1 * example.sas 2 * xref: 3 * input: blex.sas 4 * output: 5 * does - Example how to use GEE macro. 6 - The data step generates data at random. Its details 7 are not important. What matters is that it generates 8 variables:y, id, x1-x5. 9 - Notice that x2-x3 are cluster-level covariates, while 10 x4-x5 are observation-level covariates, x1=intercept. 11 ***************************************************; 12 filename BLEX "blex.sas"; 13 %include BLEX; 652 * options mprint; 653 ***************************************************; 654 data A; * generate a dataset; 655 k = 20; * # clusters; 656 n = 5 ; * cluster size; 657 beta1 = 1; * parameter values; 658 beta2 =-1; 659 beta3 = 0; 660 beta4 =-1; 661 beta5 = 1; 662 sigma = 2; 663 seed = 2141994; 664 retain x1 1 zero 0; 665 array x (*) x1-x5; 666 array beta (*) beta1-beta5; 667 do id = 1 to k; * one cluster; 668 e = rannor(seed); 669 x2 = rannor(seed); 2 The SAS System 18:39 Tuesday, August 17, 2004 670 x3 = rannor(seed); 671 do j = 1 to n; * one obs.; 672 x4 = rannor(seed); 673 x5 = rannor(seed); 674 lp = e * sigma; * linear predictor; 675 do l=1 to dim(beta); 676 lp=lp+x(l)*beta(l); 677 end; 678 p = 1/(1+exp(-lp)); 679 y = (ranuni(seed) <= p); 680 output; 681 end; * one obs.; 682 end; * one cluster; 683 keep id y x1 - x5 zero; 684 run; NOTE: The data set WORK.A has 100 observations and 8 variables. NOTE: DATA statement used: real time 0.12 seconds cpu time 0.01 seconds 685 ***************************************************; 686 title2 "A minimal run"; 687 %gee ( 688 data=A, /* required: dataset name */ 689 yvar=y, /* required: response 0/1 */ 690 xvar=x1 x2 x3 x4 x5, /* required: covariates */ 691 id=id ); /* required: cluster id */ NOTE: There were 100 observations read from the data set WORK.A. NOTE: The data set WORK.A has 100 observations and 8 variables. NOTE: PROCEDURE SORT used: real time 0.07 seconds cpu time 0.01 seconds NOTE: There were 100 observations read from the data set WORK.A. NOTE: The data set WORK._N_ has 20 observations and 1 variables. NOTE: PROCEDURE SUMMARY used: real time 0.19 seconds cpu time 0.01 seconds NOTE: IML Ready NOTE: Module SIGNON defined. NOTE: Module INFO defined. NOTE: Module PSDINV defined. NOTE: Module GET1C defined. NOTE: Module ACC1C defined. NOTE: Module CHK1 defined. NOTE: Module ADJUST defined. NOTE: Module UPDATE defined. NOTE: Module RHORANGE defined. NOTE: Module GEE4 defined. NOTE: Module GEE3 defined. NOTE: Module GEE2 defined. 3 The SAS System 18:39 Tuesday, August 17, 2004 NOTE: Module GEE1 defined. NOTE: Module GEE defined. NOTE: Module INITBETA defined. NOTE: Module GETDATA defined. NOTE: Module RESULTS1 defined. NOTE: Module RESULTS defined. 