OPTIONS NOCENTER LINESIZE=81 PAGESIZE=66 FORMCHAR = "|----|+|---+="; FILENAME in1 'C:\longpsu\schizx1.dat'; DATA ONE; INFILE IN1 ; INPUT ID imps79 imps79b imps79o int tx week sweek txswk ; if imps79b = -9 then imps79b = .; PROC FORMAT; VALUE IMPS79B 0 = 'LE Mild' 1 = 'GE Moderate'; VALUE TX 0 = 'Placebo' 1 = 'Drug'; PROC FREQ; TABLES IMPS79B * WEEK; RUN; TITLE2 'GEE Logistic Regression Model: Exchangeable Structure'; PROC GENMOD DESCENDING; CLASS ID week; MODEL imps79b = tx sweek txswk / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=ID / WITHIN=week CORRW TYPE=EXCH; run; TITLE2 'GEE Logistic Regression Model: AR(1) Structure'; PROC GENMOD DESCENDING; CLASS ID week; MODEL imps79b = tx sweek txswk / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=ID / WITHIN=week CORRW TYPE=AR(1); run; TITLE2 'GEE Logistic Regression Model: Toeplitz (banded) Structure'; PROC GENMOD DESCENDING; CLASS ID week; MODEL imps79b = tx sweek txswk / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=ID / WITHIN=week CORRW TYPE=MDEP(6); run; TITLE2 'GEE Logistic Regression Model: Unstructured'; PROC GENMOD DESCENDING; CLASS ID week; MODEL imps79b = tx sweek txswk / LINK=LOGIT DIST=BIN; REPEATED SUBJECT=ID / WITHIN=week CORRW TYPE=UN; run; /* get correlations & sds of variables across time */ TITLE2 'Correlations & sds of IMPS79b across time'; data t0;set one; if week=0; imps79b0 = imps79b; run; data t1;set one; if week=1; imps79b1 = imps79b; run; data t2;set one; if week=2; imps79b2 = imps79b; run; data t3;set one; if week=3; imps79b3 = imps79b; run; data t4;set one; if week=4; imps79b4 = imps79b; run; data t5;set one; if week=5; imps79b5 = imps79b; run; data t6;set one; if week=6; imps79b6 = imps79b; run; data comp (keep=id imps79b0-imps79b6); merge t0 t1 t2 t3 t4 t5 t6; by id; PROC CORR ; VAR IMPS79B0-IMPS79B6; RUN; The FREQ Procedure Table of imps79b by week imps79b week Frequency| Percent | Row Pct | Col Pct | 0| 1| 2| 3| 4| 5| 6| Total ---------+--------+--------+--------+--------+--------+--------+--------+ 0 | 6 | 67 | 5 | 108 | 7 | 6 | 173 | 372 | 0.37 | 4.18 | 0.31 | 6.74 | 0.44 | 0.37 | 10.79 | 23.21 | 1.61 | 18.01 | 1.34 | 29.03 | 1.88 | 1.61 | 46.51 | | 1.38 | 15.73 | 35.71 | 28.88 | 63.64 | 66.67 | 51.64 | ---------+--------+--------+--------+--------+--------+--------+--------+ 1 | 428 | 359 | 9 | 266 | 4 | 3 | 162 | 1231 | 26.70 | 22.40 | 0.56 | 16.59 | 0.25 | 0.19 | 10.11 | 76.79 | 34.77 | 29.16 | 0.73 | 21.61 | 0.32 | 0.24 | 13.16 | | 98.62 | 84.27 | 64.29 | 71.12 | 36.36 | 33.33 | 48.36 | ---------+--------+--------+--------+--------+--------+--------+--------+ Total 434 426 14 374 11 9 335 1603 27.07 26.58 0.87 23.33 0.69 0.56 20.90 100.00 GEE Logistic Regression Model: Exchangeable Structure The GENMOD Procedure Model Information Data Set WORK.ONE Distribution Binomial Link Function Logit Dependent Variable imps79b Observations Used 1603 Probability Modeled Pr( imps79b = 1 ) Class Level Information Class Levels Values ID 437 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1118 1119 