check https://mailman.ucsd.edu/pipermail/ling-r-lang-l/2011-August/000282.html you want to have large (i.e. in direction of positive infinity) logLik and small AIC/BIC (i.e. in direction of negative infinity)

also caution BIC is only valid for comparisons of not nested models (see https://en.wikipedia.org/wiki/Bayesian_information_criterion), if models are nested orient with AIC alone, if models are not nested you can orient for both AIC and BIC

For a Cox model, logLik method returns the partial likelihood.

check https://mailman.ucsd.edu/pipermail/ling-r-lang-l/2011-August/000282.html you want to have large (i.e. in direction of positive infinity) logLik and small AIC/BIC (i.e. in direction of negative infinity)

also caution BIC is only valid for comparisons of not nested models (see https://en.wikipedia.org/wiki/Bayesian_information_criterion), if models are nested orient with AIC alone, if models are not nested you can orient for both AIC and BIC