692 ***************************************************; 693 title2 "Test output datasets"; 694 %gee ( 695 data=A, /* required: dataset name */ 696 yvar=y, /* required: response 0/1 */ 697 xvar=x1 x2 x3 x4 x5, /* required: covariates */ 698 id=id, /* required: cluster id */ 699 outest=EST, /* optional: estimates dataset */ 700 outs=RES); /* optional: residuals dataset */ NOTE: Exiting IML. NOTE: The PROCEDURE IML printed pages 1-2. NOTE: PROCEDURE IML used: real time 0.47 seconds cpu time 0.17 seconds NOTE: Input data set is already sorted, no sorting done. NOTE: PROCEDURE SORT used: real time 0.00 seconds cpu time 0.01 seconds NOTE: There were 100 observations read from the data set WORK.A. NOTE: The data set WORK._N_ has 20 observations and 1 variables. NOTE: PROCEDURE SUMMARY used: real time 0.07 seconds cpu time 0.01 seconds NOTE: IML Ready NOTE: Module SIGNON defined. NOTE: Module INFO defined. NOTE: Module PSDINV defined. NOTE: Module GET1C defined. NOTE: Module ACC1C defined. NOTE: Module CHK1 defined. NOTE: Module ADJUST defined. NOTE: Module UPDATE defined. NOTE: Module RHORANGE defined. NOTE: Module GEE4 defined. NOTE: Module GEE3 defined. NOTE: Module GEE2 defined. NOTE: Module GEE1 defined. NOTE: Module GEE defined. NOTE: Module INITBETA defined. NOTE: Module GETDATA defined. NOTE: Module RESULTS1 defined. NOTE: Module DATAOUT1 defined. NOTE: Module DATAOUT defined. NOTE: Module RESULTS defined. 4 The SAS System 18:39 Tuesday, August 17, 2004 NOTE: The data set WORK.RES has 100 observations and 10 variables. NOTE: The data set WORK._DS1_ has 11 observations and 3 variables. NOTE: The data set WORK._DS2_ has 11 observations and 6 variables. NOTE: Exiting IML. NOTE: The PROCEDURE IML printed pages 3-4. NOTE: PROCEDURE IML used: real time 0.49 seconds cpu time 0.10 seconds NOTE: There were 11 observations read from the data set WORK._DS1_. NOTE: There were 11 observations read from the data set WORK._DS2_. NOTE: The data set WORK.EST has 11 observations and 9 variables. NOTE: DATA statement used: real time 0.06 seconds cpu time 0.01 seconds 701 ***************************************************; 702 proc contents data=EST; 703 title2 "Estimates of parameters and covariance matrices"; 704 run; NOTE: PROCEDURE CONTENTS used: real time 0.07 seconds cpu time 0.01 seconds NOTE: The PROCEDURE CONTENTS printed page 5. 705 ***************************************************; 706 proc print data=EST; 707 run; NOTE: There were 11 observations read from the data set WORK.EST. NOTE: The PROCEDURE PRINT printed page 6. NOTE: PROCEDURE PRINT used: real time 0.01 seconds cpu time 0.00 seconds 708 ***************************************************; 709 proc contents data=RES; 710 title2 "Fitted values and residuals"; 711 run; NOTE: PROCEDURE CONTENTS used: real time 0.02 seconds cpu time 0.01 seconds NOTE: The PROCEDURE CONTENTS printed page 7. 712 ***************************************************; 713 proc print data=RES; 714 run; NOTE: There were 100 observations read from the data set WORK.RES. NOTE: The PROCEDURE PRINT printed pages 8-9. 