On a given dataset, I am running a semiprametric Cox proportional hazards model, together with a series of parametric models (Weibul, gamma, lognormal, exponential, etc.). How can I know which is better? During my PhD, I was told by methodologists that you cannot use Likelihood-based statistics to compare parametric and semiparametric duration models. (However, some papers actually employed AIC and other measures to make this comparison.)
What can I use to compare parametric and semiparametric models? Any help is appreciated.