[Kazim Julian]

Dear Clyde and all other statisticians,

I have a quick question regarding stcrreg. I have ran the model twice, once the regular way and received the SHR results for the cause specific hazard ratio and the second time using the ", noshr" command receiving the coefficients for the model. How would I interpret the coefficients for the model? For GA_Funded the coefficient is .27, would this mean if GA_Funded is equal to 1 that would increase the probability of having the event of interest by 27%? Thank you for your time.

[Clyde Schechter]

The best way to "interpret" the coefficients in this kind of model is to ignore them and focus on the SHRs. The coefficients are the natural logarithms of the SHRs. A unit difference in GA_funded will be associated with an difference of 0.28 (coefficient rounded to 2 decimal places) in the linear combination of coeficients and variables. But that linear combination on its own has no interpretation in natural terms. In particular it is certainly nothing like the probability of the event.

By contrast, the SHR's have a natural interpretation. A unit difference in GA_funded is associated with a 100*(1.32-1) = 32% increase in the incidence rate of the failure outcome.

[Kazim Julian]

Thank you very much Clyde, I really appreciate it. From your earlier replies the interpretation is: at any point in time the probability of experiencing the outcome of interest increased by 32% if GA_Funded = 1 given that the person has not experienced any event. From the reply you also state that the actual overall effect on probability due to my variable is difficult to estimate. Would you know how to do so in Stata? The research I am currently doing is asking for an overall effect. Thank you for your insight!

[Clyde Schechter]

the interpretation is: at any point in time the probability of experiencing the outcome of interest increased by 32% if GA_Funded = 1 given that the person has not experienced any event

That's not exactly right. At any point in time, the probability of experiencing the outcome of interest at that instant or, approximately, within a very short time after that instant, is 32% higher if GA_Funded = 1, given that the person has not experienced any event up to that point. But there is nothing that can be said from this about the overall probability of experiencing the event.

To get that, you have to do more work. First, you need to pick a time horizon beyond which you are not interested in looking. Because, often, in these models, if you follow time out to infinity, ultimately the probability of an event occurring is 100%, regardless of the values of the predictor variables. It looks like you are modeling something about events that happen to people, and, maybe, more specifically they are graduate students. If the failure event is some kind of career milestone, depending on what it is, it might make sense to estimate cumulative probabilities of event out to 5 or 10 years or something like that. If it has something to do with family formation and children entering higher education then perhaps a 20 year time horizon would make more sense. You have to figure out what is reasonable in your context.

Then, what you can do is, after your -stcrreg- model you can run -stcurve-. Do that with the -at1(GA_Funded = 0)- and -at2(GA_Funded = 1)- and -failure- options. That will give you a graph of the probability of a person with average values of the other covariates experiencing the failure event as a function of time under the conditions of GA_Funded = 0 and GA_Funded = 1. Now, reading results from a graph can be an iffy proposition. So use the -outfile()- option as well to save the numbers underlying the graph. Then in those saved numbers you will see the probabilities of outcomes under both conditions, for a person with average covariates, at the various points in time. Look for your horizon time in that data set (or the closest to it) and you will find the corresponding event probabilities in the same observations.

[Kazim Julian]

Thank you very much for your insight. That is really helpful

[Kazim Julian]

Hello Clyde, I have a question for you. Is there a way to formally test that the difference in probabilities are statistically different from 0 using the method you told me above?

[Clyde Schechter]

Testing whether an overall failure probability is zero in this kind of analysis does not make any sense.

[Kazim Julian]

I am more wondering if I can test whether the differences in probability of a person with average values of the other covariates experiencing the failure event is statistically different from 0. In the reply above we used GA_Funded = 0 and GA_Funded = 1. I was wondering if I can formally test that the difference in probabilities is statistically significant.