1124 1125 1129 1136 1140 1301 1302 1303 1304 1305 1306 1307 1308 1309 1311 1312 1313 1314 1315 1316 1317 1318 1321 1329 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 ... week 7 0 1 2 3 4 5 6 Response Profile Ordered Ordered Level Value Count 1 1 1231 2 0 372 Parameter Information Parameter Effect Prm1 Intercept Prm2 tx Prm3 sweek Prm4 txswk Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1599 1362.0638 0.8518 Scaled Deviance 1599 1362.0638 0.8518 Pearson Chi-Square 1599 1465.0251 0.9162 Scaled Pearson X2 1599 1465.0251 0.9162 Log Likelihood -681.0319 Algorithm converged. The GENMOD Procedure Analysis Of Initial Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 3.7027 0.4412 2.8379 4.5675 70.42 <.0001 tx 1 -0.4054 0.4832 -1.3525 0.5417 0.70 0.4015 sweek 1 -1.1126 0.2325 -1.5683 -0.6568 22.89 <.0001 txswk 1 -0.4180 0.2557 -0.9192 0.0833 2.67 0.1022 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. GEE Model Information Correlation Structure Exchangeable Within-Subject Effect week (7 levels) Subject Effect ID (437 levels) Number of Clusters 437 Correlation Matrix Dimension 7 Maximum Cluster Size 5 Minimum Cluster Size 2 Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Col5 Col6 Col7 Row1 1.0000 0.2025 0.2025 0.2025 0.2025 0.2025 0.2025 Row2 0.2025 1.0000 0.2025 0.2025 0.2025 0.2025 0.2025 Row3 0.2025 0.2025 1.0000 0.2025 0.2025 0.2025 0.2025 Row4 0.2025 0.2025 0.2025 1.0000 0.2025 0.2025 0.2025 Row5 0.2025 0.2025 0.2025 0.2025 1.0000 0.2025 0.2025 Row6 0.2025 0.2025 0.2025 0.2025 0.2025 1.0000 0.2025 Row7 0.2025 0.2025 0.2025 0.2025 0.2025 0.2025 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 3.6578 0.4853 2.7066 4.6090 7.54 <.0001 tx -0.3816 0.5209 -1.4026 0.6394 -0.73 0.4639 sweek -1.0923 0.2515 -1.5853 -0.5992 -4.34 <.0001 txswk -0.4511 0.2694 -0.9792 0.0770 -1.67 0.0941 GEE Logistic Regression Model: AR(1) Structure GEE Model Information Correlation Structure AR(1) Within-Subject Effect week (7 levels) Subject Effect ID (437 levels) Number of Clusters 437 Correlation Matrix Dimension 7 Maximum Cluster Size 5 Minimum Cluster Size 2 Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Col5 Col6 Col7 Row1 1.0000 0.1902 0.0362 0.0069 0.0013 0.0002 0.0000 Row2 0.1902 1.0000 0.1902 0.0362 0.0069 0.0013 0.0002 Row3 0.0362 0.1902 1.0000 0.1902 0.0362 0.0069 0.0013 Row4 0.0069 0.0362 0.1902 1.0000 0.1902 0.0362 0.0069 Row5 0.0013 0.0069 0.0362 0.1902 1.0000 0.1902 0.0362 Row6 0.0002 0.0013 0.0069 0.0362 0.1902 1.0000 0.1902 Row7 0.0000 0.0002 0.0013 0.0069 0.0362 0.1902 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 3.7241 0.4912 2.7613 4.6868 7.58 <.0001 tx -0.4161 0.5258 -1.4466 0.6144 -0.79 0.4287 sweek -1.1279 0.2515 -1.6209 -0.6350 -4.48 <.0001 txswk -0.4062 0.2692 -0.9339 0.1215 -1.51 0.1313 GEE Logistic Regression Model: Toeplitz (banded) Structure GEE Model Information Correlation Structure 6-Dependent Within-Subject Effect week (7 levels) Subject Effect ID (437 levels) Number of Clusters 437 Correlation Matrix Dimension 7 Maximum Cluster Size 5 Minimum