Violation of PH assumption

Question

Running a survival analysis, assume the p-value regarding a variable is statistically significant - let's say with a positive association with the outcome. However, according to the Schoenfeld residuals, the proportional hazard (PH) assumption has is violated.

Which scenario among below could possibly happen after correcting for PH violations?

1. The p-value may not be significant anymore.
2. p-value still significant, but the size of HR may change.
3. p-value still significant, but the direction of association may be altered (i. e. a positive association may end up being negative).

The PH assumption violation usually means that there is an interaction effect that needs to be included in the model. In the simple linear regression, including a new variable may alter the direction of the existing variables' coefficients due to the collinearity. Can we use the same rationale in the case above?

Braden

The PH assumption violation usually means that there is an interaction effect that needs to be included in the model. In the simple linear regression, including a new variable may alter the direction of the existing variables' coefficients due to the collinearity. Can we use the same rationale in the case above? – Braden

I'm not an expert on Cox proportional hazard models but PH is a key assumption in the Cox proportional hazard model, So if the Schoenfeld residual shows that your hazards is not proportional, your Cox model may no longer be valid. So if you can only chose one scenario, I would chose the first. I'm not sure though, I'm not an expert on the subject, but I hope it gives you an idea – Potence

Is this homework? – Dorita

Nope. It is related to my research. – Braden

@ Soodi Milanlouei Did you manage to solve the issue? – Alexio

Answer 1

Therneau and Gramsch have written a very useful text, "Modeling Survival Data" that has an entire chapter on testing proportionality. At the end of the chapter is a section on causes and modeling alternatives, which I think can be used for answering this question. Since you mention interactions it makes your question about a particular p-value rather ambiguous and vague.

1) Certainly if you have chosen a particular measurement as the subject of your interest and it turns out the all of the effects are due to its interaction with another variable that you happened to also measure, then you may be in a position where the variable-of-interest's p-value will decrease, possibly to zero.

2) It's almost certain that modification of a model with a different structure (say will the addition of time-varying covariates or a different treatment of time) will result in a different estimated HR for a particular covariate and I think it would be impossible to predict the direction of the change.

3) As to whether to sign of the coefficient could change, I'm quite sure that would be possible as well. The scenario I'm thinking of would have a mixture of two groups say men and women and one of the groups had a sub-group whose early mortality was greatly increased, e.g. breast cancer, while the surviving members of that group would have a more favorable survival expectation. The base model might show a positive coefficient (high risk) while a model that was capable of identifying the subgroup at risk would then allow the gender-related coefficient to become negative (lower risk).

Zoogeography