Proportionality Assumption for Survival/Hazard analysis on multiple failure-time data

[Wossenseged Jemberie]

Hi,
I am conducting multiple failure analysis (hospitalization) with discontinuous risk interval with the Stata -stcox- extensions. However I am not able to find any note either from Stata or methodological papers if the proportionality assumption is relaxed for recurrent event analysis or if not, how to check proportionality assumption on such data. I had performed stphtest after time to first event analysis (standard cox), and it shows proportional assumption holds true (p-vale >0.05 for global and all covariates). But when the analysis is done with time gap (discontinuous risk interval, with reset start time after each event), the -stphtest gives opposite result. I also find it difficult to understand why we should assume the hazard stays proportional when the event occurs repeatedly (and when some have only 1-2 entry and others have 10-100 hospitalization)
I will be grateful if you can point me to the right direction

• 1. Should the proportionality assumption hold true for multiple failure analysis?

• 2. Does Stata have special procedure for checking the assumption (if yes to question 1)? For example, can I perform -stphtest on robust variance-covariance matrix?

thank you very much

[Paul Dickman]

• 1. Should the proportionality assumption hold true for multiple failure analysis?

There are two distinct questions here.

1a. Does the default Cox model assume proportional hazards for multiple failure data?
Here the answer is yes. Note that you cannot conclude "the proportional assumption holds true". PH is the null hypothesis and you cannot prove the null hypothesis. This concept is especially important for what you are doing because when restricting to only the first event you have less data and less power to reject H0. Note also that you are just testing against one specific alternative hypothesis and not all ways in which the hazards can be non-proportional. It's possible you rejected PH when analysing the complete data, but not when restricting to first events, because the hazards for subsequent failures have a different shape, or because you have more power, or a combination of the two.

1b. is proportional hazards a reasonable assumption for a specific instance of multiple failure data?
This depends on your specific data generating process.

• 1. Does Stata have special procedure for checking the assumption (if yes to question 1)? For example, can I perform -stphtest on robust variance-covariance matrix?

I don't have sufficient confidence in my answer that I would be willing to write it here. I'll leave this question for someone else to answer.