Getting Started
You can use the LIFETEST procedure to compute nonparametric estimates of the survivor functions, to compare survival curves, and to compute rank tests for association of the failure time variable with covariates.
For simple analyses, only the PROC LIFETEST and TIME statements are required. Consider a sample of survival data. Suppose that the time variable is T and the censoring variable is C with value 1 indicating censored observations. The following statements compute the product-limit estimate for the sample:
proc lifetest; time t*c(1); run;
You can use the STRATA statement to divide the data into various strata. A separate survivor function is then estimated for each stratum, and tests of the homogeneity of strata are performed. However, if the GROUP= option is also specified in the STRATA statement, the GROUP = variable is used to identify the samples whose survivor functions are to be compared and the STRATA variables are used to define the strata for the stratified tests. You can specify covariates in the TEST statement. PROC LIFETEST computes linear rank statistics to test the effects of these covariates on survival.
For example, consider the results of a small randomized trial on rats. Suppose you randomize 40 rats that have been exposed to a carcinogen into two treatment groups ( Drug X and Placebo ). The event of interest is death from cancer induced by the carcinogen. The response is the time from randomization to death. Four rats died of other causes; their survival times are regarded as censored observations. Interest lies in whether the survival distributions differ between the two treatments .
The data set Exposed contains four variables: Days (survival time in days from treatment to death), Status (censoring indicator variable: 0 if censored and 1 if not censored), Treatment (treatment indicator), and Sex (gender: F if female and M if male).
proc format; value Rx 1='Drug X' 0='Placebo'; data exposed; input Days Status Treatment Sex $ @@; format Treatment Rx.; datalines; 179 1 1 F 378 0 1 M 256 1 1 F 355 1 1 M 262 1 1 M 319 1 1 M 256 1 1 F 256 1 1 M 255 1 1 M 171 1 1 F 224 0 1 F 325 1 1 M 225 1 1 F 325 1 1 M 287 1 1 M 217 1 1 F 319 1 1 M 255 1 1 F 264 1 1 M 256 1 1 F 237 0 0 F 291 1 0 M 156 1 0 F 323 1 0 M 270 1 0 M 253 1 0 M 257 1 0 M 206 1 0 F 242 1 0 M 206 1 0 F 157 1 0 F 237 1 0 M 249 1 0 M 211 1 0 F 180 1 0 F 229 1 0 F 226 1 0 F 234 1 0 F 268 0 0 M 209 1 0 F ;
PROC LIFETEST is invoked to compute the product-limit estimate of the survivor function for each treatment and to compare the survivor functions between the two treatments.
ods html; ods graphics on; proc lifetest data=Exposed; time Days*Status(0); strata Treatment; run; ods graphics off; ods html close;
In the TIME statement, the survival time variable, Days , is crossed with the censoring variable, Status , with the value 0 indicating censoring. That is, the values of Days are considered censored if the corresponding values of Status are 0; otherwise , they are considered as event times. In the STRATA statement, the variable Treatment is specified, which indicates that the data are to be divided into strata based on the values of Treatment . PROC LIFETEST computes the product-limit estimate for each stratum and tests whether the survivor functions are identical across strata. The experimental ODS GRAPHICS statement is specified to display the estimated survivor functions.
The results of the analysis are displayed in the following figures.
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The LIFETEST Procedure Stratum 1: Treatment = Drug X Product-Limit Survival Estimates Survival Standard Number Number Days Survival Failure Error Failed Left 0.000 1.0000 0 0 0 20 171.000 0.9500 0.0500 0.0487 1 19 179.000 0.9000 0.1000 0.0671 2 18 217.000 0.8500 0.1500 0.0798 3 17 224.000* . . . 3 16 225.000 0.7969 0.2031 0.0908 4 15 255.000 . . . 5 14 255.000 0.6906 0.3094 0.1053 6 13 256.000 . . . 7 12 256.000 . . . 8 11 256.000 . . . 9 10 256.000 0.4781 0.5219 0.1146 10 9 262.000 0.4250 0.5750 0.1135 11 8 264.000 0.3719 0.6281 0.1111 12 7 287.000 0.3188 0.6813 0.1071 13 6 319.000 . . . 14 5 319.000 0.2125 0.7875 0.0942 15 4 325.000 . . . 16 3 325.000 0.1063 0.8938 0.0710 17 2 355.000 0.0531 0.9469 0.0517 18 1 378.000* 0.0531 . . 18 0 NOTE: The marked survival times are censored observations.
