Discrepancy Between Median Survival Time from Quartiles and Product Limit Estimates in PROC LIFETEST

[smackerz1988]

Hello,

I'm encountering a discrepancy between the median survival times calculated using the quartiles method and the Kaplan-Meier product limit estimates in PROC LIFETEST. Here's a brief overview of my issue:

I am analysing survival data using PROC LIFETEST  with the following SAS code:

proc lifetest data=adtte00 method=km conftype=LOGLOG plots=survival outsurv=survesti;
   time avalM * CNSR(1);
   strata trt; 
   by paramcd;
   ods output ProductLimitEstimates=KM_Estimates CensoredSummary=stat00 quartiles=med00 homtests=logrank00;
run;

When I check the output, I notice that the median survival time from the quartiles output (dataset med00) does not match the median calculated from the Kaplan-Meier product limit estimates (dataset KM Estimates). Specifically:

• Quartiles Output (med00) The median survival time is provided directly as the 50th percentile. (11.5811)
• Product Limit Estimates (KM Estimates) The closest time point where the survival probability crosses below 0.5 is used, leading to a slightly different median value. (11.3347)

Here’s an example of the output I’m seeing:

Quartiles Output:

data med00;
    input Paramcd $ Stratum trt $ Percent Estimate Transform $ LowerLimit UpperLimit;
    datalines;
TTD 1 trt1 50 11.5811 LOGLOG 10.4148 14.7844
TTD 2 trt2 50 4.5010 LOGLOG 3.5483 5.9138
;
run;

proc print data=med00;
run;

Product Limit Estimates:

data KM_Estimates;
    input Paramcd $ Stratum trt $ avalm Censor Survival Failure StdErr Failed Left;
    datalines;
TTD 1 trt1 11.2361 0 0.5112 0.4888 0.0375 86 92
TTD 1 trt1 11.3018 0 0.5056 0.4944 0.0375 88 90
TTD 1 trt1 11.3347 0 0.5000 0.5000 0.0375 89 89
TTD 1 trt1 11.8275 0 0.4944 0.5056 0.0375 90 88
TTD 1 trt1 12.4189 0 0.4888 0.5112 0.0375 91 87
;
run;

proc print data=KM_Estimates;
run;

Log:

25         GOPTIONS ACCESSIBLE;
26         ods output ProductLimitEstimates=KM_Estimates CensoredSummary=stat00 quartiles=med00 homtests= logrank00;
27         proc lifetest data=adtte00 method= km conftype=LOGLOG plots=survival outsurv = survesti;
28            time avalM * CNSR(1);
29            strata trt;
30            by paramcd;
31         run;

NOTE: Graph's name, LIFETEST, changed to LIFETES5. LIFETEST is already used or not a valid SAS name.
NOTE: 19648 bytes written to 
      /saswork/SAS_workA34500001BB1_dsprgn05.ds-grid.com/SAS_workD3CA00001BB1_dsprgn05.ds-grid.com/lifetest5.png.
NOTE: The above message was for the following BY group:
      Parameter Code=TTD
NOTE: The data set WORK.LOGRANK00 has 3 observations and 5 variables.
NOTE: The data set WORK.MED00 has 6 observations and 8 variables.
NOTE: The data set WORK.STAT00 has 3 observations and 8 variables.
NOTE: The data set WORK.KM_ESTIMATES has 271 observations and 10 variables.
NOTE: The data set WORK.SURVESTI has 235 observations and 8 variables.
NOTE: PROCEDURE LIFETEST used (Total process time):
      real time           0.90 seconds
      cpu time            0.84 seconds

Why is there a discrepancy between the median survival times calculated using the quartiles method and the product limit estimates?. Are there specific steps I can take to ensure consistent median calculations between these methods?. Any insights or guidance on resolving this discrepancy would be greatly appreciated!

[ballardw]

Please share the LOG from running your Proc Lifetest code, include the code and any notes or messages generated.

[smackerz1988]

@ballardw  Post Updated!.

[Reeza]

What is the data point just prior to the 50% percentile on the KM_Estimates table? Being a step function I think it takes a less than, not less than or equal to calculation so it's likely the prior data point.

[smackerz1988]

@Reeza  I've updated KM_Estimates table for range of values around 50% percentile

[Ksharp]

You'd better post it at Stat Forum:
https://communities.sas.com/t5/Statistical-Procedures/bd-p/statistical_procedures

My opinion is since these are two different ways to calculate median, you would not expect to get the same result.

[FreelanceReinh · Accepted solution]

Hello @smackerz1988,

---

@smackerz1988 wrote:

Why is there a discrepancy between the median survival times calculated using the quartiles method and the product limit estimates?

---

I don't see a discrepancy. Your KM_Estimates output shows that the 89th of the 178 survival times in stratum trt1 is 11.3347 and the 90th is 11.8275. Hence, all real numbers t in the closed interval [11.3347, 11.8275] qualify as "crude" (empirical) median survival times because the survival times of at least 50% (i.e., 89) of the subjects are ≤t and the survival times of at least 50% of the subjects are ≥t.

In this situation it is common to define the midpoint of that interval, (11.3347 + 11.8275)/2 = 11.5811 as the median (cf. the default QNTLDEF=5 option of PROC MEANS). This is analogous to what PROC LIFETEST does with the Kaplan-Meier estimates Ŝ(t) of the survival function: see the example for the first quartile in section Breslow, Fleming-Harrington, and Kaplan-Meier Methods of the documentation, where it says: "If Ŝ(t) is exactly equal to 0.75 from t_j to t_j+1, the first quartile is taken to be (t_j + t_j+1)/2." Which explains why you got 11.5811 as the point estimate for the median in your quartiles output med00, given that Ŝ(t) is exactly equal to 0.5 from 11.3347 to 11.8275.

[smackerz1988]

Thanks @FreelanceReinh !