Let Y_{ij} be the response count at jth repeated measure from the ith patient (i=1,cdots,N and j=1,cdots,n_i). The negative binomial mixed-effect independent model assumes that given the random effect G[i]=g[i], the count response from the same subjects i.e., Y_{ij} and Y_{ij'} are conditionally independent and follow the negative binomial distribution:
If partially marginalized posterior distribution (i.e. Reduce=1 in the computation of lmeNBBayes) is a target distribution, the DIC is computed using the focused likelihood
Let m[i] be the number of pre-measurements and n[i] be the total number of repeated measures. Then the repeated measure of a subject can be divided into a pre-measurement set and a new measurement set as Y[i]=(Y[i,pre],Y[i,new]) , where Y[i,pre]=(y[i,1],cdots,Y[i,m[i]]) and Y[i,new]=(Y[i,m[i]+1],...,Y[i,n[i]]) . Given an output of lmeNBBayes, this function computes the probability of observing the response counts as large as those new observations of subject i, y[i,new] conditional on the subject's previous observations y[i,pre] for subject i. That is, this function returns a point estimate and its asymptotic 95% confidence interval (for a parametric model) of the conditional probability for each subject:
providing 
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