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Figure 40.1: Survivor Function Estimate for the Drug X-Treated Rats
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Quartile Estimates Point 95% Confidence Interval Percent Estimate [Lower Upper) 75 319.000 262.000 325.000 50 256.000 255.000 319.000 25 255.000 217.000 256.000 Mean Standard Error 271.131 11.877 NOTE: The mean survival time and its standard error were underestimated because the largest observation was censored and the estimation was restricted to the largest event time.
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Figure 40.2: Summary Statistics of Survival Times for Drug X-Treated Rats
The median survival time for rats in this treatment is 256 days. The mean and standard error are also displayed; however, it is noted that these values are underestimated because the largest observed time is censored and the estimation is restricted to the largest event time.
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Stratum 2: Treatment = Placebo Product-Limit Survival Estimates Survival Standard Number Number Days Survival Failure Error Failed Left 0.000 1.0000 0 0 0 20 156.000 0.9500 0.0500 0.0487 1 19 157.000 0.9000 0.1000 0.0671 2 18 180.000 0.8500 0.1500 0.0798 3 17 206.000 . . . 4 16 206.000 0.7500 0.2500 0.0968 5 15 209.000 0.7000 0.3000 0.1025 6 14 211.000 0.6500 0.3500 0.1067 7 13 226.000 0.6000 0.4000 0.1095 8 12 229.000 0.5500 0.4500 0.1112 9 11 234.000 0.5000 0.5000 0.1118 10 10 237.000 0.4500 0.5500 0.1112 11 9 237.000* . . . 11 8 242.000 0.3937 0.6063 0.1106 12 7 249.000 0.3375 0.6625 0.1082 13 6 253.000 0.2812 0.7188 0.1038 14 5 257.000 0.2250 0.7750 0.0971 15 4 268.000* . . . 15 3 270.000 0.1500 0.8500 0.0891 16 2 291.000 0.0750 0.9250 0.0693 17 1 323.000 0 1.0000 0 18 0 NOTE: The marked survival times are censored observations.
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Figure 40.3: Survivor Function Estimate for Placebo-Treated Rats
Figure 40.3 and Figure 40.4 display the survival estimates and the summary statistics of the survival times for Placebo ( Treatment =0). The median survival time for rats in this treatment is 235 days.
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Quartile Estimates Point 95% Confidence Interval Percent Estimate [Lower Upper) 75 257.000 237.000 291.000 50 235.500 209.000 253.000 25 207.500 180.000 234.000 Mean Standard Error 235.156 10.211
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Figure 40.4: Summary Statistics of Survival Times for Placebo-Treated Rats
A summary of the number of censored and event observations is shown in Figure 40.5.Thefigure lists, for each stratum, the number of event and censored observations, and the percentage of censored observations.
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Summary of the Number of Censored and Uncensored Values Percent Stratum Treatment Total Failed Censored Censored 1 Drug X 20 18 2 10.00 2 Placebo 20 18 2 10.00 ---------------------------------------------------------------- Total 40 36 4 10.00
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Figure 40.5: Number of Event and Censored Observations
Results of the comparison of survival curves between the two treatments are shown in Figure 40.6. The rank tests for homogeneity indicate a significant difference between the treatments ( p =0.0175 for the log-rank test and p =0.0249 for the Wilcoxon test). Rats treated with Drug X live significantly longer than those treated with Placebo . The log-rank test, which places more weight on larger survival times, is more significant than the Wilcoxon test, which places more weight on early survival times. As noted earlier, the exponential model is not appropriate for the given survival data; consequently, the result of the likelihood ratio test should be ignored.
