In this chapter we will be using the hmohiv and the uis data sets.
Table 3.1, p. 98.
Proportional hazard model containing only the predictor age.
proc phreg data=hmohiv;
model time*censor(0) = age;
run;
<output omitted>
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.08141 0.01744 21.8006 <.0001 1.085
Table 3.2, p. 103.
Proportional hazard model with predictors age, drug and the interaction of age and drug. The data step is creating the interaction and proc phreg is running the model.
data interaction;
set hmohiv;
agedrug = age*drug;
run;
proc phreg data=interaction;
model time*censor(0) = age drug agedrug;
run;
<output omitted>
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 598.390 563.369
AIC 598.390 569.369
SBC 598.390 576.515
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.09423 0.02293 16.8939 <.0001 1.099
drug 1 1.18594 1.25651 0.8908 0.3453 3.274
agedrug 1 -0.00670 0.03374 0.0395 0.8425 0.993
Table 3.3, p. 105.
The proportional hazard model with the predictors age and drug.
proc phreg data=hmohiv;
model time*censor(0) = age drug;
run;
<output omitted>
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 598.390 563.408
AIC 598.390 567.408
SBC 598.390 572.172
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.09151 0.01849 24.5009 <.0001 1.096
drug 1 0.94108 0.25550 13.5662 0.0002 2.563
The log partial likelihood test comparing the two models, p. 105. The test statistic G is equal to the difference between the -2 LOG L values in the column called With Covariates found in the Model Fit Statistic table of the output for both models. For this comparisons the test statistic G = 563.408 – 563.369 = 0.039 which when compared to the Chi-square distribution with 1 degree of freedom gives a p-value of 0.841. The null hypothesis is that the models fit the data equally well and based on the p-value it is not possible to reject this null hypothesis. The conclusion is that the larger model which includes the interaction does not fit the data better than the smaller model. So, the interaction is not a significant predictor.
Table 3.4, p. 108.
Comparing the Efron, Breslow and Exact methods of breaking ties.
title "Exact";
proc phreg data=hmohiv;
model time*censor(0) = age drug / ties=exact;
run;
<output omitted>
Exact
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.09768 0.01874 27.1731 <.0001 1.103
drug 1 1.02263 0.25716 15.8132 <.0001 2.781
title "Breslow";
proc phreg data=hmohiv;
model time*censor(0) = age drug;
run;
<output omitted>
Breslow
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.09151 0.01849 24.5009 <.0001 1.096
drug 1 0.94108 0.25550 13.5662 0.0002 2.563
title "Efron";
proc phreg data=hmohiv;
model time*censor(0) = age drug / ties=efron;
run;
title;
<output omitted>
Efron
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
age 1 0.09714 0.01864 27.1597 <.0001 1.102
drug 1 1.01670 0.25622 15.7459 <.0001 2.764