# Another, more difficult Cox Regression/Hazard Ratio interpretation question

#### afarrey11

##### New Member
So, 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

These were run in reference to 'Event' (which was death or not)

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

I've been told to do the following:
0 (pre-step) Construct a new data set that consists only of the 102 usable observations (one person had a negative "year" value and can be ignored)
1) Using stratification, examine the effect of each variable on transplantation and event to explain why in these data transplantation has a powerful effect.
2) Do a logistic regression on the converted data to determine the coefficients for the variables (all four taken together and all four with the interaction). Compare these results with the results from the proportionate hazards model above and explain which you think is better.
3) Draw a DAG that shows the interrelationship of these variables without the time elements, and a separate one with the time elements included. Describe the difference and which you think is superior.

-So, there were only 103 observations so the pre-step is easy; just delete the last one.
-I don't know what he meant by "all four taken together and all four with the interaction." Is this a PHREG model like the proportionate hazards model originally used like in the tables?
-What form of logistic regression do I need to run? Any tips with coding this would be appreciated.
-Can SAS do DAGs (directed acyclic graphs)? I doubt it but thought I'd ask.

I have the coding for the above hazards model if that helps or is needed to help with my questions. Thank you.

Thanks.