# how to deal with dependence/interaction among covariates in a cox regression model

In case of a linear regression, if we are to account for interaction between two regressors x1 and x2, we write a model like lm(y ~ x1 + x2 + x1:x2, data=records)

Do we use a similar method/notation even in cox regression like coxph(Surv(y,censor) ~ x1 + x2 + x1:x2, data=records) ?

In other words, how does cox-regression deal with interaction/dependence among covariates?

• Could you clarify what you mean by regressors being "related"? The x1:x2 syntax examines an interaction between x1 and x2 in terms of predicting y; that is, it examines whether the influence of x1 depends on the value of x2. That's different from examining a linear dependence between x1 and x2. If x1 and x2 are highly linearly correlated so that they are close to measuring the same thing, one might expect no significant interaction as judged by the x1:x2 term in the regression. – EdM Dec 8 '14 at 22:19
• @EdM modifed my question – rk567 Dec 9 '14 at 16:03

Yes, interaction terms are specified in the same way for Cox regression as for linear regression. Interpretation of the interaction coefficients in Cox regression is probably best done in terms of the hazard ratios, shown in the exp(coef) values.

Take a look at this page from Maartin Buis: http://maartenbuis.nl/publications/interactions.html A the end of the examples list is an example interpreting coefficients in a Cox model. It uses Stata, not R, but the its the idea that counts.

His paper in the Stata Journal also brings up good points about interpreting interaction terms in non-linear models like this. Rather than sum it up, it's probably best if you read through his paper, its only 6 pages, but hits on a lot of good points.