Calculate c-hat from coxph model

Question

I am analyzing sage-grouse survival using cox proportional hazard models and need to test my global model for overdispersion by calculating a c-hat. Most people use the c_hat{AICcmodavg} function; however, this function doesn't seem to recognize the object produced by coxph models (see below). Is there any other similar functions that can produce a c-hat value for a cox's model? Thanks, Kyle

KE_global <- coxph(Surv(Start, End, Event) ~ Age+Res+Sex+Year1+DDM, data = sagr)

c_hat(KE_global, method = "pearson")

Error in c_hat.default(KE_global, method = "pearson") : Function not yet defined for this object class

Answer 1

I am not sure, and I havn't seen overdispersion done on cox hazard models before. Perhaps it isn't very surprising that this error occurs. In the official package documentation it states that:

Functions to compute an estimate of c-hat for binomial or Poisson GLM’s and GLMM’s using different estimators of overdispersion.

Checking for over- or under-dispersion is usually performed when the obsereved variance is greater than expected. In overdispersion :

A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations. This necessitates an assessment of the fit of the chosen model.

The Cox proportional hazard model is, however, semi-parametric. More importantly, it does not assume any underlying distribution in order to fit a model. See Cox Proportional-Hazards Regression for Survival Data / John Fox:

This model is semi-parametric because while the baseline hazard can take any form, the covariates enter the model linearly.