[R-sig-ME] Question on random effects glm interpretation

[Ben Bolker]

On 15-11-13 11:32 AM, Emmanuel Curis wrote:
> Thanks for these answers.
> 
> After thinking a little bit, I still have a concern with the
> survival approach.  What is in interest in the data is not really
> the time before patients are infected (at least, as far as I
> understood the practicionners problem), but the proportion of
> patients that are infected at a given moment (and, at the end, does
> this proportion change with some covariates, including period in
> the year). I'm not clear how the survival model can give this
> information (but I'm not familiar with survival analysis), but I
> thought it was more oriented toward modeling time-to-event?

  Well, these are really just different representations of the same
information.  In a canned statistical formulation (e.g. GLMM *or*
survival analysis), it's easier to deal with the constraint that
individuals are represented by a string of 0s followed by a string of
1s in the time-to-event framework.

  Given a cohort of individuals, one could construct predictions for
the expected number infected at a given time from the results of a
survival analysis (although might be easiest to do via stochastic
simulation).

  The assumption of independence of the individuals also breaks down
for infectious disease, unless the population is large enough that you
can assume randomly sampled individuals/neglect the effect of
infection status of some individuals on others' probability of
becoming infected ...

> Also, going back to the original question, for my own understanding
> of these models: is it correct to say that for a binomial GLMM to
> apply, with patient as the (only) random effect, then for a given
> patient the different Bernoulli variables must be independant,
> identically distributed as in a usual logistic regression? Or is
> this hierarchical approach too simplist?

  I think that's correct, extending your conditions slightly to say
that the variables are conditionally iid given both the identity of
the individual (latent variable) and any applicable
(time/patient-specific) fixed effects.

> 
> Thanks anyway for these quick answers,
> 
> On Fri, Nov 13, 2015 at 10:59:29AM -0500, Ben Bolker wrote: «   If
> you model the time until infection for each individual as «
> Gamma-distributed, that will be more or less equivalent to a Gamma 
> « (parametric) survival model, with the big caveat that the GLMM
> framework « is not good at handling censored data in general. « «
> I believe there is also a connection between discrete-time Cox «
> proportional hazards models and binomial GLMMs with a
> complementary « log-log link and fixed effect of time period ... «
>  «   Ben Bolker « « On 15-11-13 08:41 AM, Emmanuel Curis wrote: « >
> Dear Thierry, « > « > Thanks for the hint. « > « > Just for
> curiosity, is there any case in which survival analysis will « > be
> equivalent to the Markov model or the GLM(M) model? I remember
> having « > read somewhere that there are links  between survival
> analysis and « > logistic regression, but can't remember exactly
> which link for the « > moment... « > « > Best regards, « > « > On
> Thu, Nov 12, 2015 at 09:59:18PM +0100, Thierry Onkelinx wrote: « >
> « Dear Emmanuel, « > « « > « Maybe a survival analysis is more
> appropriate for that kind of data. « > « « > « Best regards, « > «
>  « > « ir. Thierry Onkelinx « > « Instituut voor natuur- en
> bosonderzoek / Research Institute for Nature and « > « Forest « > «
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