[R] proportion of treatment effect by a surrogate (fitting multivariate survival model)

[Vinh Nguyen]

On Mon, May 17, 2010 at 7:42 PM, Vinh Nguyen <vqnguyen at uci.edu> wrote:
> Dear R-help,
>
> I would like to compute the variance for the proportion of treatment
> effect by a surrogate in a survival model (Lin, Fleming, and De
> Gruttola 1997 in Statistics in Medicine).  The paper mentioned that
> the covariance matrix matches that of the covariance matrix estimator
> for the marginal hazard modelling of multiple events data (Wei, Lin,
> and Weissfeld 1989 JASA), and is implemented in Lin's MULCOX2, SAS,
> and S-plus.
>
> Is this the way to fit such a model in R?
> Suppose I have variables: time, delta, treatment, and surrogate.
>
> Should I repeat the dataset (2x) and stack, creating the variables:
> time1 (time repeated 2x), delta1 (delta repeated 2x), treatment1 (same
> as treatment, but 0's for the 2nd set), treatment2 (0's in first set,
> then same as treatment), and surrogate2 (0's in first set, then same
> as treatment), and id (label the subject, so each id should have 2
> observations).
>
> Thus, a dataset with n observations will become 2n observations.  To fit, do
> fit <- coxph(Surv(time1,delta1) ~ treatment1 + teatment2 + surrogate2
> + strata(id)
> ?
>

I think I figured it out.  I should use m <- rep(0:1, each=n) for
strata.  The point estimates matches that of the adjust and unadjusted
models when fitting separately (jointly fit to obtain covariances).

Thank you and let me know if I've done anything wrong.

> From here, I can obtain the variance and covariance terms for the
> coefficients of treatment1 and treatment2.  Is this the same as
> fitting 2 separate models but also obtaining the covariances of the
> two estimates?
>
> Let me know, thanks.
>
> Vinh