Pharmacometric modeling with the zero-order hold

Solving models comprised of nonlinear differential equations (DEs) in NONMEM using ADVAN6 or ADVAN13 typically requires substantially longer run times than models comprised of linear DEs, which in some cases allow for analytical solutions. Often the need to use nonlinear DE solvers results from pharmacokinetic (PK) variations over the dosing interval introducing the nonlinearity via a nonlinear transfer function, as is the case for indirect-response models and enzyme induction models. As long run times hinder model development, it is desirable to derive suitable approximations to speed up model solutions. The zero-order hold, a concept used in the field of advanced process control to optimize control decisions, provides an attractive approximation for these situations that often results in a sequential system of simpler DEs that in some cases can be solved analytically. Two examples, an indirect-response model and an enzyme induction model, demonstrate that the zero-order hold approximation provides a substantial reduction in computational time (up to ~ 140-fold) without unduly biasing the parameter estimates. These examples demonstrate that the zero-order hold approximation offers an attractive method for efficiently solving models where time-varying PK leads to a nonlinear system of DEs.