[R-sig-ME] Shrinkage of ORs in a glmm

[David Duffy]

On Mon, 7 Mar 2011, lorenz.gygax at art.admin.ch wrote:

> Dear Mixed-modelers,
>
> in a recently submitted paper, we used a glmm to estimate the risk of 
> claw injuries in dairy cows on a set of 36 farms that differed in the 
> type of flooring and were visited three times.
>
> So far, we have worked with glmmPQL but may now switch to glmer because 
> we were asked to calculate LR-tests by one of the reviewers. In 
> addition, we are asked that we shrink our estimated odds-ratios at the 
> population level. So far we have calculated these as e to the power of 
> the estimated parameters.
>
> I have thought that shrinkage happens automatically in a mixed-effects 
> model but this does not seem to be the case depending on the numerical 
> implementation (see comment of the reviewer below). Is this additional 
> shrinkage indeed necessary and is there an easy implementation on how 
> this shrinkage can be done in e.g. lme4?
>

If I understand this correctly, his comments are wrt marginal versus 
mixed-effects estimates for fixed effects.  Fitzmaurice gives some nice 
numerical examples in lecture notes online (towards the end)

http://familymed.uthscsa.edu/research08/pcrmsc/21st_2007/presentations/2%20Applied%20Longitudinal%20Analysis%20Contrasting%20Marginal%20and%20Mixed%20Effects%20Models%20Garrett%20Fitzmaurice%20Nov%2030%202007.pdf

Using PQL is also complicated by its problems with bias.

Simplest might be to fit a GEE and compare the results, but taking your 
predictions from a logistic mixed model, converting these to absolute 
risks and looking at risk differences for the different flooring 
for animals across the range of farms would address the practical 
outcomes.  The _attributable risk_ would be the predicted 
total fall in (annual) injuries if one changed all farms to the best floor 
covering.  This obviously can be specific to your universe of 36 farms, or 
extended to a larger population of farms assuming a particular 
distribution of fixed and random effects. This type of number can also be 
plugged into a cost-effectiveness analysis.

Cheers, David Duffy.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v