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 (MIXEST(k)). The objective function value (OFV) that is minimized is the sum of the OFVs for each patient (OFV(i)), which in turn is the sum across the k subpopulations (OFV(i,k)). The OFV(i,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 (IP(k)). Our objective was to explore the information gained by using IP(k) instead of or in addition to MIXEST(k) 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 IP(k) and the precision of individual parameter values based on IP(k) and MIXEST(k). For both real data-based mixture models, a substantial fraction (11% and 26%) of the patients had IP(k) values not close to 0 or 1 (IP(k) 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 IP(k), as the root mean squared error was reduced for IP(k) in all scenarios. A probability estimate such as IP(k) provides more detailed information about each individual than the discrete MIXEST(k). Individual parameter estimates based on IP(k) should be preferable whenever individual parameter estimates are to be used as study output or for simulations.