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 predictorage.

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 predictorsage,drugand the interaction ofageanddrug. The data step is creating the interaction andproc phregis 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 predictorsageanddrug.

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

Gis 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 theEfron,BreslowandExactmethods 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 2.781title "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 2.563title "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