5 The SAS System 18:39 Tuesday, August 17, 2004 NOTE: PROCEDURE PRINT used: real time 0.00 seconds cpu time 0.00 seconds 715 ***************************************************; 716 title2 "Test the offset option"; 717 %gee ( 718 data=A, /* required: dataset name */ 719 yvar=y, /* required: response 0/1 */ 720 xvar=x1 x2 x3 x4 x5, /* required: covariates */ 721 id=id, /* required: cluster id */ 722 offset=zero); /* optional: offset */ NOTE: Input data set is already sorted, no sorting done. NOTE: PROCEDURE SORT used: real time 0.00 seconds cpu time 0.01 seconds NOTE: There were 100 observations read from the data set WORK.A. NOTE: The data set WORK._N_ has 20 observations and 1 variables. NOTE: PROCEDURE SUMMARY used: real time 0.05 seconds cpu time 0.00 seconds NOTE: IML Ready NOTE: Module SIGNON defined. NOTE: Module INFO defined. NOTE: Module PSDINV defined. NOTE: Module GET1C defined. NOTE: Module ACC1C defined. NOTE: Module CHK1 defined. NOTE: Module ADJUST defined. NOTE: Module UPDATE defined. NOTE: Module RHORANGE defined. NOTE: Module GEE4 defined. NOTE: Module GEE3 defined. NOTE: Module GEE2 defined. NOTE: Module GEE1 defined. NOTE: Module GEE defined. NOTE: Module INITBETA defined. NOTE: Module GETDATA defined. NOTE: Module RESULTS1 defined. NOTE: Module RESULTS defined. NOTE: Exiting IML. NOTE: The PROCEDURE IML printed pages 10-11. NOTE: PROCEDURE IML used: real time 0.46 seconds cpu time 0.10 seconds NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414 NOTE: The SAS System used: real time 3.06 seconds cpu time 0.58 seconds 6 The SAS System 18:39 Tuesday, August 17, 2004 18:39 Tuesday, August 17, 2004 1 A minimal run Generalized estimating equations for exchangeably- correlated binary responses (version 2.3) (c) Bahjat Qaqish and Habib Moalem (1994, 1995) Department of Biostatistics CB 7400 Chapel Hill, NC 27599-7400 Data set: A Response: y Covariates: x1 x2 x3 x4 x5 Cluster ID: id Number of observations: 100 Number of covariates: 5 Number of clusters: 20 Cluster sizes: from 5 to 5 Iteration 2 rho = 0.3339094 is above the valid range and will be set to 0.3088038 Iteration 3 rho = 0.4568218 is above the valid range and will be set to 0.2080706 Iteration 4 rho = 0.4616948 is above the valid range and will be set to 0.185679 Iteration 5 rho = 0.4488915 is above the valid range and will be set to 0.1855632 Iteration 6 rho = 0.4453438 is above the valid range and will be set to 0.1861348 Iteration 7 rho = 0.445268 is above the valid range and will be set to 0.1861243 Iteration 8 18:39 Tuesday, August 17, 2004 2 A minimal run rho = 0.4453592 is above the valid range and will be set to 0.1861036 Converged, niter = 8 Number of estimable parameters = 5 Estimated intra-cluster correlation = 0.1861036 Summary of estimates and 0.95 confidence intervals: Results using the robust variance estimator: Estimate Robust SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.327519 0.9134833 0.3609884 1.3487566 0.7098211 2.5628211 X2 -0.494738 0.3524411 -1.403747 0.1603943 0.6097306 0.3055903 1.2165682 X3 -0.775563 0.3726747 -2.081073 0.0374272 0.4604443 0.2217971 0.9558691 