coxphf with frailty, Firth's correction
I don?t quite see how bootstrapping would help. Say I have 20 clusters, with 10 receiving a treatment and 10 control. Say I have 0 events in the treatment cluster and 22 events distributed amongst a handful of the control clusters. If I bootstrap, resampling at the cluster level with replacement, then no matter what I will always have 0 events in the bootstrapped treatment clusters. One can?t resample 0 events to get more than 0 events. And coxph models are divergent when one treatment class has 0 events. Furthermore the effect size estimate for a relative hazard between 0 events and >0 events will always be -Inf (on a log-hazard scale). So I won?t be able to estimate variation in the effect size from a bootstrap. Am I missing something? I could see how a reshuffling algorithm could work to get a P value?i.e. randomly relabeling 10 clusters to be treatment and 10 to be control, then estimating the effect size from a coxph frailty model, and using this to create a null distribution of effect sizes. But I still wouldn?t be able to get a confidence interval. This seems like the best approach unless Firth?s correction for monotonic likelihoods could be applied here.
On Feb 14, 2015, at 12:21 AM, David Winsemius <dwinsemius at comcast.net> wrote:
On Feb 13, 2015, at 7:49 AM, Steve Bellan wrote:
Thanks David. I?m not sure I completely follow. Are you referring to sandwich type estimators like that implemented by using cluster() instead of a frailty term? Could you please also clarify your last sentence?
I wasn't suggesting a sandwich estimator. I was imagining you would sample from a population and that some of your sample strata would have zero elements. I would expect that your boot function would trap that event and return an appropriate indicator. The bootstrap in my imagination wouldn't use p-values as the result but rather would report a high log hazard. -- David.
On Feb 12, 2015, at 10:52 PM, David Winsemius <dwinsemius at comcast.net> wrote:
On Feb 12, 2015, at 5:50 PM, Steve Bellan wrote:
Hi all, I'm fitting a coxph gamma frailty model to simulated survival data and running into situations where I have 0 events in one covariate class and the model won't converge. I'd still like a p-value in those cases as this is part of a power analysis. With enough person-time observed 20 events in one group and 0 in another is likely significant, but I want a p-value to be sure. Firth's correction in ?coxphf? seems appropriate but coxphf doesn't seem to deal with random effects. Any suggestions would be much appreciated!
I would have expected power analyses in mixed model situations to be conducted with bootstrap methods. In that setting you could just collect the zero event cases in one category and use then as part of the denominator. -- David Winsemius Alameda, CA, USA
David Winsemius Alameda, CA, USA