/* Use the GEE option in PROC GENMOD
to fit a Poisson regression model
to the epileptic seizure
data from Thall and Vail(1990). */
proc format; value trt 0 = 'Placebo'
1 = 'progabide';
proc print data=set1; run;
/* This program is stored in the file
seizure2.sas
*/
data set1;
infile 'c:\courses\st557\sas\seizures.dat';
input y1-y4 trt base age;
case = _N_;
age=(age-29);
base = base-30;
/* label base = number of siezures in
8 weeks prior to treatment
trt = treatment
age = age in years
case = subject
y1 = seizures 1-2 weeks after treatment
y2 = seizures 3-4 weeks after treatment
y3 = seizures 5-6 weeks after treatment
y4 = seizures 7-8 weeks after treatment; */
run;
/* Use the interactive data analysis
feature in SAS to examine box plots
or scatter plots for y1 through y4
versus age or base, or make those
plots with the following code */
proc sort data=set1; by trt;
proc univariate data=set1 plot; by trt;
var y1-y4 base age;
format trt trt.;
run;
proc plot data=set1;
plot (y1-y4)*base = trt;
plot (y1-y4)*age = trt;
run;
1252
1251
/* Modify the data file to put
repeated measures on different lines.
Also create a time variable. */
data set2; set set1;
y = y1; time=1; xt=time;
y = y2; time=2; xt=time;
y = y3; time=3; xt=time;
y = y4; time=4; xt=time;
run;
/* Use PROC GENMOD in SAS to fit a
log-linear model with no correlation
among repeated measurements. Standard
errors are based on independent
Poisson counts. */
proc genmod data=set2;
class case time;
model y = time trt(time) age(time)
base(time)
/ noint dist=poisson link=log
covb obstats itprint
converge=.0000001 maxit=50;
run;
output;
output;
output;
output;
1253
1254
Criteria For Assessing Goodness Of Fit
Criterion
DF
Deviance
Scaled Deviance
Pearson Chi-Square
Scaled Pearson X2
Log Likelihood
Parameter
Intercept
time
time
time
time
trt(time)
trt(time)
trt(time)
trt(time)
age(time)
age(time)
age(time)
age(time)
base(time)
base(time)
base(time)
base(time)
Scale
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
220
220
220
220
Value
Value/DF
977.2344
977.2344
1204.6348
1204.6348
2899.0845
4.4420
4.4420
5.4756
5.4756
DF
Estimate
Standard
Error
ChiSquare
Pr>ChiSq
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0.0000
1.9845
1.9603
1.9660
1.7886
-0.2417
-0.1123
-0.2127
-0.2263
0.0259
0.0056
0.0205
0.0124
0.0243
0.0199
0.0224
0.0221
1.0000
0.0000
0.0666
0.0683
0.0677
0.0739
0.0893
0.0923
0.0916
0.1011
0.0064
0.0068
0.0066
0.0074
0.0010
0.0010
0.0010
0.0011
0.0000
.
887.43
824.68
842.25
585.41
7.32
1.48
5.39
5.01
16.31
0.68
9.71
2.82
634.33
380.03
498.83
405.26
.
<.0001
<.0001
<.0001
<.0001
0.0068
0.2235
0.0203
0.0252
<.0001
0.4088
0.0018
0.0933
<.0001
<.0001
<.0001
<.0001
/* Use PROC GENMOD in SAS to fit a
log-linear model with no correlation
among repeated measurements. Standard
errors are first based on a model
with extra-Poisson variation, then
a robust covariance estimator is
used. */
proc genmod data=set2;
class case time;
make 'obstats' out=set3;
model y = time trt(time) age(time)
base(time)
/ noint dist=poisson link=log
covb obstats pscale itprint
converge=.0000001 maxit=50;
repeated subject=case / type=ind
modelse covb corrw;
run;
NOTE: The scale parameter was held fixed.
