The ICPHREG Procedure

Example 64.3 Fitting Stratified Weibull Models

(View the complete code for this example.)

This example illustrates how to fit stratified Weibull models by using the STRATA statement.

The following data set contains survival times for 36 patients who were diagnosed with a malignant kidney tumor. Most of the patients received the therapy of nephrectomy (removal of all or part of the kidney).

data hyper;
   input nephrectomy age time status @@;
   datalines;
0   1    9      1
0   1    6      1
0   1   21      1
0   2   15      1
0   2    8      1
0   2   17      1
0   3   12      1
1   1  104      0
1   1    9      1
1   1   56      1
1   1   35      1
1   1   52      1
1   1   68      1
1   1   77      0
1   1   84      1
1   1    8      1
1   1   38      1
1   1   72      1
1   1   36      1
1   1   48      1
1   1   26      1
1   1  108      1
1   1    5      1
1   2  108      0
1   2   26      1
1   2   14      1
1   2  115      1
1   2   52      1
1   2    5      0
1   2   18      1
1   2   36      1
1   2    9      1
1   3   10      1
1   3    9      1
1   3   18      1
1   3    6      1
;

The following statements convert the censored times into intervals:

data hyper;
   set hyper;
   left = time;
   if status = 0 then right = .;
   else right = time;
run;

The following statements fit a stratified Weibull proportional hazards model:

ods graphics on;
proc icphreg data=hyper plot(timerange=(0,125))=surv;
   class Age(desc);
   strata Nephrectomy;
   model (Left, Right) = Age / basehaz=splines(df=1);
run;

The "Cubic Splines Parameters" table, shown in Output 64.3.1, contains the parameters for the cubic splines. Because DF=1, it is equivalent to a Weibull distribution.

Output 64.3.1: Baseline Hazard Parameters

The ICPHREG Procedure

Cubic Spline Parameters
StrataCoefficientKnot
0Coef16
0Coef221
1Coef35
1Coef4115


The "Fit Statistics" table, shown in Output 64.3.2, contains the fit statistics.

Output 64.3.2: Model Fit Statistics

Fit Statistics
-2 Log Likelihood279.422
AIC (Smaller is Better)291.422
AICC (Smaller is Better)294.319
BIC (Smaller is Better)300.923


The table of parameter estimates is displayed in Output 64.3.3.

Output 64.3.3: Model Parameter Estimates

Analysis of Maximum Likelihood Parameter Estimates
EffectageDFEstimateStandard
Error
95% Confidence LimitsChi-SquarePr > ChiSq
Coef1 1-9.27502.8327-14.8269-3.7231  
Coef2 13.32520.99181.38145.2690  
Coef3 1-5.24080.8785-6.9627-3.5188  
Coef4 11.28610.20130.89151.6806  
age311.80050.59660.63122.96979.110.0025
age210.12720.4017-0.66020.91460.100.7515
age100.0000     


Output 64.3.4 and Output 64.3.5 show the predicted survival curves for the two strata at the reference level.

Output 64.3.4: Estimated Survival Curve at the Reference Level for Stratum 1

Estimated Survival Curve at the Reference Level for Stratum 1


Output 64.3.5: Estimated Survival Curve at the Reference Level for Stratum 2

Estimated Survival Curve at the Reference Level for Stratum 2