X4 -0.224888 0.1469881 -1.529977 0.1260225 0.7986053 0.5987088 1.0652431 X5 0.7701157 0.3012279 2.5565882 0.0105704 2.1600161 1.196882 3.8981868 Results using the naive variance estimator: Estimate Naive SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.3303719 0.9055951 0.3651502 1.3487566 0.7058632 2.5771913 X2 -0.494738 0.2887179 -1.713569 0.0866079 0.6097306 0.3462429 1.0737301 X3 -0.775563 0.364515 -2.127658 0.0333654 0.4604443 0.2253727 0.9407037 X4 -0.224888 0.2212158 -1.016602 0.3093427 0.7986053 0.5176461 1.2320587 X5 0.7701157 0.2656079 2.8994455 0.0037382 2.1600161 1.2834269 3.6353218 18:39 Tuesday, August 17, 2004 3 Test output datasets Generalized estimating equations for exchangeably- correlated binary responses (version 2.3) (c) Bahjat Qaqish and Habib Moalem (1994, 1995) Department of Biostatistics CB 7400 Chapel Hill, NC 27599-7400 Data set: A Response: y Covariates: x1 x2 x3 x4 x5 Cluster ID: id Number of observations: 100 Number of covariates: 5 Number of clusters: 20 Cluster sizes: from 5 to 5 Iteration 2 rho = 0.3339094 is above the valid range and will be set to 0.3088038 Iteration 3 rho = 0.4568218 is above the valid range and will be set to 0.2080706 Iteration 4 rho = 0.4616948 is above the valid range and will be set to 0.185679 Iteration 5 rho = 0.4488915 is above the valid range and will be set to 0.1855632 Iteration 6 rho = 0.4453438 is above the valid range and will be set to 0.1861348 Iteration 7 rho = 0.445268 is above the valid range and will be set to 0.1861243 Iteration 8 18:39 Tuesday, August 17, 2004 4 Test output datasets rho = 0.4453592 is above the valid range and will be set to 0.1861036 Converged, niter = 8 Number of estimable parameters = 5 Estimated intra-cluster correlation = 0.1861036 Summary of estimates and 0.95 confidence intervals: Results using the robust variance estimator: Estimate Robust SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.327519 0.9134833 0.3609884 1.3487566 0.7098211 2.5628211 X2 -0.494738 0.3524411 -1.403747 0.1603943 0.6097306 0.3055903 1.2165682 X3 -0.775563 0.3726747 -2.081073 0.0374272 0.4604443 0.2217971 0.9558691 X4 -0.224888 0.1469881 -1.529977 0.1260225 0.7986053 0.5987088 1.0652431 X5 0.7701157 0.3012279 2.5565882 0.0105704 2.1600161 1.196882 3.8981868 Results using the naive variance estimator: Estimate Naive SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.3303719 0.9055951 0.3651502 1.3487566 0.7058632 2.5771913 X2 -0.494738 0.2887179 -1.713569 0.0866079 0.6097306 0.3462429 1.0737301 X3 -0.775563 0.364515 -2.127658 0.0333654 0.4604443 0.2253727 0.9407037 X4 -0.224888 0.2212158 -1.016602 0.3093427 0.7986053 0.5176461 1.2320587 X5 0.7701157 0.2656079 2.8994455 0.0037382 2.1600161 1.2834269 3.6353218 18:39 Tuesday, August 17, 2004 5 Estimates of parameters and covariance matrices The CONTENTS Procedure Data Set Name: WORK.EST Observations: 11 Member Type: DATA Variables: 9 Engine: V8 Indexes: 0 Created: 18:39 Tuesday, August 