## Cox Regression/Hazard Ratio interpretation question

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# Cox Regression/Hazard Ratio interpretation question

Hi, all. I've done all the coding already for this top section, 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 have no mathematical function in the following 'tables.' The things I've put in bold are the actual assignment questions that I need to answer, the other things are just things I'm sort of asking rhetorically that can be answered if anyone finds it helpful to the questions my professor has asked, but aren't as necessary.

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

The two variables below are modeled in the proportionate hazards model but are not in the questions I've been asked to answer.  I thought it would help with the context of the HRs though.

Start - time in days after admission for surgery

Stop - time in days when patient either died or was censored

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 chance 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?

For the next question that I have not done the coding for (because I'm not entirely sure how) 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 (directed acyclic graphs that are used to pinpoint and possibly eliminate bias) 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 means 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 proportionate hazards model at the top if anyone needs that and it might help.  It is all done with PHREG modeling the effect of time waiting in the program versus when death occurred.  Please let me know if you need any additional information to help answer anything.  Thank you all!

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