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Proc lifetest survival probabilities mismatch

I am running proc lifetest on a dataset that has no censored observation, only events.

At T1 (time) = 1, Number at Risk = 33 so the survival probability should be 33/46 = 0.717.=?  Why does SAS give me 0.695?

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Re: Proc lifetest survival probabilities mismatch

Hi @CHELS,

The numbers of subjects at risk (denoted by Yi in section Breslow, Fleming-Harrington, and Kaplan-Meier Methods of the PROC LIFETEST documentation) are counted "just prior to" the respective time points, whereas the (estimated) "Survival Probability" (here: Kaplan-Meier survival estimate) takes the events at the respective time points already into account. So, at T1=1 the 13 events prior to T1=1 have left 33 of the 46 subjects in stratum 1. Then the survival estimate is updated with the 14th event, occurring at T1=1: The previous estimate (33/46=0.717...) is multiplied by (1-1/33) resulting in 32/46=0.695...

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Super User

Re: Proc lifetest survival probabilities mismatch

Show as a minimum the code you are using.

Did you look closely at row 12 and the probability. Looks awful close you your expected. Perhaps you are missing a consideration of which row you need to examine.

Super User

Re: Proc lifetest survival probabilities mismatch

Did you specify Method = LT? Or a different method? How did you choose to handle ties?

@CHELS wrote:

I am running proc lifetest on a dataset that has no censored observation, only events.

At T1 (time) = 1, Number at Risk = 33 so the survival probability should be 33/46 = 0.717.=?  Why does SAS give me 0.695?

Re: Proc lifetest survival probabilities mismatch

Hi @CHELS,

The numbers of subjects at risk (denoted by Yi in section Breslow, Fleming-Harrington, and Kaplan-Meier Methods of the PROC LIFETEST documentation) are counted "just prior to" the respective time points, whereas the (estimated) "Survival Probability" (here: Kaplan-Meier survival estimate) takes the events at the respective time points already into account. So, at T1=1 the 13 events prior to T1=1 have left 33 of the 46 subjects in stratum 1. Then the survival estimate is updated with the 14th event, occurring at T1=1: The previous estimate (33/46=0.717...) is multiplied by (1-1/33) resulting in 32/46=0.695...

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