Comparing Cox PH regression models with random effect

When to use:

Model comparison serves to choose the set of independent variables, as in comparing Cox PH regression models: we compare a full model with a reduced model, or use automatic selection. The random effect (gamma frailty for the indicated grouping variable) is shared by all compared models – in each of them the variance \(\theta\) is re-estimated, but the group structure remains the same. Selection concerns the independent variables only; whether the random effect is needed is decided by the LR test \(\theta=0\) in the Cox regression with random effect report.

Definitions of measures

Models are compared on the basis of the integrated log-likelihood, the information criteria AIC, AICc, BIC (the smaller, the better) and the likelihood ratio test for nested models: \(2(\ell_{full}-\ell_{reduced})\) follows a \(\chi^2\) distribution with degrees of freedom equal to the number of removed variables.

How to set up the analysis

Statistics \(\to\) Mixed models \(\to\) Cox PH regression with random effect – comparing models.

We indicate the survival time, the censoring variable with the Complete value, the variables of the full and reduced models (or the automatic selection criterion) and the Grouping variable (ID), shared by all models.

Results and interpretation

The report contains a fit table of the compared models (integrated log-likelihood, AIC, AICc, BIC, \(\theta\) of each model) with the LR test between them, and the coefficient tables of the models with conditional hazard ratios.