# Can I use Cox Regression here?

I have a data-set where I want to do a regression of survival probability given amount of drug injected into a subject. The more drug injected, the less likely the subject will survive after say, 3 months. Obviously the time-frame is fixed at 3 months and the independent variable (amount of drug injected) is not time-dependent. Can I still apply the Cox Regression model?

I'm not sure that I understand correctly. You say that the time-frame is fixed at three months. Does this mean that you only have data on survival yes/no after three months? In that case, you need to do a logistic regression. But if you have the date of death for each patient that dies, you can apply a Cox regression in principle.

The problem is that your dependent variable seems to be continuous. You then have to assume that there is a linear effect on the hazard ratio for the drug injected. So the difference between injecting 10 mg and 20 mg is assumed to be the same as the difference between injecting 30 mg and 40 mg. If you can make this assumption (which seems dubious to me) then you can use the variable as it is, but if not, you might want to divide the variable in categories, e.g. quintile groups, and convert these groups into dummy variables for use in the analysis.

• There are disadvantages of selecting a binary endpoint, including loss of power and having no way to handle dropouts before 3 months. Aug 30, 2015 at 12:07
• Thanks for the order. Death is the endpoint, modeled with the Cox model as time until death. From the Cox model you can get hazard ratios but also predict the probability of dying within 3m. By using time until the endpoint you get more statistical information/power (by e.g. treating a death at 3.1m as a bad outcome and by considering a death at 1w worse than a death at 3m) and are able to handle loss to follow-up. Aug 30, 2015 at 12:26
• Thank you. I understand that but I was unsure about whether Student T has survival data, including dates of death, or just data on dead or alive at a follow-up time at three months.
– JonB
Aug 30, 2015 at 12:46
• Lol, that was the misunderstanding of the day! The person who posted the question calls himself/herself Student T and I simply referred to that nickname!
– JonB
Aug 30, 2015 at 13:23
• (+1) for the first paragraph, but if the linearity assumption's dubious then a polynomial or spline basis will generally be a better way to allow for a curvilinear relationship - see What is the benefit of breaking up a continuous predictor variable?. (There's plenty about splines in RMS.) Aug 30, 2015 at 17:52