Modeling Subpopulations with the $MIXTURE Subroutine in NONMEM: Finding the Individual Probability of Belonging to a Subpopulation for the Use in Model Analysis and Improved Decision Making

In nonlinear mixed effects modeling using NONMEM, mixture models can be used for multimodal distributions of parameters. The fraction of individuals belonging to each of the subpopulations can be estimated, and the most probable subpopulation for each patient is output (MIXESTk). The objective function value (OFV) that is minimized is the sum of the OFVs for each patient (OFVi), which in turn is the sum across the k subpopulations (OFVi,k). The OFVi,k values can be used together with the total probability in the population of belonging to subpopulation k to calculate the individual probability of belonging to the subpopulation (IPk). Our objective was to explore the information gained by using IPk instead of or in addition to MIXESTk in the analysis of mixture models. Two real data sets described previously by mixture models as well as simulations were used to explore the use of IPk and the precision of individual parameter values based on IPk and MIXESTk. For both real data-based mixture models, a substantial fraction (11% and 26%) of the patients had IPk values not close to 0 or 1 (IPk between 0.25 and 0.75). Simulations of eight different scenarios showed that individual parameter estimates based on MIXEST were less precise than those based on IPk, as the root mean squared error was reduced for IPk in all scenarios. A probability estimate such as IPk provides more detailed information about each individual than the discrete MIXESTk. Individual parameter estimates based on IPk should be preferable whenever individual parameter estimates are to be used as study output or for simulations.