17, 2004 Observation Length: 72 Last Modified: 18:39 Tuesday, August 17, 2004 Deleted Observations: 0 Protection: Compressed: NO Data Set Type: Sorted: NO Label: -----Engine/Host Dependent Information----- Data Set Page Size: 8192 Number of Data Set Pages: 1 First Data Page: 1 Max Obs per Page: 113 Obs in First Data Page: 11 Number of Data Set Repairs: 0 File Name: /usr/tmp/SAS_work808300002F82_amber/est.sas7bdat Release Created: 8.0202M0 Host Created: SunOS Inode Number: 417518 Access Permission: rw-r--r-- Owner Name: qaqish File Size (bytes): 16384 -----Alphabetic List of Variables and Attributes----- # Variable Type Len Pos ----------------------------------- 4 X1 Num 8 0 5 X2 Num 8 8 6 X3 Num 8 16 7 X4 Num 8 24 8 X5 Num 8 32 3 _DEPVAR_ Char 8 64 2 _NAME_ Char 8 56 9 _RHO_ Num 8 40 1 _TYPE_ Char 8 48 18:39 Tuesday, August 17, 2004 6 Estimates of parameters and covariance matrices Obs _TYPE_ _NAME_ _DEPVAR_ X1 X2 X3 X4 X5 _RHO_ 1 PARMS Y 0.29918 -0.49474 -0.77556 -0.22489 0.77012 0.18610 2 NCOV X1 Y 0.10915 0.00740 0.03822 -0.00128 0.00421 0.18610 3 NCOV X2 Y 0.00740 0.08336 0.01494 -0.00347 -0.01372 0.18610 4 NCOV X3 Y 0.03822 0.01494 0.13287 0.00692 -0.01543 0.18610 5 NCOV X4 Y -0.00128 -0.00347 0.00692 0.04894 -0.00995 0.18610 6 NCOV X5 Y 0.00421 -0.01372 -0.01543 -0.00995 0.07055 0.18610 7 RCOV X1 Y 0.10727 -0.03050 -0.02364 -0.00009 0.03303 0.18610 8 RCOV X2 Y -0.03050 0.12421 0.06267 -0.00058 -0.03181 0.18610 9 RCOV X3 Y -0.02364 0.06267 0.13889 0.00904 -0.02873 0.18610 10 RCOV X4 Y -0.00009 -0.00058 0.00904 0.02161 -0.00729 0.18610 11 RCOV X5 Y 0.03303 -0.03181 -0.02873 -0.00729 0.09074 0.18610 18:39 Tuesday, August 17, 2004 7 Fitted values and residuals The CONTENTS Procedure Data Set Name: WORK.RES Observations: 100 Member Type: DATA Variables: 10 Engine: V8 Indexes: 0 Created: 18:39 Tuesday, August 17, 2004 Observation Length: 80 Last Modified: 18:39 Tuesday, August 17, 2004 Deleted Observations: 0 Protection: Compressed: NO Data Set Type: Sorted: NO Label: -----Engine/Host Dependent Information----- Data Set Page Size: 8192 Number of Data Set Pages: 2 First Data Page: 1 Max Obs per Page: 101 Obs in First Data Page: 77 Number of Data Set Repairs: 0 File Name: /usr/tmp/SAS_work808300002F82_amber/res.sas7bdat Release Created: 8.0202M0 Host Created: SunOS Inode Number: 417512 Access Permission: rw-r--r-- Owner Name: qaqish File Size (bytes): 24576 -----Alphabetic List of Variables and Attributes----- # Variable Type Len Pos ------------------------------------ 1 ID Num 8 0 3 Predict Num 8 16 4 Residual Num 8 24 5 StdResid Num 8 32 6 X1 Num 8 40 7 X2 Num 8 48 8 X3 Num 8 56 9 X4 Num 8 64 10 X5 Num 8 72 2 Y Num 8 8 18:39 Tuesday, August 17, 2004 8 Fitted values and residuals Obs ID Y Predict Residual StdResid X1 X2 X3 X4 X5 1 1 1 0.86462 0.13538 0.39569 1 -0.89090 -0.19936 -2.00048 0.66195 2 1 1 0.73369 0.26631 0.60247 1 -0.89090 -0.19936 -1.15315 -0.18240 3 1 1 0.68372 0.31628 0.68013 1 -0.89090 -0.19936 0.43625 -0.03313 4 1 1 0.81897 0.18103 0.47016 1 -0.89090 -0.19936 -0.74902 0.57960 5 1 1 0.47895 0.52105 1.04302 1 -0.89090 -0.19936 -0.49235 -1.41475 6 2 1 0.82326 0.17674 0.46333 1 0.87767 -1.04240 1.10918 1.44739 7 2 1 0.65335 0.34665 0.72841 1 0.87767 -1.04240 1.30975 0.33102 8 2 1 0.41960 0.58040 1.17609 1 0.87767 -1.04240 0.87813 -1.03923 9 2 1 0.63203 0.36797 0.76302 1 0.87767 -1.04240 -0.44883 -0.30308 10 2 1 0.56056 0.43944 0.88539 1 0.87767 -1.04240 0.54582 -0.39891 11 3 1 0.83220 0.16780 0.44904 1 -0.74372 -0.15954 -1.01023 0.75734 12 3 1 0.54736 0.45264 0.90938 1 -0.74372 -0.15954 -0.70260 -0.98540 13 3 1 0.54067 0.45933 0.92172 1 -0.74372 -0.15954 0.38757 -0.70205 14 3 0 0.45580 -0.45580 -0.91518 1 -0.74372 -0.15954 -1.15855 -1.59544 15 3 0 0.38497 -0.38497 -0.79115 1 -0.74372 -0.15954 0.85298 -1.38623 16 4 1 0.97962 0.02038 0.14423 1 -2.47552 -2.70254 0.97634 0.61338 17 4 1 0.97249 0.02751 0.16819 1 -2.47552 -2.70254 0.22180 -0.00614 18 4 1 0.88317 0.11683 0.36371 1 -2.47552 -2.70254 -0.14212 -2.11537 19 4 1 0.98719 0.01281 0.11391 1 -2.47552 -2.70254 -0.58635 0.76998 20 4 1 0.97744 0.02256 0.15191 1 -2.47552 -2.70254 -0.49240 0.04976 21 5 1 0.56183 0.43817 0.88312 1 0.69555 -1.23948 -1.25310 -1.23305 22 5 1 0.86944 0.13056 0.38751 1 0.69555 -1.23948 -0.39674 1.15624 23 5 1 0.73031 0.26969 0.60768 1 0.69555 -1.23948 -0.08825 0.07792 24 5 1 0.61408 0.38592 0.79274 1 0.69555 -1.23948 -0.04836 -0.60085 25 5 0 0.59047 -0.59047 -1.20075 1 0.69555 -1.23948 -0.25673 -0.78975 26 6 0 0.65756 -0.65756 -1.38572 1 0.01792 0.22118 -2.21470 0.04624 27 6 1 0.49587 0.50413 1.00830 1 0.01792 0.22118 -1.39793 -0.58392 28 6 0 0.58134 -0.58134 -1.17837 1 0.01792 0.22118 -0.66297 0.07841 29 6 0 0.53773 -0.53773 -1.07854 1 0.01792 0.22118 1.61515 0.51377 30 6 0 0.62544 -0.62544 -1.29221 1 0.01792 0.22118 0.93430 0.78435 31 7 1 0.56549 0.43451 0.87657 1 -1.28015 0.95546 1.23720 0.45476 32 7 1 0.77914 0.22086 0.53242 1 -1.28015 0.95546 0.34791 1.48987 33 7 1 0.78915 0.21085 0.51689 1 -1.28015 0.95546 -0.15094 1.42106 34 7 1 0.56515 0.43485 0.87719 1 -1.28015 0.95546 0.59589 0.26564 35 7 1 0.55254 0.44746 0.89991 1 -1.28015 0.95546 -1.58521 -0.43769 36 8 1 0.87749 0.12251 0.37366 1 -1.78965 -0.61148 -0.75627 0.18170 37 8 1 0.74964 0.25036 0.57791 1 -1.78965 -0.61148 0.37466 -0.62055 38 8 1 0.77548 0.22452 0.53808 1 -1.78965 -0.61148 -0.33496 -0.64231 39 8 1 0.88679 0.11321 0.35730 1 -1.78965 -0.61148 -0.59927 0.34380 40 8 1 0.83820 0.16180 0.43936 1 -1.78965 -0.61148 -0.60738 -0.19550 41 9 1 0.97603 0.02397 0.15672 1 -0.39519 -2.74759 -0.26452 1.32643 42 9 1 0.96631 0.03369 0.18671 1 -0.39519 -2.74759 -1.19139 0.60098 43 9 1 0.93207 0.06793 0.26997 1 -0.39519 -2.74759 -0.90697 -0.27356 44 9 1 0.91600 0.08400 0.30283 1 -0.39519 -2.74759 -0.35382 -0.41039 45 9 1 0.91704 0.08296 0.30078 1 -0.39519 -2.74759 1.29288 0.08813 46 10 1 0.95963 0.04037 0.20511 1 -2.46273 -1.34936 -0.04032 0.77297 47 10 1 0.87795 0.12205 0.37284 1 -2.46273 -1.34936 