# Cox Regression/Hazard Ratio interpretation question

#### afarrey11

##### New Member
Hi, all. I've done all the coding already for this, I just don't know how to interpret it. For an assignment, we were given this data taken from the Stanford Heart Study from 1978 or so:
I used equal signs because I thought dashes might be confusing. They haven no mathematical function in the following 'tables'

The variables in question are:
Age in years in reference to age 48
Year Waiting time in program for acceptance into the program
Surgery 0=no previous surgery; 1=previous surgery
Transplant 0=no transplant perform; 1=transplant performed

A series of Cox regression/hazard ratio tables was run, and this was the output

When run singly:
Variable = Coef = HR
Age = 0.03069 = 1.031
Year = -0.19077 = 0.826
Surgery = -0.73911 = 0.478
Transplant = 0.12567 = 1.134

When run together:
Variable = Coef = HR
Age = 0.02715 = 1.028
Year = -.014611 = 0.864
Surgery = -.063582 = 0.530
Transplant = -0.01189 = 0.988

When run together with interaction:
Variable = Coef = HR
Age = 0.02988 = 1.030
Year = -0.25211 = 0.777
Surgery = -0.66270 = 0.515
Transplant = -0.62253 = 0.537
Yr x Transplant = 0.19697 = 1.218

The question I've been asked to answer is: "Explain why transplantation is a risk for death when taken alone, is protective when used in conjunction with the other variables, and why the risk is "absorbed" by the interaction of year and transplantation. How does this cohere with the observation that survival is clearly extended by transplantation (see graph)?" (Graph shows transplantation definitively lengthens survival time).

So transplantation itself is dangerous and was more so when first being performed; surgical technique and improved immunosuppressant medications have since come into use so the change for organ rejection was higher. When the other variables are taken into account, I'd assume this risk is reduced when the other factors are considered. But I don't know why. Does anyone have any idea?

Thanks.