[R-sig-Epi] coxphf with frailty, Firth's correction

[Steve Bellan]

This is for a power analysis using simulated data and analyses. A power
analysis should use the same methods and criteria as the study which will
be eventually carried out, and since DSMB criteria are often firm and based
on p-values or confidence intervals acquired via a specified method, it
seems like rigorous power analyses should do the same.

In my example, the person-time does differ between clusters. The risk is
also variable between clusters. I agree that the small number of events is
problematic but I guess I'm concerned with how to have rigorous criteria to
decide when the effect is significant, i.e. 12 vs 0, 15 vs 0, 30 vs 0, 100
vs 0? And with the cluster-level heterogeneity I think resolving this
cutoff becomes trickier.


On Sun, Feb 15, 2015 at 3:50 PM, David Winsemius <dwinsemius at comcast.net>
wrote:

> I thought you said you were proposing doing power analyses, but here you
> are positing analysis of a particular result, and for a result which seems
> fairly extreme for a clinical study. Unless there were an extreme
> disproportion of observation time I would think the results should speak
> for themselves and be obviously statistically significant. This is more
> extreme than the classic initial studies of the effect of penicillin on
> pneumococcal meningitis. I do not see that a slavish reliance on p-values
> or confidence intervals is needed.  The "classical" analysis of confidence
> intervals for zero-event outcomes are with "exact" methods.
>
> It would seem that the only remaining question might be whether there were
> any heterogeneity in the event rates for the untreated groups and here
> (assuming a Poisson distribution weighted by the log observation time) I
> very much doubt the you should be able to show an effect unless one site
> had more than say 5 events?
>
> --
>
> David Winsemius, MD, MPH
>
>
> On Feb 15, 2015, at 9:28 AM, Steve Bellan wrote:
>
> > 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
> >>
> >
>
> David Winsemius
> Alameda, CA, USA
>
>

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