Question on random effects glm interpretation

Maybe a survival analysis is more appropriate for that kind of data.

Detailed version: our data consist of daily status of a set of
patients, the status being ? Infected ? or ? Not infected ?, during a
variable period of time. The aim is to see what changes the infection
probability.

As Thierry suggested, this type of dataset (incidence of infection) can be 
modelled as a recurrent events survival analysis.  These can be 
represented as in a discrete time framework as a poisson GLMM, or as Cox 
or parametric mixed effects survival models. One example might be various 
analyses of the "kidney" dataset of McGilchrist and Aisbett that is 
included in the BUGS manual. In R as:

brms::kidney            Infections in kidney patients
frailtyHL::kidney       Kidney Infection Data
INLA::Kidney            Kidney infection data
survival::kidney

The Markovian model appears in bivariate survival analyses covering time 
to infection and time to recovery - each may have different relevant risk 
factors - the random effect (frailty) for each individual links them 
together appropriately. You will probably also want time varying 
covariates.

Cheers, David Duffy.


| David Duffy (MBBS PhD)
| email: David.Duffy at qimrberghofer.edu.au  ph: INT+61+7+3362-0217 fax: -0101
| Genetic Epidemiology, QIMR Berghofer Institute of Medical Research
| 300 Herston Rd, Brisbane, Queensland 4006, Australia  GPG 4D0B994A