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I'm running a survival analysis to find out if some kind of regulatory intervention affects time to firms' default. After running the model I get the following results:

Hazard ratio: 1.00 P-value: 0.01

I know that hazard ratio below 1 means reduced risk of death (in this case default) and the hazard ratio above 1 means increased risk. Thus, the ratio of 1 means that risk is not affected. So what does low p-value mean in this case? Is there a significant impact of regulation as suggested by p-value or no as suggested by hazard ratio?

And one more question - should I be worried about p-value = 0.000? Does it indicate some problem with the model? Isn't this value too good?

EDIT:

to add more details of my model

  • I have over 134 thosuand firms, out of which around 6% experienced the default
  • The regulatory intervention each firm receives is applied in different point of time, and each firm can be subject to several interventions so I use survival analysis with time-varying covariates and prepare the dataset as described e.g. here:
  • Since the regulatory intervention can be partially linked to the industry in which firm operates, I control for the industry NACE code
  • I use SAS to estimate the final model, in line with this paper (page 8). My code looks like below:
PROC PHREG DATA = my_dataset;
    CLASS industry;
    MODEL (tstart, tstop)*endpt(0) = reg_intervention_dummy industry/ TIES = EFRON RL; 
RUN;

where industry is industry NACE code, reg_intervention_dummy shows if firm was subject to regulatory intervention in a given tstart-tstop period, endpt shows if the event of default occured in this period

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    $\begingroup$ This probably comes from a numerically very small difference in a very large dataset. Please edit the question to specify how many individuals were involved and how many defaults. Also, please say more about the nature of the data, the choice of what firms to include, and the choice of time = 0 for the survival analysis. It's possible, for example, that the regulatory actions were taken because of an expectation that the firm would soon default. $\endgroup$
    – EdM
    Feb 29 at 17:06
  • $\begingroup$ @EdM Thanks, I've editted the post to add more details $\endgroup$ Mar 1 at 9:24

1 Answer 1

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With over 134000 cases and ~8400 events, even a very small difference of no practical significance can show up as "statistically significant," with very low p-values. Your reported hazard ratio of 1.00 is presumably rounded off from some value very close to that, say 1.004 or 0.996. You need to extract a less aggressively rounded value from the model and then apply your understanding of the subject matter to decide whether it has any practical significance. I suspect not.

It's still not clear to me what your choice of time reference for time = 0 is, and I can't say whether your use of time-varying covariates is handling the influence of regulatory interventions properly. But the problems you ask about in the question seem to arise from the very large data set.

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  • $\begingroup$ Thanks a lot. As for the t0. What I am investigating is the impact of some COVID-related regulatory changes. I start observing firms in 2020Q1, the first regulatory intervention in my sample was taken in 2020Q2. There were several actions taken over several next quarters, each firm can be subject to several interventions. That's why I use time-dependendent covariates. As I mentioned, to accomodate for the fact that the treatment was somehow linked to the industry, I control for the industry code in my model $\endgroup$ Mar 1 at 10:24

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