Laplace approximation and its various approximations are some of the most commonly used techniques in pharmaceutical nonlinear mixed effects modelling to marginalise the the random effects. Classically, only Gaussian random effects have been used with transformations applied after the fact. In this work, the Laplace approximation framework is mathematically analysed showing the theoretical soundness of the method for many non-Gaussian random effects and various error models for a wide range of commonly used pharmacokinetic models, all of which and more are available in the Pumas.jl software for pharmaceutical modelling and simulation.