1256
1255
Criteria For Assessing Goodness Of Fit
Criterion
Deviance
Scaled Deviance
Pearson Chi-Square
Scaled Pearson X2
Parameter
Intercept
time
time
time
time
trt(time)
trt(time)
trt(time)
trt(time)
age(time)
age(time)
age(time)
age(time)
base(time)
base(time)
base(time)
base(time)
Scale
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
DF
Value
Value/DF
220
220
220
220
977.2344
178.4703
1204.6348
220.0000
4.4420
0.8112
5.4756
1.0000
GEE Model Information
DF
Estimate
Standard
Error
ChiSquare
Pr > ChiSq
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0.0000
1.9845
1.9603
1.9660
1.7886
-0.2417
-0.1123
-0.2127
-0.2263
0.0259
0.0056
0.0205
0.0124
0.0243
0.0199
0.0224
0.0221
2.3400
0.0000
0.1559
0.1597
0.1585
0.1730
0.2090
0.2159
0.2144
0.2366
0.0150
0.0158
0.0154
0.0174
0.0023
0.0024
0.0024
0.0026
0.0000
.
162.07
150.61
153.82
106.91
1.34
0.27
0.98
0.91
2.98
0.12
1.77
0.51
115.85
69.40
91.10
74.01
.
<.0001
<.0001
<.0001
<.0001
0.2474
0.6029
0.3212
0.3388
0.0843
0.7241
0.1829
0.4733
<.0001
<.0001
<.0001
<.0001
Correlation Structure
Subject Effect
Number of Clusters
Correlation Matrix Dimension
Maximum Cluster Size
Minimum Cluster Size
Independent
case (59 levels)
59
4
4
4
Working Correlation Matrix
Row1
Row2
Row3
Row4
Col1
1.0000
0.0000
0.0000
0.0000
Col2
0.0000
1.0000
0.0000
0.0000
Col3
0.0000
0.0000
1.0000
0.0000
Col4
0.0000
0.0000
0.0000
1.0000
NOTE: The scale parameter was estimated by the square
root of Pearson's Chi-Square/DOF.
1257
1258
Analysis Of GEE Parameter Estimates
Model-Based Standard Error Estimates
Analysis Of GEE Parameter Estimates
Empirical Standard Error Estimates
Parameter
Estimate
Standard
Error
Intercept
time
time
time
time
trt(time)
trt(time)
trt(time)
trt(time)
age(time)
age(time)
age(time)
age(time)
base(time)
base(time)
base(time)
base(time)
0.0000
1.9845
1.9603
1.9660
1.7886
-0.2417
-0.1123
-0.2127
-0.2263
0.0259
0.0056
0.0205
0.0124
0.0243
0.0199
0.0224
0.0221
0.0000
0.1627
0.1200
0.2730
0.1180
0.1940
0.1614
0.3289
0.1676
0.0154
0.0094
0.0157
0.0097
0.0020
0.0014
0.0018
0.0012
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
Parameter
Z
.
12.20
16.33
7.20
15.16
-1.25
-0.70
-0.65
-1.35
1.68
0.59
1.30
1.28
12.30
14.29
12.51
19.10
Pr > |Z|
.
<.0001
<.0001
<.0001
<.0001
0.2128
0.4865
0.5179
0.1769
0.0937
0.5526
0.1934
0.2013
<.0001
<.0001
<.0001
<.0001
Estimate
Intercept
time
1
time
2
time
3
time
4
trt(time) 1
trt(time) 2
trt(time) 3
trt(time) 4
age(time) 1
age(time) 2
age(time) 3
age(time) 4
base(time) 1
base(time) 2
base(time) 3
base(time) 4
Scale
NOTE: The scale
0.0000
1.9845
1.9603
1.9660
1.7886
-0.2417
-0.1123
-0.2127
-0.2263
0.0259
0.0056
0.0205
0.0124
0.0243
0.0199
0.0224
0.0221
2.3400
parameter
Standard
Error
Z
Pr > |Z|
0.0000
0.1559
0.1597
0.1585
0.1730
0.2090
0.2159
0.2144
0.2366
0.0150
0.0158
0.0154
0.0174
0.0023
0.0024
0.0024
0.0026
.
12.73
12.27
12.40
10.34
-1.16
-0.52
-0.99
-0.96
1.73
0.35
1.33
0.72
10.76
8.33
9.54
8.60
.
<.0001
<.0001
<.0001
<.0001
0.2474
0.6029
0.3212
0.3388
0.0843
0.7241
0.1829
0.4733
<.0001
<.0001
<.0001
<.0001
was held fixed.
1259
/* Use PROC GENMOD in SAS to obtain
GEE estimates of coefficients in a
log-linear model with an exchangeable
correlation structure for repeated
measurements. Standard errors are
based on this correlation structure.
Results for a robust covariance
estimator are also provided. */
proc genmod data=set2;
class case time;
make 'obstats' out=set4;
model y = time trt(time) age(time)
base(time)
/ noint dist=poisson link=log
covb obstats pscale itprint
converge=.0000001 maxit=50;
repeated subject=case / type=exch
modelse covb corrw;
run;
1260
GEE Model Information
Correlation Structure
Subject Effect
Number of Clusters
Correlation Matrix Dimension
Maximum Cluster Size
Minimum Cluster Size
Exchangeable
case (59 levels)
59
4
4
4
Working Correlation Matrix
Row1
Row2
Row3
Row4
1261
Col1
1.0000
0.3947
0.3947
0.3947
Col2
0.3947
1.0000
0.3947
0.3947
Col3
0.3947
0.3947
1.0000
0.3947
Col4
0.3947
0.3947
0.3947
1.0000
1262
Analysis Of GEE Parameter Estimates
Model-Based Standard Error Estimates
Analysis Of GEE Parameter Estimates
Empirical Standard Error Estimates
Parameter
Estimate
Standard
Error
Intercept
time
time
time
time
trt(time)
trt(time)
trt(time)
trt(time)
age(time)
age(time)
age(time)
age(time)
base(time)
base(time)
base(time)
base(time)
0.0000
1.9809
1.9570
1.9624
1.7850
-0.2378
-0.1036
-0.2057
-0.2206
0.0255
0.0051
0.0201
0.0118
0.0243
0.0199
0.0224
0.0221
0.0000
0.1629
0.1207
0.2740
0.1194
0.1935
0.1632
0.3301
0.1694
0.0155
0.0097
0.0158
0.0098
0.0019
0.0014
0.0018
0.0012
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
Z
Pr > |Z|
.
12.16
16.21
7.16
14.95
-1.23
-0.63
-0.62
-1.30
1.65
0.52
1.27
1.21
12.47
14.12
12.46
19.00
.
<.0001
<.0001
<.0001
<.0001
0.2192
0.5256
0.5331
0.1928
0.0998
0.5997
0.2036
0.2259
<.0001
<.0001
<.0001
<.0001
Parameter
Estimate
Standard
Error
Z
Intercept
0.0000
0.0000
.
time
1
1.9809
0.1560
12.70
time
2
1.9570
0.1599
12.24
time
3
1.9624
0.1587
12.36
time
4
1.7850
0.1732
10.31
trt(time) 1 -0.2378
0.2089
-1.14
trt(time) 2 -0.1036
0.2157
-0.48
trt(time) 3 -0.2057
0.2143
-0.96
trt(time) 4 -0.2206
0.2365
-0.93
age(time) 1
0.0255
0.0150
1.70
age(time) 2
0.0051
0.0158
0.32
age(time) 3
0.0201
0.0154
1.31
age(time) 4
0.0118
0.0174
0.68
base(time) 1
0.0243
0.0022
10.80
base(time) 2
0.0199
0.0024
8.31
base(time) 3
0.0224
0.0023
9.55
base(time) 4
0.0221
0.0026
8.62
Scale
2.3400
NOTE: The scale parameter was held fixed.
proc genmod data=set2;
class case time;
make 'obstats' out=set5;
model y = time trt(time) age(time)
base(time)
/ noint dist=poisson link=log
covb obstats itprint
converge=.000001 maxit=50;
repeated subject=case / type=un
modelse covb corrw;
run;
.
<.0001
<.0001
<.0001
<.0001
0.2548
0.6312
0.3370
0.3508
0.0885
0.7474
0.1903
0.4954
<.0001
<.0001
<.0001
<.0001
1264
1263
/* Use PROC GENMOD in SAS to obtain
GEE estimates of coefficients in a
log-linear model with an unstructured
correlation structure for repeated
measurements. Standard errors are
based on the model and also on a
robust covariance estimator.
(This procedure failed to converge.) */
Pr > |Z|
GEE Model Information
Correlation Structure
Subject Effect
Number of Clusters
Correlation Matrix Dimension
Maximum Cluster Size
Minimum Cluster Size
Unstructured
case (59 levels)
59
4
4
4
ERROR: Error in estimation routine.
1265
1266