Interpreting hazard rate for multiple failures

[HeeSung Kim]

Dear Statalister,

This question has been cross-posted here, but it has not received much traffic nor answers: http://stats.stackexchange.com/quest...tiple-failures

I'm trying to run survival analysis of Cox proportional model with panel data that consists of IDs and time variable. Each individuals are allowed to fail more than once in the sample period. My understanding of hazard rate is probability of the individual failing at time t, given that he has not failed before. However, I failed to understand the interpretation of hazard rate for cases with multiple failures.

I'm running my analysis in Stata with the following command:

stset time, id(id) failure(fail==1) exit(time .) origin(time==0)
stcox x1 x2 x3
stcurve, hazard

How can I interpret the graph producted by stcurve, hazard, if multiple failure per subject is observed in the data? Does it still mean probability of the individual failing at time t, given that he has not failed before time t, of does it mean probability of the individual failing at time t, given that he has not failed since the last failure?

My dataset is structed in the following way:

clear
input float ID str8 Time float(fail x1 x2 x3 time)
1 "1990mar1" 0   .3488717  .5551032 .11966132 120
1 "1990jun1" 0   .2668857   .875991  .7542434 121
1 "1990sep1" 1   .1366463 .20470947  .6950234 122
1 "1990dec1" 0 .028556867  .8927587  .6866152 123
1 "1991mar1" 1   .8689333  .5844658  .9319346 124
1 "1991jun1" 0   .3508549  .3697791  .4548882 125
2 "1990mar1" 0  .07110509  .8506309  .0674011 120
2 "1990jun1" 1  .32336795  .3913819  .3379889 121
end

x1 x2 x3 is random variables generated through runiform just for the purpose of this post. Is this the right setup for the data to be analyzed as multiple failure per subject? Is specifying exit(time .) enough to prepare the data as multiple failure analysis?

[Clyde Schechter]

Does it still mean probability of the individual failing at time t, given that he has not failed before time t, of does it mean probability of the individual failing at time t, given that he has not failed since the last failure?

It means the probability of failing at time t given that he has not failed since the last failure (or since becoming at risk if there are no previous failures). In effect, the clock gets reset to zero at each failure.

[HeeSung Kim]

Thank you Clyde! That was what I was hoping for.

[Steve Samuels]

Your setup is not correct for multiple failure time. See: http://www.stata.com/support/faqs/st...ure-time-data/