0.10152 -0.73766 48 10 1 0.93602 0.06398 0.26145 1 -2.46273 -1.34936 -1.03443 -0.14765 49 10 0 0.80273 -0.80273 -2.01724 1 -2.46273 -1.34936 1.08867 -1.18919 50 10 0 0.89745 -0.89745 -2.95834 1 -2.46273 -1.34936 -1.35565 -0.90858 51 11 0 0.55899 -0.55899 -1.12585 1 0.03887 0.72243 -1.89699 0.11790 52 11 1 0.36952 0.63048 1.30623 1 0.03887 0.72243 1.22003 0.02652 53 11 0 0.14358 -0.14358 -0.40945 1 0.03887 0.72243 1.96081 -1.38239 54 11 1 0.44105 0.55895 1.12576 1 0.03887 0.72243 1.27552 0.42886 55 11 0 0.37568 -0.37568 -0.77572 1 0.03887 0.72243 1.21278 0.05862 18:39 Tuesday, August 17, 2004 9 Fitted values and residuals Obs ID Y Predict Residual StdResid X1 X2 X3 X4 X5 56 12 0 0.56731 -0.56731 -1.14504 1 0.98414 -0.22431 0.11594 0.40345 57 12 1 0.65795 0.34205 0.72103 1 0.98414 -0.22431 0.76822 1.09161 58 12 1 0.57580 0.42420 0.85832 1 0.98414 -0.22431 0.89246 0.67524 59 12 0 0.30096 -0.30096 -0.65614 1 0.98414 -0.22431 0.89481 -0.81517 60 12 0 0.24964 -0.24964 -0.57680 1 0.98414 -0.22431 -0.30623 -1.50061 61 13 1 0.62346 0.37654 0.77715 1 1.93971 -0.05060 -1.37778 1.05909 62 13 1 0.62238 0.37762 0.77893 1 1.93971 -0.05060 1.68435 1.94732 63 13 0 0.33678 -0.33678 -0.71260 1 1.93971 -0.05060 0.79476 0.15877 64 13 0 0.38480 -0.38480 -0.79087 1 1.93971 -0.05060 -1.67006 -0.29034 65 13 0 0.42835 -0.42835 -0.86564 1 1.93971 -0.05060 1.22972 0.79104 66 14 0 0.89764 -0.89764 -2.96132 1 -0.78685 -0.94973 -0.56436 0.80418 67 14 0 0.85021 -0.85021 -2.38241 1 -0.78685 -0.94973 0.66572 0.59848 68 14 0 0.81637 -0.81637 -2.10852 1 -0.78685 -0.94973 0.07375 0.10844 69 14 0 0.86539 -0.86539 -2.53557 1 -0.78685 -0.94973 0.38553 0.67847 70 14 0 0.71452 -0.71452 -1.58204 1 -0.78685 -0.94973 -0.12490 -0.69560 71 15 0 0.59895 -0.59895 -1.22208 1 1.37411 -0.23615 -0.26551 0.69974 72 15 0 0.62450 -0.62450 -1.28962 1 1.37411 -0.23615 -0.29137 0.83190 73 15 0 0.33730 -0.33730 -0.71343 1 1.37411 -0.23615 0.05157 -0.60545 74 15 0 0.23838 -0.23838 -0.55946 1 1.37411 -0.23615 0.71159 -1.04406 75 15 0 0.32986 -0.32986 -0.70159 1 1.37411 -0.23615 -0.46513 -0.79978 76 16 1 0.22905 0.77095 1.83464 1 -0.44056 1.09389 -1.28595 -1.52140 77 16 0 0.37602 -0.37602 -0.77629 1 -0.44056 1.09389 -1.80416 -0.75439 78 16 0 0.39348 -0.39348 -0.80545 1 -0.44056 1.09389 -0.31012 -0.22231 79 16 0 0.67822 -0.67822 -1.45178 1 -0.44056 1.09389 0.31183 1.48932 80 16 1 0.41716 0.58284 1.18201 1 -0.44056 1.09389 -0.26431 -0.08134 81 17 1 0.92870 0.07130 0.27709 1 1.48456 -2.17922 1.26782 2.07390 82 17 1 0.96384 0.03616 0.19370 1 1.48456 -2.17922 -0.72486 2.42174 83 17 1 0.85207 0.14793 0.41667 1 1.48456 -2.17922 0.86483 0.89670 84 17 1 0.92908 0.07092 0.27630 1 1.48456 -2.17922 -1.20602 1.35890 85 17 1 0.72264 0.27736 0.61953 1 1.48456 -2.17922 1.27138 -0.01470 86 18 1 0.48310 0.51690 1.03439 1 -0.51471 -0.39247 -2.37192 -1.89486 87 18 1 0.82142 0.17858 0.46626 1 -0.51471 -0.39247 0.75628 1.08799 88 18 1 0.50696 0.49304 0.98617 1 -0.51471 -0.39247 1.46271 -0.65109 89 18 