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

[Ben Bolker]

  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
> « team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> « Kliniekstraat 25
> « 1070 Anderlecht
> « Belgium
> « 
> « To call in the statistician after the experiment is done may be no more
> « than asking him to perform a post-mortem examination: he may be able to say
> « what the experiment died of. ~ Sir Ronald Aylmer Fisher
> « The plural of anecdote is not data. ~ Roger Brinner
> « The combination of some data and an aching desire for an answer does not
> « ensure that a reasonable answer can be extracted from a given body of data.
> « ~ John Tukey
> « 
> « 2015-11-12 18:12 GMT+01:00 Emmanuel Curis <emmanuel.curis at parisdescartes.fr>
> « :
> « 
> « > Dear all,
> « >
> « > With a colleague, we are discussing about the appropriateness of a
> « > random effects mixed effects generalized linear model (more
> « > specifically, logistic regression) in a given experimental situation,
> « > and wonder about it's correct interpretation.
> « >
> « > Short version: is it correct to interpret random effects glm, with a
> « > single random effect, as hierarchical models as random effects linear
> « > models ?
> « >
> « > Detailed version: our data consist of daily status of a set of
> « > patients, the status beeing « Infected » or « Not infected », during a
> « > variable period of time. The aim is to see what changes the infection
> « > probability.
> « >
> « > A proposed approach was to use a random effect logistic regression to
> « > evaluate this probability, with patient as a random effect.
> « >
> « > However, we have one concern with that approach: interpretating it in
> « > a hierarchical model idea, it seems that for a given patient, the
> « > model should be a binomial one, in other words that the set of
> « > Bernoulli variables observed each day for a given patient should be
> « > independent, identically distributed. But this is obviously not the
> « > case here: the variable is 0 until infection occurs (if it occurs),
> « > and 1 after.  Consequently, we fear that the probability estimated in
> « > the glmm will have no real meaningful interpretation.
> « >
> « > Are we right with this hierarchical interpretation of the GLMM
> « > (logistic) model, or is this fear not justified, and the
> « > interpretation of the GLMM more complex, but would lead to correct and
> « > interpretable estimations of infection probability?
> « >
> « > As an alternative approach, we thought about a two-states Markov
> « > chain, and working on transition probabilities from the « non-infected »
> « > to the « infected » state. It seems to model what happens more
> « > closely.  Is there any link between such a model and the logistic GLMM
> « > described above, or another kind of GLMM model?
> « >
> « > And, semantic question, is such a model also in the scope of « random
> « > effects » model and could be discussed here, in case help is needed, or
> « > is it out of the scope of this list?
> « >
> « > Thanks in advance for your opinions,
> « > Best regards,
> « >
> « > --
> « >                                 Emmanuel CURIS
> « >                                 emmanuel.curis at parisdescartes.fr
> « >
> « > Page WWW: http://emmanuel.curis.online.fr/index.html
> « >
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