The LIFEREG Procedure

Example 55.5 Probability Plotting—Right Censoring

The following statements create a SAS data set containing observed and right-censored lifetimes of 70 diesel engine fans (Nelson, 1982):

data Fan;
   input Lifetime Censor@@;
   Lifetime = Lifetime / 1000;
   datalines;
 450 0    460 1   1150 0   1150 0   1560 1
1600 0   1660 1   1850 1   1850 1   1850 1
1850 1   1850 1   2030 1   2030 1   2030 1
2070 0   2070 0   2080 0   2200 1   3000 1
3000 1   3000 1   3000 1   3100 0   3200 1
3450 0   3750 1   3750 1   4150 1   4150 1
4150 1   4150 1   4300 1   4300 1   4300 1
4300 1   4600 0   4850 1   4850 1   4850 1
4850 1   5000 1   5000 1   5000 1   6100 1
6100 0   6100 1   6100 1   6300 1   6450 1
6450 1   6700 1   7450 1   7800 1   7800 1
8100 1   8100 1   8200 1   8500 1   8500 1
8500 1   8750 1   8750 0   8750 1   9400 1
9900 1  10100 1  10100 1  10100 1  11500 1
;

Some of the fans had not failed at the time the data were collected, and the unfailed units have right-censored lifetimes. The variable LIFETIME represents either a failure time or a censoring time, in thousands of hours. The variable CENSOR is equal to 0 if the value of LIFETIME is a failure time, and it is equal to 1 if the value is a censoring time. The following statements use the LIFEREG procedure to produce the probability plot with an inset for the engine lifetimes:

ods graphics on;
proc lifereg data=Fan;
   model Lifetime*Censor( 1 ) = / d = Weibull;
   probplot
   ppout
   npintervals=simul;
   inset;
run;
ods graphics off;

The resulting graphical output is shown in Output 55.5.1. The estimated CDF, a line representing the maximum likelihood fit, and pointwise parametric confidence bands are plotted in the body of Output 55.5.1. The values of right-censored observations are plotted along the bottom of the graph. The Cumulative Probability Estimates table is also created in Output 55.5.2.

Output 55.5.1: Probability Plot for the Fan Data


Output 55.5.2: CDF Estimates

Cumulative Probability Estimates
Lifetime Cumulative
Probability
Simultaneous 95%
Confidence Limits
Kaplan-Meier
Estimate
Kaplan-Meier
Standard Error
Lower Upper
0.45 0.0071 0.0007 0.2114 0.0143 0.0142
1.15 0.0215 0.0033 0.2114 0.0288 0.0201
1.15 0.0360 0.0073 0.2168 0.0433 0.0244
1.6 0.0506 0.0125 0.2304 0.0580 0.0282
2.07 0.0666 0.0190 0.2539 0.0751 0.0324
2.07 0.0837 0.0264 0.2760 0.0923 0.0361
2.08 0.1008 0.0344 0.2972 0.1094 0.0392
3.1 0.1189 0.0436 0.3223 0.1283 0.0427
3.45 0.1380 0.0535 0.3471 0.1477 0.0460
4.6 0.1602 0.0653 0.3844 0.1728 0.0510
6.1 0.1887 0.0791 0.4349 0.2046 0.0581
8.75 0.2488 0.0884 0.6391 0.2930 0.0980