The AIC can be extracted through
extractAIC.coxme <- function(x){
loglik <- x$loglik + c(0, 0, x$penalty)
chi1 <- 2*diff(loglik[1:2])
chi2 <- 2*diff(loglik[c(1,3)])
c(chi1 - 2*x$df[1], chi2 - 2*x$df[2])
}
fit <- coxme(Surv(time, status) ~ age + sex + (1|ph.ecog), lung)
extractAIC(fit)
See the print.coxme function https://github.com/cran/coxme/blob/master/R/print.coxme.R