[R] covariate selection in cox model (counting process)

Mayeul KAUFFMANN mayeul.kauffmann at tiscali.fr
Wed Jul 28 04:06:43 CEST 2004

>No, I mean recurrent events.  With counting process notation but no
>recurrent revents the partial likelihood is still valid, and the approach
>of treating it as a real likelihood for AIC (and presumably BIC) makes
>Roughly speaking, you can't tell there is dependence until you see
>multiple events.

Thanks a lot, I got it (well, I hope so)!

I've read in several places that events in the Andersen-Gill model must be
"conditionnaly independent", which is sometimes more precisely written as
"conditionnaly independent given the covariates"

or even more precisely:

"the Andersen-Gill (AG) model assumes that each [individual] has a
multi-event counting process with independent increments. The observed
increments must be conditionally independent given the history of all
observable information up to the event times."

Then, there is still another option. In fact, I already modelled
explicitely the influence of past events with a "proximity of last event"
covariate, assuming the dependence on the last event decreases at a
constant rate (for instance, the proximity covariate varies from 1 to 0.5
in the first 10 years after an event, then from 0.5 to 0.25 in the next
ten years, etc).

With a well chosen modelisation of the dependence effect, the events
become conditionnaly independent, I do not need a +cluster(id) term, and I
can use fit$loglik to make a covariate selection based on BIC, right?

Thanks a lot again for your time.

Univ. Pierre Mendes France
Grenoble - France

PS: I wrongly concluded from the R statement "(Note: the likelihood ratio
and score tests assume independence of observations within a cluster, the
Wald and robust score tests do not). " that it meant independence between
two consecutive observations (without any event). It made sense to  me
because when only one covariate changes for a given individual, and with a
small change, there is a new observation, with a risk very simlar to the
risk for the previous observation. But there is still independence with
respect to the question of recurrent event. Maybe the warning should be
rewritten saying "assume *conditionnal* independence of *events* (given
the covariates)"

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