The 2-D survival function is expressed as
$S(t1,t2)=C(S1(t1),S2(t2))$, where $S1(t1)$, $S2(t2)$
are marginal survival functions and $C(u1,u2)$ is a 2-D copula.
The marginal survival functions are estimated via the marginal
hazards as in sshzd, and the copula is estimated
nonparametrically by calling sscopu2. When symmetry=TRUE, a common marginal survial function
S1(t)=S2(t) is estimated, and a symmetric copula is estimated such
that $C(u1,u2)=C(u2,u1)$.
Covariates can be incorporated in the marginal hazard models as in
sshzd, including parametric terms via partial
and frailty terms via random. Arguments formula1 and
formula2 are typically model formulas of the same form as the
argument formula in sshzd, but when
partial or random are needed, formula1 and
formula2 should be lists with model formulas as the first
elements and partial/random as named elements; when
necessary, variable configurations (that are done via argument
type in sshzd) should also be entered as named
elements of lists formula1/formula2.
When symmetry=TRUE, parallel model formulas must be
consistent of each other, such as
l{
formula1=list(Surv(t1,d1)~t1*u1,partial=~z1,random=~1|id1)
formula2=list(Surv(t2,d2)~t2*u2,partial=~z2,random=~1|id2)
}
where pairs t1-t2, d2-d2 respectively
are different elements in data, pairs u1-u2,
z1-z2 respectively may or may not be different
elements in data, and factors id1 and id2
are typically the same but at least should have the same levels.