# Survival Analysis account for repeated measures?

I know from work in mixed effect models and generalized estimation equations that it is important to correct for bias resulting from collecting multiple samples from the same subjects over time.

Looking at the cox proportional hazards model for survival, it is not clear if/how it corrects for the bias resulting from the collection of longitudinal data.

Does a cox model do correct for subject bias due to repeated measurements? Does it need to?

## 1 Answer

The Cox model itself does not. But simple extensions make this possible.

The short answer is that, for a marginal model, the score equations for the regression coefficients turn out to be the same as in the Cox model. What is incorrect are the standard errors. In R with the survival package, you can use the +cluster(id) option in the formula. This provides some "robust" standard errors, and is in the spirit of a GEE-like approach.

For a random effects model, the Cox model can be extended with a "frailty" term. Then, the results are interpreted as conditional on the random effect. This can also be done with the +frailty(id) option, or with the coxme package.

For both there is a lot of literature out there and any decent Survival Analysis textbook should cover these two extensions (a starting point would be the so-called "Andersen-Gill" model).

• In fact, at this time there is also a full blown Cox mixed effects model (a frailty model is a very similar to a random intercepts model). See R's coxme package. – Cliff AB Jun 18 '16 at 16:40
• Also, in practice, Cox analysis is often based on covariate values collected at time of entry into the study, so that the only multiple "samples" taken are whether an "event" has occurred during follow up. – EdM Jun 18 '16 at 17:31