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

[Vinh Nguyen]

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)
?

>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