median survival not reached in proc lifetest when there are only 2 patients and one had event

[fengyuwuzu]

I have a subgroup with only 2 patients. One patient had event and the other one censored. Since there are only two patients and one had event, the median survival time would be the when the patient had event - at that time, survival rate reached 50%.

However, the median survival from Proc Lifetest is missing, which means not reached. 

Does any one has an explanation on this? Below is a dummy data set and a simple program for testing. 

data test;
input id aval cnsr;
datalines;
1 2.4 0
2 3.9 1
;
run;

ods select none;
proc lifetest data=test;
ods output means = mean_surv quartiles= median_surv;
time aval * cnsr(1);
run;
ods select all;

[fengyuwuzu]

I tried with 4 patients, 2 had events, and 2 censored later than event time. 

In this case, median survival is also missing. 

data test;
input id aval cnsr;
datalines;
1 2.4 0
2 3.4 0
3 4.2 1
4 5.4 1
;
run;
proc lifetest data=test method=km;
time aval * cnsr(1);
run;

6 patients, with half events and half censored, still the same. 

data test;
input id aval cnsr;
datalines;
1 2.4 0
2 3.4 0
3 4.2 0
4 5.4 1
5 5.5 1
6 6.0 1
;
run;

[fengyuwuzu]

This is a general situation: if we have even number of patients, half of them had events first, and rest of them censored and censored time later than all event time, in this case, median survival will be missing (median not reached). 

Not sure how to explain this. 

[fengyuwuzu · Accepted solution]

I contacted SAS tech support, and got the answer:

I think it's because your survival function never drops below 0.5 is why there is no median computed.

Just because half the patients have had an event doesn't mean the median has been reached.  It depends on the computed survival function.   The median is the first time at which the survival function goes below S(t) = 0.5.