Cox regression with enourmous Hazard Ratio (logarithmic)

[Philipp Gild]

Dear forum,

I have encountered a problem in that for my Cox regression my output gives enourmous Hazard Ratios for my outcome (disease recurrece), such as 1.33e+10.


A) First I would like to give you the specifics:
I have a project, where I assess the impact of reponse to chemotherapy (i.e. "pres" a variable with 3 levels: complete, partial, no response) on disease recurrence within my given follow up. Displayed graphically (Kaplan Meier plot), the outcome is quite impressive:

However, when I run a Cox regression, adjusted for other variables (age, smoking status, etc), my ouput displays grotesque Hazard ratios:

The problem remains, even if a run a univariable model. I believe the issue here is collinearity in that for example "No response" predicts my outcome (disease recurrence) almost perfectly and therefore has a very large HR.

B) My questions are be the following:

-Do you find my explanation plausible (s. above)?
-Is there a solution, i.e. a way to run the cox model (uni- or multivariable; as I only have 37 events I´d fear an overfit) and have more approachible HRs?
-Lastly, if I run the cox regression without a prefix/factorial (by that I mean omitting "i." for categorial) for my independent variable of choice ("pres"), I get a HR of approximately 6. I do however not know, how STATA runs that specific regression, if "pres" is not specified:
Does it treat the first level of the variable as reference against the other two levels which would be "partial" and "no response"?

Thank you very much for your help and taking time to read this !

[Clyde Schechter]

Your explanation is correct. Based on the graph you show, it appears that there are no failure events at all in the group called Complete Response. So the hazard for that group is zero, which means that the hazard ratio for any group that does have an event will be infinitely large. The huge numbers you are getting are Stata's approximation to infinity.

Replacing i.pres by pres causes Stata to treat pres as if it were a continuous variable, and there is no "reference" value. In this case, it is able to come up with a finite estimate of the hazard ratio because it, in effect, blends the infinite hazard ratio between Complete and Partial responses with the finite hazard ratio between Partial and No Response and finds a "compromise" value. This is meaningful only if in some meaningful sense a Partial Response can be considered to be half way between no response and complete response (which I doubt). I think the best thing you can do is to simply note that no failure events occur in the Complete Response group, and then do the Cox modeling just with the No and Partial response groups. (Alternatively, find a more complete data set that has an appreciable number of failure events in the Complete Response group, if that's feasible.)

[Joseph Coveney]

I don't get this: if there is only a "Partial response" or a "No response", then how could there be such a thing as "Disease recurrence"? It never unrecurred in the first place.

Clyde, if most on the list are like me, then few are very familiar with this kind of thing; could you edify us here?

[Clyde Schechter]

Well, we would have to ask the original poster to be sure what he has in mind, but I assume that the partial or no response refers to the state of the original tumor, where as the recurrence outcome refers to the development of metastatic tumor at a distant site. So, for example, with breast cancer one might first classify patients according to how the breast tumor itself, and nearby lymph nodes, respond to initial treatment with, say, surgery, radiation and chemotherapy or hormonal treatment, and then follow those patients observing the time to development of tumor spread to, for example, lung, brain, liver, or bones (those are the commonest sites of breast cancer metastasis).

I agree that the term "recurrence" is a bit misleading if the original tumor did not appear to completely disappear. But the term is sometimes used that way. And, then again, even when we have what appears clinically to be a complete response, at the microscopic level there may be surviving nests of cancer cells that we cannot detect with existing technologies and that go on to seed metastatic disease. So even in patients that we characterize as having a complete response, the tumor may never have really unrecurred either.

[Joseph Coveney]

Clyde, thanks. What you describe (early outcome as a predictor of later outcome) makes sense of it to me now.

So, I guess that a better y-axis label on the Kaplan-Meier graph would be something like "Distant-metastasis-free Survival". If I were a medical journal editor, a label indicating that all three groups had 100% "Disease recurrence" at time zero would make me uncomfortable somehow.

[Philipp Gild]

First of all thank you both and especially Clyde for the swift reply; this is very helpful and reassuring!

As for the y-axis label you are correct: It has to read "reccurrence-free survival".
The term "recurrence" in this case needs some explanation; these were patients who had upfront chemotherapy and then received tumor extirpation. The definition of response the chemotherapy is based on the disease stage taken from the tumor specimen in comparison to the stage prior to chemotherapy (i.e. the tumor could have "shrunk" or show partial response, there could be no evidence of disease "complete response", or tumor the same size or bigger "no response" )

[Joseph Coveney]

Thanks for the closure and follow-up with clarification of the nomenclature.