[R] estimating survival function from Cox model

[Terry Therneau]

The standard error of the curve cannot be extracted from the summary information you have.
The variance is made up of two terms, one of which is a sum over all the death times, of a 
quadratic term per death time.  That term involves the variance matrix of the Cox model 
coefficients, the target value for x (the curve you want to calculate) and the average 
value of x at that time in the data set from which the Cox model was created.
   Just like linear regression, the se are higher when you predict "far from the center" 
of the original data set.

Terry Therneau


On 12/18/2013 05:00 AM, r-help-request at r-project.org wrote:
> Hi, I have some questions on how to estimate the survival function from a Cox model. I know how to do this in R using survfit().
>
>
> But let's say the model was done is another software, and I was only given the estimate of baseline cumulative hazard "A0(t=10)" at the specified time "t=10" (baseline cumulative hazard refers to when covariate X=0)and the beta estimate "b" for the covariate used in Cox model "X".
>
>
> So the survival function at time 10 for a given covariate value x can be calculated as:
>
> A(t=10|X=x) = exp(b*x)*A0(t=10) where A is cumulative hazard when X=x
> S(t=10|X=x) = exp(-A(t=10|X=x)) where S is survival function to be calculated
>
> Now I want to calculate confidence interval for S(t=10|X=x). I think I need to calculate the CI for cumulative hazard A(t=10|X=x) first and then exponentiate it to get CI for S, based on the relationship S = exp(-A).
>
> To get CI for A, I need to calculate the estimate of standard error of A. I know the other software can give me the standard error of A0, the baseline cumulative hazard. Based on the relationship A = exp(b*x)*A0, I guess I'll need the standard error for b. But how do I calculate the standard error for A based on standard errors for A0 and b?
>
> Any insights would be greatly appreciated!
>
> John