I'm using coxph for a survival model, using three cualitative variables as independent. I know there is not an interaction between them so I just did the following model:
fit <- coxph(Surv(Time, status) ~ factor(v1) + factor(v2) + factor(v3)
My problem is that I need the confidence interval of the product between them. I can estimate by hand the one of a product of two using the formula
Var(v1*v2) = v1^2 Var(v2) + v2^2 Var(v1) + 2v1v2COV(v1v2)
But I don't know how to do it for the product of the three of them, I mean, I have three estimators b1, b2, b3 of v1, v2 and v3 respectively.
I want to know how to estimate the confidence intervals of exp(v1 + v2 + v3) that is the Hazard ratio of a person having the three risk factors.
I wonder if there is any form to do it with R, with the package survival or with another package
