Section: New Results

Between-subject and within-subject model mixtures for classifying HIV treatment response

Participants : Cyprien Mbogning, Kevin Bleakley, Marc Lavielle.

We have proposed a method for classifying individuals into clinically-relevant population subgroups [5] . This is achieved by treating “subgroup” as a categorical covariate whose value is unknown for each individual, and predicting its value using mixtures of models that represent “typical” longitudinal data from each subgroup. Under a nonlinear mixed effects model framework, two types of model mixtures were developed:

• Between-Subject Model Mixtures (BSMM) assume that each individual's longitudinal data follows one of $M$ “base” models, but we do not necessarily know a priori which one. Individual $i$ thus has a label $z_i=m\in \{1,...,M\}$ referring to the model that is supposed to have generated it. We have shown how to extract a posteriori estimates of the probability that each individual was generated by each of the base models; this can be used to predict which type of patient we have: non-responder, responder or rebounder.

• Within-Subject Model Mixtures (WSMM) make the hypothesis that the model mixture occurs within each individual. In the HIV example, this means that we consider that each patient is partially a non-responder, partially a responder and partially a rebounder. This is perhaps more biologically plausible than BSMMs in the sense that each individual's response may be due to their own particular combination of virus strains, cell populations, etc. Within the NLMEM framework, this means including individual “model proportion” parameters into the model and having to estimate them along with the other parameters of the NLMEM. It turns out that this does not require any mathematical extensions to a typical NLMEM. But we can use the estimated proportions to help categorize patients, especially those who do not naturally fall into one of the three “typical” categories.

An application to longitudinal viral load data for HIV-positive patients were used to predict whether they are responding – completely, partially or not at all – to a new drug treatment.