R help - Mar 2012 - how to write crossed and nested random effects in a model

Dear R Users,

I have a question based on my research. I am analyzing reader-based
diagnostic data set.  My study involves diabetic patients who were evaluated
for treatable diabetic retinopathy based on the presence or absence of two
pathologies in their eyes.  Pathologies were identified using the clinical
examination (Gold standard method). In addition it can be identified by
taking digital images of patients? eyes and this method is cost effective.
Finally two readers go over the images independently and patients are
diagnosed as either positive or negative for the pathologies.
My objective is, estimation the sensitivity and specificity of reader-based
diagnostic method.

I am going to fit multivariate probit model. But the problem has complex
correlation structure. We have three different correlation: readers results
are correlated, patients left and right eyes are correlated and pathologies
are correlated since all based on the retina in the eye.

Could anyone help me out how to address these correlations in a model using
random effects? 

Also I think patients and readers are crossed each other since each reader
go over each patients? images. And eye eyes are nested with patients and
pathologies are nested with in the eye.  Is this crossed and nested
interpretation true?  If then how can I include these effects as random
terms to the model?

My response is readers ? diagnosed values. Per patient I have 8 values (2
pathologies, left and right eye and 2 readers) 
Explanatory variables are actual disease status of each pathology for left
and right eyes.

Thanks


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Niroshan <wnnperer <at> ucalgary.ca> writes:
> I have a question based on my research. I am analyzing reader-based
> diagnostic data set.  My study involves diabetic patients who were
evaluated
> for treatable diabetic retinopathy based on the presence or absence of two
> pathologies in their eyes.  Pathologies were identified using the clinical
> examination (Gold standard method). In addition it can be identified by
> taking digital images of patients? eyes and this method is cost effective.
> Finally two readers go over the images independently and patients are
> diagnosed as either positive or negative for the pathologies.
> My objective is, estimation the sensitivity and specificity of reader-based
> diagnostic method.
> 
> I am going to fit multivariate probit model. But the problem has complex
> correlation structure. We have three different correlation: readers results
> are correlated, patients left and right eyes are correlated and pathologies
> are correlated since all based on the retina in the eye.
> 
> Could anyone help me out how to address these correlations in a model using
> random effects? 
> 
> Also I think patients and readers are crossed each other since each reader
> go over each patients? images. And [snip] eyes are nested with patients and
> pathologies are nested with in the eye.  Is this crossed and nested
> interpretation true?  If then how can I include these effects as random
> terms to the model?
> 
> My response is readers ? diagnosed values. Per patient I have 8 values (2
> pathologies, left and right eye and 2 readers) 
> Explanatory variables are actual disease status of each pathology for left
> and right eyes.
> 

   I think that *in principle* (if you are using lme4, which is
probably the most convenient option for dealing with crossed REs) you
probably want

 ~ pathology + (pathology|reader)+(pathology|patient/eye)

  The fixed effect term says that pathologies may vary in their
overall frequency.  The first RE term says that different readers can
vary, in a pathology-specific way (if they just differed overall in
their sensitivity you would want (1|reader) instead); the second says
that there is variance among eyes (within patients) in all pathologies
(and that they may be correlated).

  A few cautions about this:

* I'm not sure I got it right

* You might want to forward this (along with my answer, so we're not
starting from scratch) to r-sig-mixed-models at r-project.org , where
there is more expertise in mixed models.

* if you have the _same_ two readers for all of your patients (as
opposed to two different readers chosen at random out of a large,
possibly overlapping pool), then it isn't be practical to treat them
as a random effect, no matter how much sense it makes philosophically
-- use pathology*reader instead.

* You may need a moderately large amount of data to fit this model ...