Cluster Size 2 Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Col5 Col6 Col7 Row1 1.0000 0.1858 0.4617 0.2274 0.3062 0.1099 -0.0303 Row2 0.1858 1.0000 0.1858 0.4617 0.2274 0.3062 0.1099 Row3 0.4617 0.1858 1.0000 0.1858 0.4617 0.2274 0.3062 Row4 0.2274 0.4617 0.1858 1.0000 0.1858 0.4617 0.2274 Row5 0.3062 0.2274 0.4617 0.1858 1.0000 0.1858 0.4617 Row6 0.1099 0.3062 0.2274 0.4617 0.1858 1.0000 0.1858 Row7 -0.0303 0.1099 0.3062 0.2274 0.4617 0.1858 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 3.5160 0.4438 2.6462 4.3858 7.92 <.0001 tx -0.2063 0.4846 -1.1561 0.7436 -0.43 0.6704 sweek -1.0219 0.2316 -1.4758 -0.5679 -4.41 <.0001 txswk -0.5256 0.2527 -1.0210 -0.0303 -2.08 0.0376 GEE Logistic Regression Model: Unstructured GEE Model Information Correlation Structure Unstructured Within-Subject Effect week (7 levels) Subject Effect ID (437 levels) Number of Clusters 437 Correlation Matrix Dimension 7 Maximum Cluster Size 5 Minimum Cluster Size 2 Algorithm converged. Working Correlation Matrix Col1 Col2 Col3 Col4 Col5 Col6 Col7 Row1 1.0000 0.0655 -0.0369 0.0043 -0.0485 -0.0415 -0.0160 Row2 0.0655 1.0000 0.4943 0.2304 0.0495 0.4943 0.0554 Row3 -0.0369 0.4943 1.0000 -0.4943 0.0000 0.0000 -0.3140 Row4 0.0043 0.2304 -0.4943 1.0000 0.4943 0.2848 0.2309 Row5 -0.0485 0.0495 0.0000 0.4943 1.0000 0.4943 0.4943 Row6 -0.0415 0.4943 0.0000 0.2848 0.4943 1.0000 0.4037 Row7 -0.0160 0.0554 -0.3140 0.2309 0.4943 0.4037 1.0000 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 3.6317 0.4692 2.7121 4.5514 7.74 <.0001 tx -0.2733 0.5063 -1.2657 0.7192 -0.54 0.5894 sweek -1.0748 0.2424 -1.5498 -0.5998 -4.43 <.0001 txswk -0.4795 0.2617 -0.9924 0.0334 -1.83 0.0669 Correlations & sds of IMPS79b across time The CORR Procedure 7 Variables: imps79b0 imps79b1 imps79b2 imps79b3 imps79b4 imps79b5 imps79b6 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum imps79b0 434 0.98618 0.11690 428.00000 0 1.00000 imps79b1 426 0.84272 0.36449 359.00000 0 1.00000 imps79b2 14 0.64286 0.49725 9.00000 0 1.00000 imps79b3 374 0.71123 0.45380 266.00000 0 1.00000 imps79b4 11 0.36364 0.50452 4.00000 0 1.00000 imps79b5 9 0.33333 0.50000 3.00000 0 1.00000 imps79b6 335 0.48358 0.50048 162.00000 0 1.00000 Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations imps79b0 imps79b1 imps79b2 imps79b3 imps79b4 imps79b5 imps79b6 imps79b0 1.00000 0.16699 . 0.01192 . . -0.05016 0.0006 . 0.8190 . . 0.3623 434 423 14 371 11 9 332 imps79b1 0.16699 1.00000 0.82808 0.43524 0.23905 0.44721 0.13067 0.0006 0.0016 <.0001 0.4790 0.2666 0.0179 423 426 11 368 11 8 328 imps79b2 . 0.82808 1.00000 . . . 0.33333 . 0.0016 . . . 0.6667 14 11 14 1 0 0 4 imps79b3 0.01192 0.43524 . 1.00000 0.74536 0.60000 0.46669 0.8190 <.0001 . 0.0338 0.1158 <.0001 371 368 1 374 8 8 320 imps79b4 . 0.23905 . 0.74536 1.00000 . 1.00000 . 0.4790 . 0.0338 . <.0001 11 11 0 8 11 1 5 imps79b5 . 0.44721 . 0.60000 . 1.00000 . . 0.2666 . 0.1158 . . 9 8 0 8 1 9 1 imps79b6 -0.05016 0.13067 0.33333 0.46669 1.00000 . 1.00000 0.3623 0.0179 0.6667 <.0001 <.0001 . 332 328 4 320 5 1 335