[R] how to write crossed and nested random effects in a model

[Niroshan]

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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