Fluorite | Level 6

## How can MST exists in Proc Lifetest when more than 50% of observations are censored?

Hello,

I'm using the following code to perform a survival analysis, just looking for the general survival information for my cases:

``````proc lifetest data = combine2;
time days_survived*censor(1);
run;``````

Here, I have 42 cases, 6 with missing censor information (and thus were deleted), and of the remaining 36, 63.89% were censored. This seems to be done appropriately given the output box I received from proc lifetest below:

It is my understanding that when over 50% of your cases are censored the median survival time does not exist. Using the proc lifetest code above, in which over 50% of my cases are censored, I received the following output:

Here is the other survival output in case it helps:

How is it that Proc Lifetest can compute a median survival time when more than 50% of the cases are censored? I'm using SAS 9.4.

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Accepted Solutions

## Re: How can MST exists in Proc Lifetest when more than 50% of observations are censored?

Hello @whitknee48 and welcome to the SAS Support Communities!

More than 50% of observations may be censored, but whether median survival time can be estimated or not also depends on when they were censored. The formula for the median survival time (see section "Breslow, Fleming-Harrington, and Kaplan-Meier Methods" in the documentation) uses Kaplan-Meier estimates (you used the default, KM, of option METHOD= of the PROC LIFETEST statement). Their values can very well drop below 0.5 if many subjects were censored early (as is the case in your data). Then the median survival time can be calculated. (Censored subjects are not expected to survive indefinitely.)

PROC LIFETEST usually plots a survival curve by default. So, you should have got this graph (showing that the survival curve clearly drops below 0.5):

If you added, say, 1000 to the days_survived values of sufficiently many censored observations, you'd see the difference in the survival curve and get a missing MST.

PS: Next time please post test data in the form of a data step, not as pictures.

2 REPLIES 2

## Re: How can MST exists in Proc Lifetest when more than 50% of observations are censored?

Hello @whitknee48 and welcome to the SAS Support Communities!

More than 50% of observations may be censored, but whether median survival time can be estimated or not also depends on when they were censored. The formula for the median survival time (see section "Breslow, Fleming-Harrington, and Kaplan-Meier Methods" in the documentation) uses Kaplan-Meier estimates (you used the default, KM, of option METHOD= of the PROC LIFETEST statement). Their values can very well drop below 0.5 if many subjects were censored early (as is the case in your data). Then the median survival time can be calculated. (Censored subjects are not expected to survive indefinitely.)

PROC LIFETEST usually plots a survival curve by default. So, you should have got this graph (showing that the survival curve clearly drops below 0.5):

If you added, say, 1000 to the days_survived values of sufficiently many censored observations, you'd see the difference in the survival curve and get a missing MST.

PS: Next time please post test data in the form of a data step, not as pictures.

Fluorite | Level 6

## Re: How can MST exists in Proc Lifetest when more than 50% of observations are censored?

Thanks @FreelanceReinh. This was very helpful!

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