Getting Started


PROC PHREG syntax is similar to that of the other regression procedures in the SAS System. For simple uses, only the PROC PHREG and MODEL statements are required.

Consider the following data from (Kalbfleisch and Prentice 1980). Two groups of rats received different pretreatment regimes and then were exposed to a carcinogen. Investigators recorded the survival times of the rats from exposure to mortality from vaginal cancer. Four rats died of other causes, so their survival times are censored. Interest lies in whether the survival curves differ between the two groups.

The data set Rats contains the variable Days (the survival time in days), the variable Status (the censoring indicator variable: 0 if censored and 1 if not censored), and the variable Group (the pretreatment group indicator).

  data Rats;   label Days ='Days from Exposure to Death';   input Days Status Group @@;   datalines;   143 1 0   164 1 0   188 1 0   188 1 0   190 1 0   192 1 0   206 1 0   209 1 0   213 1 0   216 1 0   220 1 0   227 1 0   230 1 0   234 1 0   246 1 0   265 1 0   304 1 0   216 0 0   244 0 0   142 1 1   156 1 1   163 1 1   198 1 1   205 1 1   232 1 1   232 1 1   233 1 1   233 1 1   233 1 1   233 1 1   239 1 1   240 1 1   261 1 1   280 1 1   280 1 1   296 1 1   296 1 1   323 1 1   204 0 1   344 0 1   ;   run;  

In the MODEL statement, the response variable, Days , is crossed with the censoring variable, Status , with the value that indicates censoring enclosed in parentheses (0). The values of Days are considered censored if the value of Status is 0; otherwise , they are considered event times.

  proc phreg data=Rats;   model Days*Status(0)=Group;   run;  

Results of the PROC PHREG analysis appear in Figure 54.1. Since Group takes only two values, the null hypothesis for no difference between the two groups is identical to the null hypothesis that the regression coefficient for Group is 0. All three tests in the Testing Global Null Hypothesis: BETA=0 table (see the section Testing the Global Null Hypothesis on page 3246) suggest that the survival curves for the two pretreatment groups may not be the same. In this model, the hazards ratio (or risk ratio) for Group ,defined as the exponentiation of the regression coefficient for Group , is the ratio of the hazard functions between the two groups. The estimate is 0.551, implying that the hazard function for Group =1 is smaller than that for Group =0. In other words, rats in Group =1 lived longer than those in Group =0.

start figure
  The PHREG Procedure   Model Information   Data Set                 WORK.RATS   Dependent Variable       Days          Days from Exposure to Death   Censoring Variable       Status   Censoring Value(s)       0   Ties Handling            BRESLOW   Summary of the Number of Event and Censored Values   Percent   Total       Event    Censored    Censored   40          36           4       10.00   Convergence Status   Convergence criterion (GCONV=1E-8) satisfied.   Model Fit Statistics   Without           With   Criterion     Covariates     Covariates     2 LOG L         204.317        201.438   AIC              204.317        203.438   SBC              204.317        205.022   Testing Global Null Hypothesis: BETA=0   Test                 Chi-Square       DF     Pr > ChiSq   Likelihood Ratio         2.8784        1         0.0898   Score                    3.0001        1         0.0833   Wald                     2.9254        1         0.0872   Analysis of Maximum Likelihood Estimates   Parameter     Standard                               Hazard   Variable   DF     Estimate        Error   Chi-Square   Pr > ChiSq      Ratio   Group       1   0.59590      0.34840       2.9254       0.0872      0.551  
end figure

Figure 54.1: Comparison of Two Survival Curves

In this example, the comparison of two survival curves is put in the form of a proportional hazards model. This approach is essentially the same as the log-rank (Mantel-Haenszel) test. In fact, if there are no ties in the survival times, the likelihood score test in the Cox regression analysis is identical to the log-rank test. The advantage of the Cox regression approach is the ability to adjust for the other variables by including them in the model. For example, the present model could be expanded by including a variable that contains the initial body weights of the rats.

Next, consider a simple test of the validity of the proportional hazards assumption. The proportional hazards model for comparing the two pretreatment groups is given by the following:

click to expand

The ratio of hazards is e ² 1 , which does not depend on time. If the hazard ratio changes with time, the proportional hazards model assumption is invalid. Simple forms of departure from the proportional hazards model can be investigated with the following time-dependent explanatory variable x = x ( t ):

click to expand

Here, log( t ) is used instead of t to avoid numerical instability in the computation. The constant, 5.4, is the average of the logs of the survival times and is included to improve interpretability. The hazard ratio in the two groups then becomes e ² 1 ˆ’ 5 . 4 ² 2 t ² 2 , where ² 2 is the regression parameter for the time-dependent variable x . The term e ² 1 represents the hazard ratio at the geometric mean of the survival times. A nonzero value of ² 2 would imply an increasing ( ² 2 > 0) or decreasing ( ² 2 < 0) trend in the hazard ratio with time.

The MODEL statement in this analysis also includes the time-dependent explanatory variable X , which is defined within the procedure by the programming statement that follows the MODEL statement. At each event time, subjects in the risk set (those alive just before the event time) have their X values changed accordingly .

  proc phreg data=Rats;   model Days*Status(0)=Group X;   X=Group*(log(Days)   5.4);   run;  
start figure
  The PHREG Procedure   Analysis of Maximum Likelihood Estimates   Parameter     Standard                               Hazard   Variable   DF     Estimate        Error   Chi-Square   Pr > ChiSq      Ratio   Group       1   0.59976      0.34837       2.9639       0.0851      0.549   X           1   0.22952      1.82489       0.0158       0.8999      0.795  
end figure

Figure 54.2: A Simple Test of Trend in the Hazard Ratio

The analysis of the parameter estimates is displayed in Figure 54.2. The Wald chisquare statistic for testing the null hypothesis that ² 2 = 0 is 0.0158. The statistic is not statistically significant when compared to a chi-square distribution with one degree of freedom ( p = 0 . 8999). Thus, you can conclude that there is no evidence of an increasing or decreasing trend over time in the hazard ratio. See the Examples section beginning on page 3272 for additional illustrations of PROC PHREG usage.




SAS.STAT 9.1 Users Guide (Vol. 5)
SAS.STAT 9.1 Users Guide (Vol. 5)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 98

flylib.com © 2008-2017.
If you may any questions please contact us: flylib@qtcs.net