1 0.72311 0.27689 0.61879 1 -0.51471 -0.39247 0.72994 0.34528 90 18 1 0.87350 0.12650 0.38055 1 -0.51471 -0.39247 -0.69751 1.19096 91 19 1 0.81828 0.18172 0.47124 1 -1.18101 0.44121 -1.20462 0.89931 92 19 1 0.72736 0.27264 0.61223 1 -1.18101 0.44121 -0.54557 0.41202 93 19 1 0.79275 0.20725 0.51131 1 -1.18101 0.44121 0.14463 1.08141 94 19 0 0.49999 -0.49999 -0.99999 1 -1.18101 0.44121 1.11610 -0.37697 95 19 0 0.13728 -0.13728 -0.39891 1 -1.18101 0.44121 1.65032 -2.60764 96 20 1 0.90233 0.09767 0.32900 1 0.32727 -0.93924 -0.36553 1.65626 97 20 1 0.70772 0.29228 0.64264 1 0.32727 -0.93924 -0.43425 -0.10260 98 20 1 0.55855 0.44145 0.88901 1 0.32727 -0.93924 1.75302 -0.30669 99 20 0 0.48750 -0.48750 -0.97531 1 0.32727 -0.93924 0.83785 -0.94440 100 20 1 0.58685 0.41315 0.83906 1 0.32727 -0.93924 -0.30668 -0.75797 18:39 Tuesday, August 17, 2004 10 Test the offset option Generalized estimating equations for exchangeably- correlated binary responses (version 2.3) (c) Bahjat Qaqish and Habib Moalem (1994, 1995) Department of Biostatistics CB 7400 Chapel Hill, NC 27599-7400 Data set: A Response: y Covariates: x1 x2 x3 x4 x5 Offset: zero Cluster ID: id Number of observations: 100 Number of covariates: 5 Number of clusters: 20 Cluster sizes: from 5 to 5 Iteration 2 rho = 0.3339094 is above the valid range and will be set to 0.3088038 Iteration 3 rho = 0.4568218 is above the valid range and will be set to 0.2080706 Iteration 4 rho = 0.4616948 is above the valid range and will be set to 0.185679 Iteration 5 rho = 0.4488915 is above the valid range and will be set to 0.1855632 Iteration 6 rho = 0.4453438 is above the valid range and will be set to 0.1861348 Iteration 7 rho = 0.445268 is above the valid range and will be set to 0.1861243 18:39 Tuesday, August 17, 2004 11 Test the offset option Iteration 8 rho = 0.4453592 is above the valid range and will be set to 0.1861036 Converged, niter = 8 Number of estimable parameters = 5 Estimated intra-cluster correlation = 0.1861036 Summary of estimates and 0.95 confidence intervals: Results using the robust variance estimator: Estimate Robust SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.327519 0.9134833 0.3609884 1.3487566 0.7098211 2.5628211 X2 -0.494738 0.3524411 -1.403747 0.1603943 0.6097306 0.3055903 1.2165682 X3 -0.775563 0.3726747 -2.081073 0.0374272 0.4604443 0.2217971 0.9558691 X4 -0.224888 0.1469881 -1.529977 0.1260225 0.7986053 0.5987088 1.0652431 X5 0.7701157 0.3012279 2.5565882 0.0105704 2.1600161 1.196882 3.8981868 Results using the naive variance estimator: Estimate Naive SE z p-val Odds Ratio CI-lower CI-upper X1 0.2991832 0.3303719 0.9055951 0.3651502 1.3487566 0.7058632 2.5771913 X2 -0.494738 0.2887179 -1.713569 0.0866079 0.6097306 0.3462429 1.0737301 X3 -0.775563 0.364515 -2.127658 0.0333654 0.4604443 0.2253727 0.9407037 X4 -0.224888 0.2212158 -1.016602 0.3093427 0.7986053 0.5176461 1.2320587 X5 0.7701157 0.2656079 2.8994455 0.0037382 2.1600161 1.2834269 3.6353218