Combined proportional and additive residual error models in population pharmacokinetic modelling

In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparison between approaches is still lacking.

The theoretical background of the methods is described. Method VAR assumes that the variance of the residual error is the sum of the statistically independent proportional and additive components; this method can be coded in three ways. Method SD assumes that the standard deviation of the residual error is the sum of the proportional and additive components. Using datasets from literature and simulations based on these datasets, the methods are compared using NONMEM.

The different coding of methods VAR yield identical results. Using method SD, the values of the parameters describing residual error are lower than for method VAR, but the values of the structural parameters and their inter-individual variability are hardly affected by the choice of the method.

Both methods are valid approaches in combined proportional and additive residual error modelling, and selection may be based on OFV. When the result of an analysis is used for simulation purposes, it is essential that the simulation tool uses the same method as used during analysis.