Use of mixture model may not be suitable here, if the underlying distribution of eta's for the different subgroups is not normally distributed. Based on the description, it looks like you have 3 degenerate eta distributions(ETA ~0 for no AE; ETA ~1 for 25% AE and ETA ~10 for 7% with all AE), which violates the normality assumption.
Upon quick search, I came across this article, where they have described almost a similar situation as yours. They have used a two part mixture distribution to take care of the large proportions of the subjects with no AE. Hope it is helpful. http://www.ncbi.nlm.nih.gov/pubmed/14977163 Kowalski, Kenneth G., Lynn McFadyen, Matthew M. Hutmacher, Bill Frame, and Raymond Miller. "A Two-Part Mixture Model for Longitudinal Adverse Event Severity Data." Journal of Pharmacokinetics and Pharmacodynamics 30, no. 5 (October 2003): 315-36. Thanks. Mathangi Gopalakrishnan, MS, PhD Research Assistant Professor Center for Translational Medicine (CTM) School of Pharmacy, UMB Ph: 410-706-7842 www.ctm.umaryland.edu<http://www.ctm.umaryland.edu/> From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Mark Sale Sent: Friday, February 19, 2016 5:30 PM To: nmusers@globomaxnm.com Subject: [NMusers] Mixture model with logistic regression Has anyone every tried to use a mixture model with logistic regression? I have data on a AE in several hundred patients, measured multiple times (10-20 times per patient). Examining the data it is clear that, independent of drug concentration, there is very wide distribution of this AE, 68% of the patients never have the AE, 25% have it about 20% of the time and the rest have it pretty much continuously, regardless of drug concentration. (in ordinary logistic regression, just glm in R, there is also a nice concentration effect on the AE in addition). Running the usual logistic model, not surprisingly, I get a really big ETA on the intercept, with 68% of the people having ETA small negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly predictive of the post hoc ETA. I thought I could use a mixture model, with 3 modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd distribution, still with the really large OMEGA for the intercept. Even when I FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd distribution (and OMEGA), and it still gave me a very small difference in the intercept for the 2nd and 3rd populations. Is there an issue with using mixture models with logistic regression? I'm just using FOCE, Laplacian, without interaction, and LIKE. Any ideas? Mark Mark Sale M.D. Vice President, Modeling and Simulation Nuventra, Inc. (tm) 2525 Meridian Parkway, Suite 280 Research Triangle Park, NC 27713 Office (919)-973-0383 ms...@nuventra.com<ms...@kinetigen.com> www.nuventra.com<http://www.nuventra.com>
