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st: random-effects SROC model in gllamm


From   "Ben Dwamena" <bdwamena@med.umich.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: random-effects SROC model in gllamm
Date   Sun, 16 Dec 2007 03:16:39 -0500

I would appreciate assistance with a gllamm or xtmelogit code for the model described below for combining multiple 2 by 2 results of a binary diagnostic test with binary reference test outcome:

The # of positive test results from the ith study in the disease grp is y_i1 

and for the normal grp y_i0, follow binomial distributions such that 

y_ij ~bin(N_ij, eta_ij)

where N_ij is the # of test results in the group and 
eta_ij is the true rate of positive results.

D_i and S_i are random-effects that describe how accuracy and implicit threshold , respectively, vary by studies such that:

D_i = logit(eta_i1) - logit(eta_i0)
S_i = logit(eta_i1) + logit(eta_i0)

D_i is normally distributed with mean A+B*S_i and variance  sigma_D^2
S_i is normally distributed with mean S and variance sigma_S^2

Thanks for your assisstance.
Sincerely,
Ben

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