Model Fit Statistics

Suppose the model contains p estimable parameters. Then the following two criteria are displayed for model fit statistics:

  • –2 log likelihood:

    \[ -2\mbox{ Log L}=-2 \log (L(\hat{\bbeta })) \]

    where $L(.)$ is a partial pseudo-likelihood function for the corresponding TIES= option as described in the section Partial Likelihood Function for the Cox Model, and $\hat{\bbeta }$ is the maximum pseudo-log-likelihood estimate of the proportional hazards regression coefficients.

  • Akaike’s information criterion (AIC):

    \[ \mbox{AIC}=-2\mbox{ Log L}+2p \]

The AIC statistic provides a different way of adjusting the log-likelihood statistic for the number of estimable parameters in the model.

Neither of these criteria is adjusted for the complex sample design, and both criteria are sensitive to the scale of the weights.