Nothing
# Misc. functions
################################################################################
# Measures of dependence
tau.empirical <- function(theta, frailty, N=1000) {
dat <- genfrail(N=N, K=2, theta=theta, frailty=frailty,
censor.distr="none", covar.distr="none",
Lambda_0_inv=function(t, c=0.01, d=4.6) (t^(1/d))/c)
xy <- matrix(dat$time, ncol=2, byrow=TRUE)
cor(xy[,1], xy[,2], method="kendall")
}
tau.numerical <- function(theta, frailty) {
lt <- ltfrailty[[frailty]]
4 * integrate(Vectorize(function(s) {
s * lt(0, s, theta) * lt(2, s, theta)
}), 0, Inf)$value - 1
}
# Numerically determine theta given Kendall's tau
theta.given.tau <- function(tau, frailty) {
uniroot(function(theta) {
tau.numerical(theta, frailty) - tau
}, c(lb.frailty[[frailty]], min(ub.frailty[[frailty]], 100)))$root
}
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