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Test of Equality over Strata Pr > Test Chi-Square DF Chi-Square Log-Rank 5.6485 1 0.0175 Wilcoxon 5.0312 1 0.0249 2Log(LR) 0.1983 1 0.6561 | |
Figure 40.6: Results of the 2-sample Tests
Figure 40.7: Plot of Estimated Survivor Functions (Experimental)
This graphical display is requested by specifying the experimental ODS GRAPHICS statement. For general information about ODS graphics, see Chapter 15, Statistical Graphics Using ODS. For specific information about the graphics available in the LIFETEST procedure, see the section ODS Graphics on page 2190.
Next, suppose male rats and female rats are thought to have different survival rates, and you want to assess the treatment effect while adjusting for the gender differences. By specifying the variable Sex in the STRATA statement as a stratifying variable and by specifying the variable Treatment in the GROUP= option, you can carry out a stratified test to test Treatment while adjusting for Sex . The test statistics are computed by pooling over the strata defined by the values of Sex , thus controlling for the effect of Sex . The NOTABLE option is added to the PROC LIFETEST statement to avoid estimating a survival curve for each gender.
proc lifetest data=Exposed notable; time Days*Status(0); strata Sex / group=Treatment; run;
Results of the stratified tests are shown in Figure 40.8. The treatment effect is statistically significant for both the log-rank test ( p =0.0071) and the Wilcoxon test ( p =0.0150). As compared to the results of the unstratified tests in Figure 40.6,the significance of the treatment effect has been sharpened by controlling for the effect of the gender of the subjects.
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The LIFETEST Procedure Stratified Test of Equality over Group Pr > Test Chi-Square DF Chi-Square Log-Rank 7.2466 1 0.0071 Wilcoxon 5.9179 1 0.0150
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Figure 40.8: Results of the Stratified 2-sample Tests
Since Treatment is a binary variable, another way to study the effect of Treatment is to carry out a censored linear rank test with Treatment as an independent variable. Although this test is less popular than the 2-sample test, nevertheless, in situations where the independent variables are continuous and are difficult to discretize, it may be infeasible to perform the k -sample test. To compute the censored linear rank statistics to test the Treatment effect, Treatment is specified in the TEST statement.
proc lifetest data=Exposed notable; time Days*Status(0); test Treatment; run;
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The LIFETEST Procedure Univariate Chi-Squares for the Wilcoxon Test Test Standard Pr > Variable Statistic Deviation Chi-Square Chi-Square Treatment 3.9525 1.7524 5.0875 0.0241 Univariate Chi-Squares for the Log-Rank Test Test Standard Pr > Variable Statistic Deviation Chi-Square Chi-Square Treatment 6.2708 2.6793 5.4779 0.0193
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Figure 40.9: Results of Linear Rank Tests of Treatment
Results of the linear rank tests are shown Figure 40.9. The p -values are very similar to those of the 2-sample tests in Figure 40.6.
With Sex as a prognostic factor that you want to control, you can compute a stratified linear rank statistic to test the effect of Treatment by specifying Sex in the STRATA statement and Treatment in the TEST statement. The NOTEST option is specified in the STRATA statement to suppress the k -sample tests for Sex .
proc lifetest data=Exposed notable; time Days*Status(0); strata Sex / notest; test Treatment; run;
Results of the stratified linear rank tests are shown in Figure 40.10.The p -values are very similar to those of the stratified 2-sample tests in Figure 40.8.
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The LIFETEST Procedure Univariate Chi-Squares for the Wilcoxon Test Test Standard Pr > Variable Statistic Deviation Chi-Square Chi-Square Treatment 4.2372 1.7371 5.9503 0.0147 Univariate Chi-Squares for the Log-Rank Test Test Standard Pr > Variable Statistic Deviation Chi-Square Chi-Square Treatment 6.8021 2.5419 7.1609 0.0075
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Figure 40.10: Result of Stratified Linear Rank Tests of Treatment
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