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

Vinh Nguyen vqnguyen at uci.edu
Tue May 18 19:18:39 CEST 2010

```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
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

```