# Cox Regression Assumption

#### Q&A

##### New Member
Hi all,

My Cox regression model doesn't validate the proportional hazards hypothesis. I think the other two assumptions are easy to verify.
I used the 'strata' function in my model [ strata(hospital) ], but the proportional hazards assumption is still not validated.
How can I do to validate this assumption.
Because if this assumtion is not verified, the model is not correct no ?

Thanks for help.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
General text from web, "In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. If proportional hazards holds, the graphs of the survival function should look “parallel”, in the sense that they should have basically the same shape, should not cross, and should start close and then diverge slowly through follow up time. Earlier in the seminar we graphed the Kaplan-Meier survivor function estimates for males and females, and gender appears to adhere to the proportional hazards assumption."

I think I only had this issue once a long time ago. I believe if it is violated you have to add some type of interaction term with time. There was an epi paper in the last years talking about this and the severity, but can't remember the conclusions. This also seems like something Frank Harrel would have comments on.

I would be interested in what you find out, so I would be prepared if I face this again.

#### Q&A

##### New Member
General text from web, "In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. If proportional hazards holds, the graphs of the survival function should look “parallel”, in the sense that they should have basically the same shape, should not cross, and should start close and then diverge slowly through follow up time. Earlier in the seminar we graphed the Kaplan-Meier survivor function estimates for males and females, and gender appears to adhere to the proportional hazards assumption."

I think I only had this issue once a long time ago. I believe if it is violated you have to add some type of interaction term with time. There was an epi paper in the last years talking about this and the severity, but can't remember the conclusions. This also seems like something Frank Harrel would have comments on.

I would be interested in what you find out, so I would be prepared if I face this again.

Yes, my Kaplan-Meier curves do cross each other. I've also seen articles saying that if you have this kind of problem, if the proportional hazards assumption is violated, you can add a stratification or an interaction term.

You say interaction term, what exactly is that? How do you choose it? What does it depend on?
I had put this solution out of my head because I didn't understand the articles on the net

#### Q&A

##### New Member
An in the strata function, we can use a temporal variable , time variable ?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Do you know the cause of the crossing. This may help you frame it. Causes can include: people switching treatments, differential disease progression, heterogeneous treatment effects (subgroups), and accelerated or delayed treatment effect.

NPH is likely present in every study to some extent. Restricted mean survival difference seems like another approach. I am no expert in this area. I have done about 1 PHREG every other year for the last 18 years. So I am just trying to recall this stuff every once and awhile.

#### Q&A

##### New Member
Do you know the cause of the crossing. This may help you frame it. Causes can include: people switching treatments, differential disease progression, heterogeneous treatment effects (subgroups), and accelerated or delayed treatment effect.

NPH is likely present in every study to some extent. Restricted mean survival difference seems like another approach. I am no expert in this area. I have done about 1 PHREG every other year for the last 18 years. So I am just trying to recall this stuff every once and awhile.
what do you mean by "crossing"?
I have to evalue variables that have impact in the death of these individuals , and it's the model that gives me variables responsible for the death.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Non-proportional hazards means the horizontal distance between the survival curves (for categorical covariates) is not uniform. So estimates of the hazards wont explicitly represent the change pattern accurately. The proportional hazards can be partially seen by looking at the plot and crossing curves (AKA above your KM curves) can be a sign of this. However the crossing can represent a change in the hazards - which there likely needs to be a reason why things change. This is what I am inquiring about.

Restricted mean survival attempts to provide an estimate, similarly to median survival, contrasting the mean difference between the curves.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I solicited a recommendation for a related article. This one on RMST seems like a nice entry level piece and may have STATA code attached.

#### Q&A

##### New Member
Hello again,
I'm working with R, so for the non proportional hazard assumption, I used the coxzph function.

But I have other questions in generally in Cox Model if you can help me.
1/ If my observed data is less than my censored data, is that a problem?
(56 observations for my observed data and 239 for my censored observations)
2/ My data is chronological.
A patient who enters the study in 2011 does not have the same treatment dose as a patient who enters in 2015 or 2020. The dose increases gradually over time, (strictly increasing dose vs. time curve).
I have other time-dependent variables as well.
3/ If all Cox regression assumptions are verified, model's results are 100% correct? Are the results reliable and accurate?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
So you are saying only 56/295 had a documented outcome?

#### Q&A

##### New Member
I just said that on one case, I have a model with 239 deaths (censored observations) and 56 still in life.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Right censoring:
Insufficient follow-up;
Lost to follow-up;
Patient withdraws from study.

You have 56 censored and 239 events.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
why are the doses different? Are they dependent on another variable (e.g., bioassay)?