Hi,
I have been performing survival analysis using Cox regression models, and I encountered situation when after adding time-varying effect for a variable X (X*time; variable violated the PH assumption), the added interaction with time was significant in the model, but the main effect of variable X was not, as illustarted below:
Model without interaction with time:
coef exp(coef) se(coef) z Pr(>|z|)
factor(X)1 0.4633 1.5894 0.1625 2.852 0.004 **
Model with interaction between X and time:
coef exp(coef) se(coef) z Pr(>|z|)
factor(X)1 -0.3978 0.6718 0.4444 -0.895 0.371
tt(factor(X)) 0.6230 1.8645 0.2816 2.212 0.027 *
In the study we are interested in the effect of the X variable on the survival outcome, and after inclusion of the time-varying effect X*time, I am no longer sure about the value of the variable X in describing the risk of the outcome, as the main effect is now not significant.
Is the significance of time-varying effect of variable X enough to assume that the variable X is significant for the outcome risk, even though the main effect is no longer significant in such scenario?
Or, do both of them, the main effect of X and the time-varying effect of X have to be significant in the model to be able to say that X is significant for the outcome?
Any help in interpreting these is very welcome.
In my experience the best way to interpret a Cox regression is to look at the Kaplan Meier plot. You haven't mentioned your software but there's a very simple R program for doing this in jarad lander R for everyone available for download from the z-library. Best wishes, David Booth BTW I attached a paper that gives an example.. Best wishes David Booth
Thanks David,
I ran a Kaplan-Meier: the two lines cross early in the study, and only then we can see a quite ood separation. If I understand well, perhaps it isn't surprising that the variable has a time-varying effect (increasing with time).
I also inspected the proportional hazard (PH) assumption for this variable using the cox.zph function in survival R package - the red horizontal line represents the averaged coefficient (beta) as in the Cox model (model that operates under assumption of PH), while the thin, black line is the "real" beta for the variable. The test for proportional hazard for variable X did not indicate significant departure from PH (p = 0.079, PH is violated when p < 0.05), but the added time-varying effect is significant, which is reflected by the Kaplan-Meier and the plotted coefficient over time.
Regarding the interpretation of significance of the terms in the model, I received some advise from a biostatistician: in a model where a time-varying effect is included as an interaction term (as opposed to splitting the time and calculating HR for time intervals), the main effect represents the HR where the interaction term is equal to 0 (if it's a simple X*time interaction, the inyteraction is equal 0 when time=0; it might differ in situations where there is a time transformation, for example log(time), etc.). Bottom line, even if the main effect isn't significant in the model, the (time-varying) effect of the variable is still interesting.
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