Theoretical and Numerical Investigation of the Consistency of Model Comparisons in Pharmacometrics

Pharmacokinetic (PK) and pharmacodynamic (PD) models are essential tools in drug development, making the selection of an appropriate model critically important. When using likelihood ratio tests (LRTs) to compare nested models, it is crucial to ensure their validity, especially when parameters are fixed. This work examines the continuity of likelihood functions as a necessary condition for LRT validity within the framework of population modeling. By decomposing the Objective Function Value (OFV), we identify scenarios where parameter fixing leads to non-continuous likelihood behavior, potentially invalidating the LRT application. A proof and numerical examples illustrate that while fixing population parameters maintains continuity through compensatory behavior of terms within the OFV, fixing individual parameters introduces discontinuities. Overall, this work underscores the need for careful consideration of parameter fixation in population models: It shows that population parameters can be fixed without violating the continuity condition for LRTs and suggests that introducing covariates may provide a viable alternative for fixing individual parameters. Further investigation into the sufficiency of continuity as a condition for the LRT's validity is needed.