHIN=timec CORRW TYPE=UN; CONTRAST 'h1 at last timepoint' helmert1 1 helmert1*time 4 / WALD; CONTRAST 'h2 at last timepoint' helmert2 1 helmert2*time 4 / WALD; CONTRAST 'h3 at last timepoint' helmert3 1 helmert3*time 4 / WALD; CONTRAST 'group x time interaction' helmert1*time 1, helmert2*time 1, helmert3*time 1 / WALD; TITLE 'with linear time by treatment'; PROC GENMOD DESCENDING; CLASS id timec; MODEL quit = time time*time helmert1 helmert2 helmert3 racew helmert1*time helmert2*time helmert3*time helmert1*time*time helmert2*time*time helmert3*time*time / LINK=LOGIT DIST=BIN OBSTATS; REPEATED SUBJECT=id / WITHIN=timec CORRW TYPE=UN; CONTRAST 'h1 at last timepoint' helmert1 1 helmert1*time 4 helmert1*time*time 16 / WALD; CONTRAST 'h2 at last timepoint' helmert2 1 helmert2*time 4 helmert2*time*time 16 / WALD; CONTRAST 'h3 at last timepoint' helmert3 1 helmert3*time 4 helmert3*time*time 16 / WALD; CONTRAST 'quadratic group x time' helmert1*time*time 1, helmert2*time*time 1, helmert3*time*time 1 / WALD; CONTRAST 'lin & quad group x time' helmert1*time 1, helmert2*time 1, helmert3*time 1, helmert1*time*time 1, helmert2*time*time 1, helmert3*time*time 1/ WALD; ODS LISTING EXCLUDE OBSTATS; ODS OUTPUT OBSTATS=two; TITLE 'with quadratic and linear time by treatment'; RUN; DATA three; SET two; /* figure out the group of each subject */ IF helmert1 EQ -1 THEN group = 1; /* controls */ IF helmert2 EQ -1 THEN group = 2; /* no-shows */ IF helmert3 EQ -1 THEN group = 3; /* groups */ IF helmert3 EQ 1 THEN group = 4; /* enhanced */ PROC SORT; BY group time; PROC MEANS; VAR PRED; BY group time; RUN; main effects model The GENMOD Procedure Model Information Data Set WORK.ONE Distribution Binomial Link Function Logit Dependent Variable quit Observations Used 1744 Class Level Information Class Levels Values id 489 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 ... timec 4 1 2 3 4 Response Profile Ordered Total Value quit Frequency 1 1 383 2 0 1361 PROC GENMOD is modeling the probability that quit='1'. Parameter Information Parameter Effect Prm1 Intercept Prm2 time Prm3 time*time Prm4 helmert1 Prm5 helmert2 Prm6 helmert3 Prm7 racew Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1737 1776.6303 1.0228 Scaled Deviance 1737 1776.6303 1.0228 Pearson Chi-Square 1737 1754.0313 1.0098 Scaled Pearson X2 1737 1754.0313 1.0098 Log Likelihood -888.3151 Algorithm converged. Analysis Of Initial Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 -0.9832 0.1053 -1.1895 -0.7769 87.26 <.0001 time 1 -0.6746 0.1403 -0.9496 -0.3997 23.12 <.0001 time*time 1 0.1419 0.0338 0.0757 0.2080 17.65 <.0001 helmert1 1 0.4893 0.1214 0.2514 0.7272 16.25 <.0001 helmert2 1 0.2577 0.0906 0.0801 0.4353 8.08 0.0045 helmert3 1 0.1950 0.0886 0.0213 0.3687 4.84 0.0278 racew 1 0.4275 0.1404 0.1523 0.7026 9.27 0.0023 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. GEE Model Information Correlation Structure Unstructured Within-Subject Effect timec (4 levels) Subject Effect id (489 levels) Number of Clusters 489 Correlation Matrix Dimension 4 Maximum Cluster Size 4 Minimum Cluster Size 1 Algorithm converged. The GENMOD Procedure Working Correlation Matrix Col1 Col2 Col3 Col4 Row1 1.0000 0.2834 0.3173 0.2474 Row2 0.2834 1.0000 0.4410 0.2770 Row3 0.3173 0.4410 1.0000 0.5365 Row4 0.2474 0.2770 0.5365 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept -0.9990 0.1119 -1.2182 -0.7798 -8.93 <.0001 time -0.6330 0.1262 -0.8804 -0.3857 -5.02 <.0001 time*time 0.1317 0.0288 0.0752 0.1881 4.57 <.0001 helmert1 0.5826 0.1697 0.2500 0.9152 3.43 0.0006 helmert2 0.2881 0.1213 0.0503 0.5259 2.37 0.0176 helmert3 0.2019 0.1194 -0.0321 0.4359 1.69 0.0909 racew 0.3583 0.2003 -0.0343 0.7509 1.79 0.0736 with linear time by treatment . . . . . . . . . GEE Model Information Correlation Structure Unstructured Within-Subject Effect timec (4 levels) Subject Effect id (489 levels) Number of Clusters 489 Correlation Matrix Dimension 4 Maximum Cluster Size 4 Minimum Cluster Size 1 The GENMOD Procedure Working Correlation Matrix Col1 Col2 Col3 Col4 Row1 1.0000 0.2946 0.3304 0.2532 Row2 0.2946 1.0000 0.4489 0.2832 Row3 0.3304 0.4489 1.0000 0.5142 Row4 0.2532 0.2832 0.5142 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept -1.0149 0.1157 -1.2417 -0.7882 -8.77 <.0001 time -0.6190 0.1265 -0.8669 -0.3711 -4.89 <.0001 time*time 0.1321 0.0288 0.0757 0.1885 4.59 <.0001 helmert1 0.7653 0.2067 0.3601 1.1705 3.70 0.0002 helmert2 0.3338 0.1383 0.0627 0.6048 2.41 0.0158 helmert3 0.2694 0.1379 -0.0009 0.5396 1.95 0.0508 racew 0.3530 0.2004 -0.0398 0.7458 1.76 0.0782 time*helmert1 -0.1415 