[R] Simplifying coxme models

[Bert Gunter]

As you seem to be wandering in the wilderness here, it sounds like you
should really be seeking local statistical help that can provide a
fuller 1-1 discussion, rather than posting on the internet.
Alternatively, although you are working within R, your questions are
primarily about statistical matters, for which stats.stackexchange.com
is a better fit. We tend to be more focused on R programming and
features rather than statistics on this list, although they certainly
overlap.

Of course, you may get lucky -- Terry is often generous with his time
and advice -- but if you do not...

Cheers,
Bert



On Sat, Dec 21, 2013 at 9:22 AM, David Gibbs <dgibbs7 at gatech.edu> wrote:
> Hello all,
>
> I have some questions about specifying a coxme model and then simplifying
> it after reading the coxme documentation and posts here. The situation is
> this:
>
> I glued 4 pieces of small coral fragments onto small ceramic tiles, which I
> placed at 4 distances east and west of 10 large coral colonies (i.e. site).
> Thus, each tile represents one distance-direction-site combination. I
> checked the small coral fragments daily to see which had died overnight and
> at the end of the experiment some were still alive (thus, censored). I
> therefore had 4 fragments per tile*4 distances*2 directions*10 sites = 320
> small fragments. Distance and direction are fixed effects, while the tile
> that each fragment is on and the site are random effects. In addition, each
> large colony is a different size, so the size of the large colonies should
> be a random effect, too (SiteSize).
>
> The model I wrote to express this is:
> mefull<-coxme(Surv(death, censor) ~ Distance*Direction+(1|Site/Tile)
> +(1|SiteSize))
>
> First, can anyone tell me if this properly specifies the situation I
> described above?
>
> After running this model, I found that neither fixed effect nor their
> interaction was significant. Also, the standard deviation for Site and
> SiteSize are identical (~1.12), which seems strange to me. Is there a
> reason for that? The fact that they are both greater than 1 indicates to me
> that they contribute a lot of variation to survival. Is that correct?
>
> My next major question is how to simplify this model. My instinct (and
> based on reading Terry Therneau's manuals and other posts here) is to
> remove each random effect in turn and compare the AICs of the integrated
> log-likelihood of the resulting models; the higher AIC is the preferred
> model in this formulation. Is that correct?
>
> However, I'd also like to try to try to simplify the model through removal
> of the non-significant fixed effects, starting with their interaction. How
> can I do this while also removing random effects? What terms should I start
> with removing, or does the order not matter as long as I start with
> higher-order terms (i.e. interaction)? Can I try as many combinations as I
> like or do issues with multiple tests come into play?
>
> Some options are removing one of the random effects (me2) or removing the
> interaction between the fixed effects but keeping the random effects in
> place (me3).
> me2<-coxme(surv ~ Distance*Direction+(1|Site/Tile))
> me3<-coxme(surv ~ Distance+Direction+(1|Site/Tile)+(1|SiteSize))
>
> When I run these and other combinations of factors, their AIC is always
> lower than that of the full model, which suggests to me that the full model
> is best. Any guidance on how to simplify this model would be greatly
> appreciated.
>
> Finally, to compare the model with random effects to one without, can I
> compare the NULL log-likelihood with the integrated log-likelihood? From my
> understanding of the coxme manual, the one closer to 0 is the better model,
> so if the integrated one is closer to 0 then the model with random effects
> is preferred over the one without random effects.
>
> Thanks very much for your time and help.
>
> David Gibbs
> Georgia Institute of Technology
>
>         [[alternative HTML version deleted]]
>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

(650) 467-7374