# Interpretation of hazard rate for multiple 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 time $t$. 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 produced 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 $t$, or does it mean probability of the individual failing at time $t$, given that he has not failed since the last failure?

If applicable, my dataset is structured in the following way:

id time fail
1  0  0
1  1  0
1  2  1
1  3  0
1  4  1
2  0  0
2  1  1


Related, but not fully answering my specific question: Cox proportional model with multiple failures for same subjects

• Take a look at my comments to Bjorn's answer to the question you have linked. You might not have seen those sources. – Michael R. Chernick Mar 31 '17 at 15:38
• @MichaelChernick Thank you for your reference! While I don't doubt that they will be useful, those references are not readily available to me. Do you have any insights from those references that may be applicable to my question? – Hosea Mar 31 '17 at 15:49
• – Hosea Apr 5 '17 at 14:46

As per answer from http://www.statalist.org/forums/forum/general-stata-discussion/general/1382221-interpreting-hazard-rate-for-multiple-failures, it turns out that in this particular case, the hazard rate is indeed probability of failing at time $t$, given that he has not failed since the last failure, which is what I desired to see.