0.0715 -0.2816 -0.0014 -1.98 0.0478 time*helmert2 -0.0348 0.0509 -0.1345 0.0650 -0.68 0.4945 time*helmert3 -0.0501 0.0532 -0.1545 0.0542 -0.94 0.3463 Contrast Results for GEE Analysis Chi- Contrast DF Square Pr > ChiSq Type h1 at last timepoint 1 0.71 0.3989 Wald h2 at last timepoint 1 1.13 0.2883 Wald h3 at last timepoint 1 0.13 0.7143 Wald group x time interaction 3 5.30 0.1513 Wald with quadratic and linear time by treatment . . . . . . . . . . . GEE Model Information Correlation Structure Unstructured Within-Subject Effect timec (4 levels) Subject Effect id (489 levels) Number of Clusters 489 Correlation Matrix Dimension 4 Maximum Cluster Size 4 Minimum Cluster Size 1 Working Correlation Matrix Col1 Col2 Col3 Col4 Row1 1.0000 0.3005 0.3328 0.2586 Row2 0.3005 1.0000 0.4507 0.2893 Row3 0.3328 0.4507 1.0000 0.5154 Row4 0.2586 0.2893 0.5154 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept -1.0103 0.1172 -1.2401 -0.7805 -8.62 <.0001 time -0.6312 0.1310 -0.8879 -0.3745 -4.82 <.0001 time*time 0.1353 0.0297 0.0771 0.1936 4.55 <.0001 helmert1 0.8690 0.2262 0.4256 1.3124 3.84 0.0001 helmert2 0.4354 0.1514 0.1385 0.7322 2.87 0.0040 helmert3 0.2743 0.1493 -0.0182 0.5669 1.84 0.0661 racew 0.3544 0.2001 -0.0378 0.7466 1.77 0.0766 time*helmert1 -0.5085 0.2356 -0.9702 -0.0468 -2.16 0.0309 time*helmert2 -0.3892 0.1870 -0.7556 -0.0227 -2.08 0.0374 time*helmert3 -0.0506 0.1999 -0.4425 0.3412 -0.25 0.8000 time*time*helmert1 0.0870 0.0523 -0.0154 0.1894 1.66 0.0960 time*time*helmert2 0.0855 0.0425 0.0021 0.1689 2.01 0.0444 time*time*helmert3 0.0003 0.0462 -0.0902 0.0908 0.01 0.9948 Contrast Results for GEE Analysis Chi- Contrast DF Square Pr > ChiSq Type h1 at last timepoint 1 0.90 0.3419 Wald h2 at last timepoint 1 1.79 0.1814 Wald h3 at last timepoint 1 0.17 0.6832 Wald quadratic group x time 3 5.91 0.1158 Wald lin & quad group x time 6 10.98 0.0891 Wald group=1 time=0 The MEANS Procedure Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 109 0.1460541 0.0211692 0.1324699 0.1787410 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=1 time=1 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 97 0.1368347 0.0200095 0.1241541 0.1680833 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=1 time=2 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 92 0.1396916 0.0204312 0.1265954 0.1712195 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=1 time=4 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 77 0.1864522 0.0261974 0.1684060 0.2239885 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=2 time=0 The MEANS Procedure Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 190 0.2632623 0.0335116 0.2388780 0.3090752 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=2 time=1 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 175 0.2035154 0.0279471 0.1838947 0.2430949 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=2 time=2 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 161 0.1760424 0.0248779 0.1591555 0.2124650 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=2 time=4 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 139 0.1939786 0.0266439 0.1762110 0.2336458 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=3 time=0 The MEANS Procedure Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 86 0.3189928 0.0190312 0.3142921 0.3951453 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=3 time=1 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 82 0.1835201 0.0140373 0.1799650 0.2382695 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=3 time=2 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 80 0.1400144 0.0115775 0.1370438 0.1845727 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=3 time=4 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 70 0.2268783 0.0157381 0.2230316 0.2903485 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=4 time=0 The MEANS Procedure Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 104 0.4559720 0.0320141 0.4423869 0.5306898 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=4 time=1 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 100 0.2658838 0.0254576 0.2556638 0.3286637 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=4 time=2 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 96 0.1923095 0.0209868 0.1836831 0.2428355 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ group=4 time=4 Analysis Variable : Pred N Mean Std Dev Minimum Maximum ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ 86 0.2599217 0.0242537 0.2506874 0.3228827 ャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャャ