|
|
|
||||
|
|
|||||
page 105 Table 4.1 Simple logistic regression models for the UIS (n = 575).
NOTE: We have bolded the relevant output.
data uis41;
set 'd:\hosmerdata\uis';
run;
proc genmod data=uis41 descending;
model dfree = age / dist=bin link=logit waldci;
estimate '10 year increase in age' age 10 /exp ;
run;
The GENMOD Procedure
Model Information
Data Set WORK.UIS41
Distribution Binomial
Link Function Logit
Dependent Variable DFREE
Observations Used 575
Probability Modeled Pr( DFREE = 1 )
Response Profile
Ordered Ordered
Level Value Count
1 0 428
2 1 147
Parameter Information
Parameter Effect
Prm1 Intercept
Prm2 AGE
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 573 652.3309 1.1384
Scaled Deviance 573 652.3309 1.1384
Pearson Chi-Square 573 575.1709 1.0038
Scaled Pearson X2 573 575.1709 1.0038
Log Likelihood -326.1654
Algorithm converged.
Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 -1.6602 0.5111 -2.6619 -0.6585 10.55 0.0012
AGE 1 0.0182 0.0153 -0.0119 0.0482 1.40 0.2363
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.
The GENMOD Procedure
Contrast Estimate Results
Standard Chi-
Label Estimate Error Alpha Confidence Limits Square Pr > ChiSq
10 year increase in age 0.1817 0.1534 0.05 -0.1190 0.4825 1.40 0.2363
Exp(10 year increase in age) 1.1993 0.1840 0.05 0.8878 1.6201
proc genmod data=uis41 descending;
model dfree = beck / dist=bin link=logit waldci;
estimate '5 point increase in beck' beck 5 /exp ;
run;
The GENMOD Procedure
Model Information
Data Set WORK.UIS41
Distribution Binomial
Link Function Logit
Dependent Variable DFREE
Observations Used 575
Probability Modeled Pr( DFREE = 1 )
Response Profile
Ordered Ordered
Level Value Count
1 0 428
2 1 147
Parameter Information
Parameter Effect
Prm1 Intercept
Prm2 BECK
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 573 653.0924 1.1398
Scaled Deviance 573 653.0924 1.1398
Pearson Chi-Square 573 575.1216 1.0037
Scaled Pearson X2 573 575.1216 1.0037
Log Likelihood -326.5462
Algorithm converged.
Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 -0.9273 0.2003 -1.3199 -0.5347 21.43 <.0001
BECK 1 -0.0082 0.0103 -0.0285 0.0120 0.63 0.4265
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.
The GENMOD Procedure
Contrast Estimate Results
Standard Chi-
Label Estimate Error Alpha Confidence Limits Square
5 point increase in beck -0.0411 0.0517 0.05 -0.1425 0.0602 0.63
Exp(5 point increase in beck) 0.9597 0.0496 0.05 0.8672 1.0621
Contrast Estimate Results
Label Pr > ChiSq
5 point increase in beck 0.4265
Exp(5 point increase in beck)
proc logistic data=uis41 desc;
model dfree = ndrugtx;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 645.890
SC 660.083 654.598
-2 Log L 653.729 641.890
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 11.8392 1 0.0006
Score 9.7585 1 0.0018
Wald 9.2203 1 0.0024
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -0.7678 0.1303 34.7133 <.0001
NDRUGTX 1 -0.0749 0.0247 9.2203 0.0024
The LOGISTIC Procedure
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
NDRUGTX 0.928 0.884 0.974
Association of Predicted Probabilities and Observed Responses
Percent Concordant 54.6 Somers' D 0.203
Percent Discordant 34.3 Gamma 0.228
Percent Tied 11.1 Tau-a 0.077
Pairs 62916 c 0.602
proc logistic data=uis41 desc;
model dfree = ivhx2 ivhx3;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 646.376
SC 660.083 659.440
-2 Log L 653.729 640.376
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 13.3525 2 0.0013
Score 13.4161 2 0.0012
Wald 13.1585 2 0.0014
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -0.6797 0.1417 22.9977 <.0001
IVHX2 1 -0.4810 0.2657 3.2773 0.0702
IVHX3 1 -0.7748 0.2166 12.7997 0.0003
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
IVHX2 0.618 0.367 1.041
IVHX3 0.461 0.301 0.704
Association of Predicted Probabilities and Observed Responses
Percent Concordant 41.5 Somers' D 0.185
Percent Discordant 23.0 Gamma 0.287
Percent Tied 35.5 Tau-a 0.071
Pairs 62916 c 0.593
proc logistic data=uis41 desc;
model dfree = race;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 653.105
SC 660.083 661.814
-2 Log L 653.729 649.105
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 4.6235 1 0.0315
Score 4.7791 1 0.0288
Wald 4.7378 1 0.0295
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -1.1939 0.1142 109.3946 <.0001
RACE 1 0.4592 0.2110 4.7378 0.0295
The LOGISTIC Procedure
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
RACE 1.583 1.047 2.393
Association of Predicted Probabilities and Observed Responses
Percent Concordant 24.7 Somers' D 0.091
Percent Discordant 15.6 Gamma 0.226
Percent Tied 59.8 Tau-a 0.035
Pairs 62916 c 0.545
proc logistic data=uis41 desc;
model dfree = treat;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 652.551
SC 660.083 661.259
-2 Log L 653.729 648.551
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 5.1782 1 0.0229
Score 5.1626 1 0.0231
Wald 5.1266 1 0.0236
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -1.2978 0.1433 82.0211 <.0001
TREAT 1 0.4371 0.1931 5.1266 0.0236
The LOGISTIC Procedure
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
TREAT 1.548 1.060 2.260
Association of Predicted Probabilities and Observed Responses
Percent Concordant 30.7 Somers' D 0.109
Percent Discordant 19.8 Gamma 0.215
Percent Tied 49.5 Tau-a 0.041
Pairs 62916 c 0.554
proc logistic data=uis41 desc;
model dfree = site;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 656.063
SC 660.083 664.772
-2 Log L 653.729 652.063
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 1.6659 1 0.1968
Score 1.6921 1 0.1933
Wald 1.6874 1 0.1939
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -1.1527 0.1171 96.9397 <.0001
SITE 1 0.2642 0.2034 1.6874 0.1939
The LOGISTIC Procedure
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
SITE 1.302 0.874 1.940
Association of Predicted Probabilities and Observed Responses
Percent Concordant 24.6 Somers' D 0.057
Percent Discordant 18.9 Gamma 0.131
Percent Tied 56.4 Tau-a 0.022
Pairs 62916 c 0.529
page 106 Table 4.2 Results of fitting a multivariable model containing the covariates significant at the 0.25 level in Table 4.1.
proc logistic data=uis41 desc;
model dfree = age ndrugtx ivhx2 ivhx3 race treat site / alpha=.25;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 635.248
SC 660.083 670.083
-2 Log L 653.729 619.248
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.4806 7 <.0001
Score 32.6795 7 <.0001
Wald 30.6395 7 <.0001
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -2.4054 0.5548 18.7975 <.0001
AGE 1 0.0504 0.0173 8.4550 0.0036
NDRUGTX 1 -0.0615 0.0256 5.7559 0.0164
IVHX2 1 -0.6033 0.2872 4.4118 0.0357
IVHX3 1 -0.7327 0.2523 8.4328 0.0037
RACE 1 0.2261 0.2233 1.0251 0.3113
TREAT 1 0.4425 0.1993 4.9302 0.0264
SITE 1 0.1486 0.2172 0.4681 0.4939
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
AGE 1.052 1.017 1.088
NDRUGTX 0.940 0.894 0.989
IVHX2 0.547 0.312 0.960
IVHX3 0.481 0.293 0.788
RACE 1.254 0.809 1.942
TREAT 1.557 1.053 2.300
SITE 1.160 0.758 1.776
Association of Predicted Probabilities and Observed Responses
Percent Concordant 66.6 Somers' D 0.336
Percent Discordant 33.0 Gamma 0.337
Percent Tied 0.4 Tau-a 0.128
Pairs 62916 c 0.668
page 107 Figure 4.2 Univariable lowess smoothed logit versus AGE.The smoothing algorithm below is based on Stata's lowess program with logit option. The discrepancy between the two plots by Stata and SAS is due to the difference between the algorithms used by Stata and SAS for Loess smoothing.
proc loess data = uis; model dfree = age /smooth=.6; ods output OutputStatistics=a; run; proc sql; /*compute the total number of obs*/ select count(dfree) into :total from uis; quit; data b1; set a; adjust = 1/&total; small = .0001; if pred < small then pred = adjust; else if pred > 1 - small then pred = 1 - adjust; pred = log(pred/(1-pred)); run; proc sort data = b1; by age; run; goptions reset = all; symbol i = join v=star; axis1 order = (20 to 56 by 9) minor=none; axis2 order = (-1.5 to .5 by .5) minor = none label=(a=90 'Smoothed Logit'); proc gplot data = b1; format age 3.0 pred 5.1; plot pred*age /vaxis=axis2 haxis=axis1 ; run; quit;
page 107 Table 4.3 Results of the quartile analyses of AGE from the multivariable model containing the variable shown in the model in Table 4.2.
data table4_3;
input quartile midpt number age coeff;
cards;
1 24 148 24 0
2 30.5 144 30.5 -.165864
3 35.5 166 35.5 .4693399
4 47.5 117 47.5 .595771
;
run;
proc print data=table4_3;
run;
Obs quartile midpt number age coeff
1 1 24.0 148 24.0 0.00000
2 2 30.5 144 30.5 -0.16586
3 3 35.5 166 35.5 0.46934
4 4 47.5 117 47.5 0.59577
proc sort data=uis41;
by age;
run;
data uis41a;
set uis41;
age1 = (_n_ <= 148);
age2 = (_n_ >= 149) & (_n_ <= 292);
age3 = (_n_ >= 293) & (_n_ <= 458) ;
age4 = (_n_ >= 459) ;
run;
proc logistic data=uis41a desc;
model dfree = age2 age3 age4 ndrugtx ivhx2 ivhx3 race treat site / CLPARM=both;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UIS41A
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 639.042
SC 660.083 682.586
-2 Log L 653.729 619.042
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.6869 9 <.0001
Score 32.7145 9 0.0001
Wald 30.6492 9 0.0003
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -1.0549 0.2706 15.1988 <.0001
age2 1 -0.1659 0.2909 0.3250 0.5686
age3 1 0.4693 0.2707 3.0067 0.0829
age4 1 0.5957 0.3125 3.6344 0.0566
NDRUGTX 1 -0.0587 0.0255 5.3185 0.0211
IVHX2 1 -0.5545 0.2854 3.7764 0.0520
IVHX3 1 -0.6726 0.2519 7.1312 0.0076
RACE 1 0.2787 0.2238 1.5502 0.2131
TREAT 1 0.4431 0.2000 4.9054 0.0268
SITE 1 0.1582 0.2188 0.5228 0.4696
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
age2 0.847 0.479 1.498
age3 1.599 0.941 2.718
age4 1.814 0.983 3.348
NDRUGTX 0.943 0.897 0.991
IVHX2 0.574 0.328 1.005
IVHX3 0.510 0.312 0.836
RACE 1.321 0.852 2.049
TREAT 1.557 1.052 2.305
SITE 1.171 0.763 1.799
Association of Predicted Probabilities and Observed Responses
Percent Concordant 66.2 Somers' D 0.330
Percent Discordant 33.2 Gamma 0.332
Percent Tied 0.7 Tau-a 0.126
Pairs 62916 c 0.665
Profile Likelihood Confidence
Interval for Parameters
Parameter Estimate 95% Confidence Limits
Intercept -1.0549 -1.5955 -0.5327
age2 -0.1659 -0.7410 0.4027
age3 0.4693 -0.0577 1.0054
age4 0.5957 -0.0161 1.2118
NDRUGTX -0.0587 -0.1122 -0.0121
IVHX2 -0.5545 -1.1266 -0.00495
The LOGISTIC Procedure
Profile Likelihood Confidence
Interval for Parameters
Parameter Estimate 95% Confidence Limits
IVHX3 -0.6726 -1.1721 -0.1830
RACE 0.2787 -0.1647 0.7142
TREAT 0.4431 0.0528 0.8380
SITE 0.1582 -0.2747 0.5844
Wald Confidence Interval for Parameters
Parameter Estimate 95% Confidence Limits
Intercept -1.0549 -1.5852 -0.5246
age2 -0.1659 -0.7360 0.4043
age3 0.4693 -0.0612 0.9998
age4 0.5957 -0.0167 1.2082
NDRUGTX -0.0587 -0.1086 -0.00882
IVHX2 -0.5545 -1.1138 0.00476
IVHX3 -0.6726 -1.1662 -0.1789
RACE 0.2787 -0.1600 0.7174
TREAT 0.4431 0.0510 0.8351
SITE 0.1582 -0.2707 0.5871
page 108 Figure 4.3 Plot of estimated logistic regression coefficients versus approximate quartile midpoints of AGE.
symbol1 i=join ; proc gplot data=table4_3; plot coeff*age / vref=0; run; quit;
page 109 Table 4.4 Summary of the use of the method of fractional polynomials for AGE.
NOTE: The values in the column titled deviance are under the heading -2 Log L intercepts and covariates in the SAS output.
data uistbl44; set uis41; agethree=age**3; age_2 = age**(-2); run;
NOTE: Line 1: Not in model
proc logistic data=uistbl44 desc;
model dfree = ndrugtx ivhx2 ivhx3 race treat site;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.UISTBL44
Response Variable DFREE
Number of Response Levels 2
Number of Observations 575
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value DFREE Frequency
1 1 147
2 0 428
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 655.729 641.801
SC 660.083 672.281
-2 Log L 653.729 627.801
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 25.9282 6 0.0002
Score 24.7124 6 0.0004
Wald 23.3984 6 0.0007
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -0.9462 0.2264 17.4734 <.0001
NDRUGTX 1 -0.0523 0.0246 4.5227 0.0334
IVHX2 1 -0.3853 0.2731 1.9903 0.1583
IVHX3 1 -0.4994 0.2354 4.4990 0.0339
RACE 1 0.2973 0.2205 1.8179 0.1776
TREAT 1 0.4117 0.1974 4.3494 0.0370
SITE 1 0.1784 0.2151 0.6883 0.4067
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
NDRUGTX 0.949 0.904 0.996
IVHX2 0.680 0.398 1.162
IVHX3 0.607 0.383 0.963
RACE 1.346 0.874 2.074
TREAT 1.509 1.025 2.222
SITE 1.195 0.784 1.822
Association of Predicted Probabilities and Observed Responses
Percent Concordant 63.9 Somers' D 0.288
Percent Discordant 35.0 Gamma 0.292
Percent Tied 1.1 Tau-a 0.110
Pairs 62916 c 0.644
NOTE: Line 2: Linear
proc logistic data=uistbl44 desc; model dfree = age ndrugtx ivhx2 ivhx3 race treat site; run;The LOGISTIC Procedure Model Information Data Set WORK.UISTBL44 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 635.248 SC 660.083 670.083 -2 Log L 653.729 619.248 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 34.4806 7 <.0001 Score 32.6795 7 <.0001 Wald 30.6395 7 <.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -2.4054 0.5548 18.7975 <.0001 AGE 1 0.0504 0.0173 8.4550 0.0036 NDRUGTX 1 -0.0615 0.0256 5.7559 0.0164 IVHX2 1 -0.6033 0.2872 4.4118 0.0357 IVHX3 1 -0.7327 0.2523 8.4328 0.0037 RACE 1 0.2261 0.2233 1.0251 0.3113 TREAT 1 0.4425 0.1993 4.9302 0.0264 SITE 1 0.1486 0.2172 0.4681 0.4939 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits AGE 1.052 1.017 1.088 NDRUGTX 0.940 0.894 0.989 IVHX2 0.547 0.312 0.960 IVHX3 0.481 0.293 0.788 RACE 1.254 0.809 1.942 TREAT 1.557 1.053 2.300 SITE 1.160 0.758 1.776 Association of Predicted Probabilities and Observed Responses Percent Concordant 66.6 Somers' D 0.336 Percent Discordant 33.0 Gamma 0.337 Percent Tied 0.4 Tau-a 0.128 Pairs 62916 c 0.668NOTE: Line 3: J = 1proc logistic data=uistbl44 desc; model dfree = agethree ndrugtx ivhx2 ivhx3 race treat site; run; The LOGISTIC Procedure Model Information Data Set WORK.UISTBL44 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 634.882 SC 660.083 669.717 -2 Log L 653.729 618.882 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 34.8466 7 <.0001 Score 33.0920 7 <.0001 Wald 30.8612 7 <.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.3032 0.2583 25.4622 <.0001 agethree 1 0.000014 4.648E-6 8.9327 0.0028 NDRUGTX 1 -0.0620 0.0257 5.8134 0.0159 IVHX2 1 -0.5961 0.2869 4.3184 0.0377 IVHX3 1 -0.7142 0.2500 8.1632 0.0043 RACE 1 0.2355 0.2230 1.1152 0.2909 TREAT 1 0.4349 0.1992 4.7634 0.0291 SITE 1 0.1437 0.2174 0.4370 0.5086 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits agethree 1.000 1.000 1.000 NDRUGTX 0.940 0.894 0.988 IVHX2 0.551 0.314 0.967 IVHX3 0.490 0.300 0.799 RACE 1.266 0.817 1.959 TREAT 1.545 1.045 2.283 SITE 1.155 0.754 1.768 Association of Predicted Probabilities and Observed Responses Percent Concordant 66.5 Somers' D 0.335 Percent Discordant 33.0 Gamma 0.337 Percent Tied 0.5 Tau-a 0.128 Pairs 62916 c 0.667G = 619.248 - 618.882 = .366
NOTE: Line 4: J = 2proc logistic data=uistbl44 desc; model dfree = ndrugtx agethree age_2 ivhx2 ivhx3 race treat site; run; The LOGISTIC Procedure Model Information Data Set WORK.UISTBL44 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 636.769 SC 660.083 675.958 -2 Log L 653.729 618.769 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 34.9602 8 <.0001 Score 33.1864 8 <.0001 Wald 31.0132 8 0.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.0496 0.7957 1.7401 0.1871 NDRUGTX 1 -0.0620 0.0257 5.8171 0.0159 agethree 1 0.000012 8.098E-6 2.0724 0.1500 age_2 1 -153.9 457.6 0.1131 0.7367 IVHX2 1 -0.6058 0.2882 4.4192 0.0355 IVHX3 1 -0.7264 0.2526 8.2703 0.0040 RACE 1 0.2282 0.2241 1.0371 0.3085 TREAT 1 0.4393 0.1997 4.8384 0.0278 SITE 1 0.1459 0.2175 0.4502 0.5022 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits NDRUGTX 0.940 0.894 0.988 agethree 1.000 1.000 1.000 age_2 <0.001 <0.001 >999.999 IVHX2 0.546 0.310 0.960 IVHX3 0.484 0.295 0.793 RACE 1.256 0.810 1.949 TREAT 1.552 1.049 2.295 SITE 1.157 0.756 1.772 Association of Predicted Probabilities and Observed Responses Percent Concordant 66.6 Somers' D 0.337 Percent Discordant 32.9 Gamma 0.339 Percent Tied 0.5 Tau-a 0.128 Pairs 62916 c 0.668 G = 618.882 - 618.769 = .479
page 110 Figure 4.4 Univariable lowess smoothed logit versus number of previous drug treatments (NDRGTX).
The smoothing algorithm below is based on Stata's lowess program with logit option. The discrepancy between the two plots by Stata and SAS is due to the difference between the algorithms used by Stata and SAS for Loess smoothing.
proc loess data = uis; model dfree = ndrugtx /smooth=.5; ods output OutputStatistics=a; run; proc means data = a; var pred; run; proc sql; /*compute the total number of obs*/ select count(dfree) into :total from uis; quit; data b1; set a; adjust = 1/&total; small = .0001; if pred < small then pred = adjust; else if pred > 1 - small then pred = 1 - adjust; pred = log(pred/(1-pred)); run; proc sort data = b1; by ndrugtx; run; goptions ftext = swiss htitle = 5 htext = 3 gunit = pct border cback = white hsize = 5in vsize = 4in; filename outgraph 'd:\temp\alr2.gif'; goptions gsfname = outgraph dev = gif570; symbol i = join v=star; axis1 order = (0 to 40 by 5) minor=none; axis2 order = (-2 to -.5 by .5) minor = none; proc gplot data = b1; format ndrugtx 3.0 ; plot pred*ndrugtx /vaxis=axis2 haxis=axis1 ; run; quit;
page 110 Table 4.5 Results of the design variable analysis of number of previous drug treatments (NDRGTX) from the multivariable model containing the variables shown in the model in Table 4.2.
data uis42; set uis41; grp = .; if ndrugtx=0 then grp = 1; if ndrugtx=1 or ndrugtx=2 then grp = 2; if 3<=ndrugtx<16 then grp = 3; if ndrugtx>15 then grp = 4; if grp = 2 then grp2 = 1; else grp2 = 0; if grp = 3 then grp3 = 1; else grp3 = 0; if grp = 4 then grp4 = 1; else grp4 = 0; run; proc logistic data=uis42 desc; model dfree = age grp2 grp3 grp4 ivhx2 ivhx3 race treat site / CLPARM=both; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS42 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 638.638 SC 660.083 682.182 -2 Log L 653.729 618.638 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 35.0906 9 <.0001 Score 34.5976 9 <.0001 Wald 32.5146 9 0.0002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -2.6601 0.6060 19.2711 <.0001 AGE 1 0.0506 0.0173 8.5540 0.0034 grp2 1 0.4060 0.3090 1.7262 0.1889 grp3 1 -0.1537 0.3117 0.2432 0.6219 grp4 1 -0.5852 0.6206 0.8894 0.3457 IVHX2 1 -0.6478 0.2898 4.9958 0.0254 IVHX3 1 -0.7955 0.2542 9.7909 0.0018 RACE 1 0.2412 0.2244 1.1551 0.2825 TREAT 1 0.4199 0.1997 4.4230 0.0355 SITE 1 0.1619 0.2206 0.5385 0.4630 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits AGE 1.052 1.017 1.088 grp2 1.501 0.819 2.750 grp3 0.858 0.466 1.580 grp4 0.557 0.165 1.880 IVHX2 0.523 0.296 0.923 IVHX3 0.451 0.274 0.743 RACE 1.273 0.820 1.976 TREAT 1.522 1.029 2.251 SITE 1.176 0.763 1.812 Association of Predicted Probabilities and Observed Responses Percent Concordant 66.2 Somers' D 0.330 Percent Discordant 33.2 Gamma 0.332 Percent Tied 0.6 Tau-a 0.126 Pairs 62916 c 0.665 Profile Likelihood Confidence Interval for Parameters Parameter Estimate 95% Confidence Limits Intercept -2.6601 -3.8671 -1.4871 AGE 0.0506 0.0168 0.0848 grp2 0.4060 -0.1906 1.0244 grp3 -0.1537 -0.7559 0.4696 grp4 -0.5852 -1.9302 0.5550 IVHX2 -0.6478 -1.2289 -0.0898 The LOGISTIC Procedure Profile Likelihood Confidence Interval for Parameters Parameter Estimate 95% Confidence Limits IVHX3 -0.7955 -1.2996 -0.3012 RACE 0.2412 -0.2037 0.6775 TREAT 0.4199 0.0302 0.8140 SITE 0.1619 -0.2745 0.5916 Wald Confidence Interval for Parameters Parameter Estimate 95% Confidence Limits Intercept -2.6601 -3.8477 -1.4724 AGE 0.0506 0.0167 0.0845 grp2 0.4060 -0.1997 1.0117 grp3 -0.1537 -0.7646 0.4572 grp4 -0.5852 -1.8015 0.6311 IVHX2 -0.6478 -1.2158 -0.0797 IVHX3 -0.7955 -1.2938 -0.2972 RACE 0.2412 -0.1987 0.6810 TREAT 0.4199 0.0286 0.8113 SITE 0.1619 -0.2705 0.5943 data table4_4; input group midpoint number coeff; cards; 1 0 79 0 2 1.5 173 .406 3 9 294 -.154 4 28 29 -.585 ; run; proc print data=table4_4; run; Obs group midpoint number coeff 1 1 0.0 79 0.000 2 2 1.5 173 0.406 3 3 9.0 294 -0.154 4 4 28.0 29 -0.585
page 111 Figure 4.5 Plot of estimated logistic regression coefficients from Table 4.4 versus the midpoints of number of previous drug treatment groups.
symbol1 i=join value=circle; proc gplot data=table4_4; plot coeff*midpoint / vref=0; run; quit;
page 112 Figure 4.6 Plot of the univariable lowess smoothed logit (o) and the multivariable adjusted logit (+) from the J = 2 fractional polynomial model versus number of previous drug treatments (NDRGTX).
NOTE: We were unable to reproduce this graph.
page 113 Table 4.7 Results of fitting the multivariable model with the two term fractional polynomial transformation of NDRGTX.
NOTE: Everything regarding the constant in this output is different from what is shown in the book, and we don't know why.
data uis43; set uis41; ndrgfp1 = ((ndrugtx+1)/10)**(-1); ndrgfp2 = ndrgfp1*log((ndrugtx+1)/10); run; proc logistic data=uis43 desc; model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 631.451 SC 660.083 670.640 -2 Log L 653.729 613.451 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 40.2777 8 <.0001 Score 38.7032 8 <.0001 Wald 36.1456 8 <.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -4.3137 0.7925 29.6321 <.0001 AGE 1 0.0544 0.0175 9.6928 0.0018 ndrgfp1 1 0.9814 0.2888 11.5446 0.0007 ndrgfp2 1 0.3611 0.1099 10.8050 0.0010 IVHX2 1 -0.6088 0.2911 4.3740 0.0365 IVHX3 1 -0.7238 0.2556 8.0213 0.0046 RACE 1 0.2477 0.2242 1.2205 0.2693 TREAT 1 0.4224 0.2004 4.4435 0.0350 SITE 1 0.1732 0.2210 0.6144 0.4331 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits AGE 1.056 1.020 1.093 ndrgfp1 2.668 1.515 4.700 ndrgfp2 1.435 1.157 1.780 IVHX2 0.544 0.307 0.962 IVHX3 0.485 0.294 0.800 RACE 1.281 0.826 1.988 TREAT 1.526 1.030 2.259 SITE 1.189 0.771 1.834 Association of Predicted Probabilities and Observed Responses Percent Concordant 67.2 Somers' D 0.348 Percent Discordant 32.4 Gamma 0.349 Percent Tied 0.5 Tau-a 0.133 Pairs 62916 c 0.674
page 115 Table 4.9 Preliminary final model containing significant main effects and interactions.
proc logistic data=uis43 desc; model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site age*ndrgfp1 race*site; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 619.963 SC 660.083 667.861 -2 Log L 653.729 597.963 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 55.7660 10 <.0001 Score 52.0723 10 <.0001 Wald 47.2784 10 <.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -6.8429 1.2193 31.4989 <.0001 AGE 1 0.1166 0.0289 16.3137 <.0001 ndrgfp1 1 1.6687 0.4071 16.8000 <.0001 ndrgfp2 1 0.4336 0.1169 13.7585 0.0002 IVHX2 1 -0.6346 0.2987 4.5134 0.0336 IVHX3 1 -0.7049 0.2616 7.2623 0.0070 RACE 1 0.6841 0.2641 6.7074 0.0096 TREAT 1 0.4349 0.2038 4.5559 0.0328 SITE 1 0.5162 0.2549 4.1013 0.0429 AGE*ndrgfp1 1 -0.0153 0.00603 6.4177 0.0113 RACE*SITE 1 -1.4294 0.5298 7.2799 0.0070 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits ndrgfp2 1.543 1.227 1.940 IVHX2 0.530 0.295 0.952 IVHX3 0.494 0.296 0.825 TREAT 1.545 1.036 2.303 Association of Predicted Probabilities and Observed Responses Percent Concordant 69.7 Somers' D 0.398 Percent Discordant 29.9 Gamma 0.399 Percent Tied 0.4 Tau-a 0.152 Pairs 62916 c 0.699
page 123 Table 4.11 Log-likelihood for the model at each step and likelihood ratio test statistics (G), degrees-of-freedom (df), and p-values for two methods of selecting variables for a final model from a summary table.
NOTE: The following code gives the log likelihood and the values for method 1.
proc logistic data=uis43 desc; model dfree = ; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. -2 Log L = 653.7289 Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.0687 0.0956 124.9675 <.0001 proc logistic data=uis43 desc; model dfree = ndrugtx; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 645.890 SC 660.083 654.598 -2 Log L 653.729 641.890 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 11.8392 1 0.0006 Score 9.7585 1 0.0018 Wald 9.2203 1 0.0024 Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -0.7678 0.1303 34.7133 <.0001 NDRUGTX 1 -0.0749 0.0247 9.2203 0.0024 The LOGISTIC Procedure Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits NDRUGTX 0.928 0.884 0.974 Association of Predicted Probabilities and Observed Responses Percent Concordant 54.6 Somers' D 0.203 Percent Discordant 34.3 Gamma 0.228 Percent Tied 11.1 Tau-a 0.077 Pairs 62916 c 0.602
NOTE: To get the value of G, you need to compare the two models by doing some calculations by hand:
-2*(-326.864-(-320.945)) = 11.84
proc logistic data=uis43 desc; model dfree = ndrugtx treat; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 642.860 SC 660.083 655.923 -2 Log L 653.729 636.860 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 16.8690 2 0.0002 Score 14.8924 2 0.0006 Wald 14.2225 2 0.0008 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -0.9991 0.1691 34.9214 <.0001 NDRUGTX 1 -0.0739 0.0245 9.1221 0.0025 TREAT 1 0.4348 0.1948 4.9830 0.0256 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits NDRUGTX 0.929 0.885 0.974 TREAT 1.545 1.054 2.263 Association of Predicted Probabilities and Observed Responses Percent Concordant 58.8 Somers' D 0.232 Percent Discordant 35.5 Gamma 0.246 Percent Tied 5.7 Tau-a 0.089 Pairs 62916 c 0.616
-2*(-320.945-(-318.430)) = 5.03
proc logistic data=uis43 desc; model dfree = ndrugtx treat ivhx2 ivhx3; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 640.050 SC 660.083 661.822 -2 Log L 653.729 630.050 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 23.6784 4 <.0001 Score 22.3908 4 0.0002 Wald 21.3059 4 0.0003 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -0.7714 0.1878 16.8787 <.0001 NDRUGTX 1 -0.0542 0.0246 4.8559 0.0276 TREAT 1 0.4215 0.1965 4.6009 0.0320 IVHX2 1 -0.4024 0.2711 2.2040 0.1377 IVHX3 1 -0.5804 0.2289 6.4281 0.0112 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits NDRUGTX 0.947 0.903 0.994 TREAT 1.524 1.037 2.241 IVHX2 0.669 0.393 1.138 IVHX3 0.560 0.357 0.877 Association of Predicted Probabilities and Observed Responses Percent Concordant 62.2 Somers' D 0.269 Percent Discordant 35.3 Gamma 0.276 Percent Tied 2.5 Tau-a 0.103 Pairs 62916 c 0.635
-2*(-318.430-(-315.025)) = 6.81
proc logistic data=uis43 desc; model dfree = ndrugtx treat ivhx2 ivhx3 age ; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 632.587 SC 660.083 658.713 -2 Log L 653.729 620.587 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 33.1420 5 <.0001 Score 31.1565 5 <.0001 Wald 29.3324 5 <.0001 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -2.3327 0.5484 18.0956 <.0001 NDRUGTX 1 -0.0637 0.0256 6.1858 0.0129 TREAT 1 0.4513 0.1986 5.1649 0.0230 IVHX2 1 -0.6237 0.2847 4.7989 0.0285 IVHX3 1 -0.8056 0.2445 10.8542 0.0010 AGE 1 0.0526 0.0172 9.3378 0.0022 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits NDRUGTX 0.938 0.892 0.987 TREAT 1.570 1.064 2.318 IVHX2 0.536 0.307 0.936 IVHX3 0.447 0.277 0.722 AGE 1.054 1.019 1.090 Association of Predicted Probabilities and Observed Responses Percent Concordant 65.5 Somers' D 0.315 Percent Discordant 34.0 Gamma 0.317 Percent Tied 0.5 Tau-a 0.120 Pairs 62916 c 0.658
-2*(-315.025-(-310.293)) = 9.46
NOTE: The following code gives the log likelihood and the values for method 2.
-2*(-326.864-(-310.293)) = 33.14
-2*(-320.945-(-310.293)) = 21.30
-2*(-318.430-(-310.293)) = 16.27
-2*(-315.025-(-310.293)) = 9.46
page 126 Table 4.12 Results of applying stepwise variable selection using the score test to select and maximum likelihood test to remove covariates at each step to the UIS data. Results are presented at each step in terms of the p-values to enter (below the horizontal line), and the p-value to remove (above the horizontal line) in each column. The asterisk denotes the maximum p-value to remove at each step.
proc logistic data=uis43 desc; class ivhx; model dfree = ivhx age ndrugtx treat race site beck / selection=stepwise slentry=0.15 slstay=0.20 details; run; The LOGISTIC Procedure Model Information Data Set WORK.UIS43 Response Variable DFREE Number of Response Levels 2 Number of Observations 575 Link Function Logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value DFREE Frequency 1 1 147 2 0 428 Stepwise Selection Procedure Class Level Information Design Variables Class Value 1 2 IVHX 1 1 0 2 0 1 3 -1 -1 Step 0. Intercept entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr ChiSq Intercept 1 -1.0687 0.0956 124.9675 .0001 The LOGISTIC Procedure Residual Chi-Square Test Chi-Square DF Pr ChiSq 32.6798 8 .0001 Analysis of Effects Not in the Model Score Effect DF Chi-Square Pr ChiSq IVHX 2 13.4161 0.0012 AGE 1 1.4063 0.2357 NDRUGTX 1 9.7585 0.0018 TREAT 1 5.1626 0.0231 RACE 1 4.7791 0.0288 SITE 1 1.6921 0.1933 BECK 1 0.6331 0.4262 Step 1. Effect IVHX entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 646.376 SC 660.083 659.440 -2 Log L 653.729 640.376 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 13.3525 2 0.0013 Score 13.4161 2 0.0012 Wald 13.1585 2 0.0014 The LOGISTIC Procedure Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 13.1585 0.0014 Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.0983 0.1040 111.4532 <.0001 IVHX 1 1 0.4186 0.1324 10.0021 0.0016 IVHX 2 1 -0.0624 0.1663 0.1408 0.7075 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits IVHX 1 vs 3 2.170 1.420 3.318 IVHX 2 vs 3 1.342 0.778 2.314 Association of Predicted Probabilities and Observed Responses Percent Concordant 41.5 Somers' D 0.185 Percent Discordant 23.0 Gamma 0.287 Percent Tied 35.5 Tau-a 0.071 Pairs 62916 c 0.593 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 20.1460 6 0.0026 Analysis of Effects in Model Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 13.1585 0.0014 The LOGISTIC Procedure Analysis of Effects Not in the Model Score Effect DF Chi-Square Pr > ChiSq AGE 1 7.3328 0.0068 NDRUGTX 1 4.9318 0.0264 TREAT 1 4.5504 0.0329 RACE 1 2.1112 0.1462 SITE 1 0.5585 0.4549 BECK 1 0.0824 0.7741 Step 2. Effect AGE entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 641.096 SC 660.083 658.514 -2 Log L 653.729 633.096 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 20.6325 3 0.0001 Score 20.4581 3 0.0001 Wald 19.7426 3 0.0002 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 18.6217 <.0001 AGE 1 7.2173 0.0072 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -2.5942 0.5727 20.5193 <.0001 IVHX 1 1 0.5610 0.1446 15.0424 0.0001 IVHX 2 1 -0.1200 0.1691 0.5037 0.4779 AGE 1 0.0454 0.0169 7.2173 0.0072 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits IVHX 1 vs 3 2.724 1.716 4.322 IVHX 2 vs 3 1.378 0.796 2.388 AGE 1.046 1.012 1.082 Association of Predicted Probabilities and Observed Responses Percent Concordant 60.7 Somers' D 0.239 Percent Discordant 36.8 Gamma 0.245 Percent Tied 2.5 Tau-a 0.091 Pairs 62916 c 0.620 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 12.8529 5 0.0248 Analysis of Effects in Model Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 18.6217 <.0001 AGE 1 7.2173 0.0072 Analysis of Effects Not in the Model Score Effect DF Chi-Square Pr > ChiSq NDRUGTX 1 6.2094 0.0127 TREAT 1 5.0083 0.0252 RACE 1 1.4228 0.2330 SITE 1 0.5078 0.4761 BECK 1 0.0021 0.9636 Step 3. Effect NDRUGTX entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 655.729 635.805 SC 660.083 657.577 -2 Log L 653.729 625.805 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 27.9241 4 <.0001 Score 26.1214 4 <.0001 Wald 24.7400 4 <.0001 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 11.8349 0.0027 AGE 1 8.7808 0.0030 NDRUGTX 1 6.0226 0.0141 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -2.5107 0.5759 19.0072 <.0001 IVHX 1 1 0.4699 0.1484 10.0285 0.0015 IVHX 2 1 -0.1201 0.1705 0.4958 0.4813 AGE 1 0.0508 0.0171 8.7808 0.0030 NDRUGTX 1 -0.0632 0.0258 6.0226 0.0141 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits IVHX 1 vs 3 2.270 1.408 3.659 IVHX 2 vs 3 1.258 0.721 2.195 AGE 1.052 1.017 1.088 NDRUGTX 0.939 0.893 0.987 Association of Predicted Probabilities and Observed Responses Percent Concordant 64.2 Somers' D 0.291 Percent Discordant 35.1 Gamma 0.293 Percent Tied 0.7 Tau-a 0.111 Pairs 62916 c 0.646 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 6.5523 4 0.1615 Analysis of Effects in Model Wald Effect DF Chi-Square Pr > ChiSq IVHX 2 11.8349 0.0027 AGE 1 8.7808 0.0030 NDRUGTX 1 6.0226 0.0141 The LOGISTIC Procedure Analysis of Effects Not in the Model Score Effect DF Chi-Square Pr > ChiSq TREAT 1 5.2017 0.0226 RACE 1 1.2039 0.2726 SITE 1 0.2416 0.6231 BECK 1 0.0011 0.9738
Step 4. Effect TREAT entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept &nb
