\(S(t_1, t_2) = C(S_1(t_1), S_2(t_2))\) with Kaplan-Meier
margins – Sklar's theorem on the survival scale. The family choice
says where in time the association acts: Clayton lower-tail (early
events), Gumbel upper-tail (late), Frank neither. Mirrors
morie.fn.copfr and, with family = "clayton",
morie.fn.clyfr.
Usage
morie_copula_survival(
time1,
event1,
time2,
event2,
family = "clayton",
theta = NULL
)
Arguments
- time1, time2
numeric observed times.
- event1, event2
binary event indicators.
- family
copula family.
- theta
parameter; inverted from the sample tau if NULL.
Value
list: family, theta, tau_sample, joint_survival, s1, s2,
n_pairs, method.
References
Clayton, D. G. (1978). Biometrika 65(1), 141-151.
Sklar, A. (1959). Publ. Inst. Statist. Univ. Paris 8, 229-231.
Examples
set.seed(1)
t1 <- rexp(30)
t2 <- t1 + rexp(30, 5)
morie_copula_survival(t1, rep(1, 30), t2, rep(1, 30))$tau_sample
#> [1] 0.8758621
