You might try a google search on "Bayesian methods for diagnostic tests" to see what other folks in this area may have tried.  That 10% incidence of the Xray variable may make this very difficult to establish a relationship, especially in terms of how many subjects might be needed to get reasonable credible intervals on the probability.   SteveDenham ... View more

Let's go through these by number:   My questions are: Does my action plan for addressing this exploratory question seem correct? Not really sure why you collapsed a multinomial response down to a binomial, but I think your approach is defensible.  It seems like a good start, in any case. Am I correct in keeping only those participants that have both a baseline visit, as well as visit 5 assessment for the final analysis dataset, and excluding the rest? Or is this problematic? If yes, what are some correct alternatives? This is certainly a case where, if the data are MNAR (missing, not at random), you might want to restrict the analysis to the complete records.  However, if your data are MAR or MCAR, the maximum likelihood analysis can handle the missing values. Are there any pre-modeling visualization techniques that I can/should use to further explore my data? Is it ok to use boxplots to look at look at the distribution of my continuous variable at each level of the binary outcome? Should I maybe use point-biserial correlation first to see if there’s any evidence of a relationship at all between my predictor and dependent variable before fitting the model? If yes, is there such a thing as point-biserial correlation for repeated measures data, or should I just use the baseline values of the variables? What do you expect to learn from the boxplots?  The point-biserial issue can be addressed by a cluster approach--plot time vs independent variable with the binary outcome as two different colors - see the second example in PROC FASTCLUS as an approach..   Is my model setup correct/complete? Your model assumes that the values at the various visits are not correlated.  You may wish to impose some sort of covariance structure on visit. How can I check to see if my model fits the data well? I know that for regular linear models, there’s residual plots, QQ plots, check for outliers and influential points etc. But not sure what kind of model diagnostics are best for GLMMs? This is undoubtedly one of the hardest questions in GLMMs.  You have two outcomes, so you may want to look at cutpoints in your model for classification of false positives and false negatives (ROC curve).  GLIMMIX doesn't do this automatically like LOGISTIC, but I am sure there are examples on the web of how to do this with DATA steps and PROC SGPLOT. Any other suggestions/recommendations? Not at this stage, but eventually you will probably want to work with the multinomial response.  At that point, things get much fuzzier (in my opinion). SteveDenham ... View more

Recall that for a Poisson distribution the mean equals the variance.  By specifying RANDOM residual without indicating a subject you have confounded the R side variance with the residual variance.  With 3 visits per subject, perhaps this code will help (no guarantee, though):   proc glimmix data= mydata; class id Gender visit_no ; nloptions maxiter=2000 tech=nrridg; model Length_of_ICU_stay= gender Age varA visit_no/ dist=poi link=log solution; random visit_no/type=cs residual subject=id; output out=gmxout pearson=pearson; run /* Or this, for a G side approach */ proc glimmix data= mydata method=laplace; class id Gender visit_no ; nloptions maxiter=2000 tech=nrridg; model Length_of_ICU_stay= gender Age varA / dist=poi link=log solution; random visit_no/type=cs subject=id; output out=gmxout pearson=pearson; run;; I chose a compound symmetry variance structure as I doubt that the visits are equally spaced in time, even if indexed as 1, 2 and 3.  A heterogeneous compound symmetry (csh) may give a superior fit, but simpler is usually better and has a higher chance of converging.  I also added an NLOPTIONS statement that could result in convergence, if you are hitting up against the default 20 iteration limit.   SteveDenham.       ... View more

Check the GENMOD documentation. In the Details section, it gives the methods for calculating confidence intervals by the two available methods (likelihood ratio and Wald).  Neither of those use the closed formulas you present.   SteveDenham ... View more

Specifying TYPE=HF in the REPEATED statement can accomplish this.  However, I suspect you missed the point I was trying to make.  Consider other covariance structures - I really doubt that HF will lead to the smallest corrected AIC - it will probably not be the best fit for your model.  This avoids making a sphericity assumption, which is really not necessary (see the chapter on Repeated Measures in any edition of SAS for Mixed Models for a discussion).   SteveDenham ... View more