Models for time-varying covariates in population pharmacokinetic-pharmacodynamic analysis

If appropriately accounted for in a pharmacokinetic (PK)-pharmacodynamic (PD) model, time-varying covariates can provide additional information to that obtained from time-constant covariates. The aim was to present and apply two models applicable to time-varying covariates that capture such additional information.

The first model estimates different covariate-parameter relationships for within- and between-individual variation in covariate values, by splitting the standard covariate model into a baseline covariate (BCOV) effect and a difference from baseline covariate (DCOV) effect. The second model allows the magnitude of the covariate effect to vary between individuals, by inclusion of interindividual variability in the covariate effect. The models were applied to four previously analysed data sets.

The models were applied to 10 covariate-parameter relationships and for three of these the first extended model resulted in a significant improvement of the fit. Even when this model did not improve the fit significantly, it provided useful information because the standard covariate model, which assumes within- and between-patient covariate relationships of the same magnitude, was only supported by the data in four cases. The inclusion of BCOV was not supported in two cases and DCOV was unnecessary in three cases. In one case, significantly different, nonzero, relationships were found for DCOV and BCOV. The second extended model was found to be significant for four of the 10 covariate-parameter relationships.

On the basis of the examples presented, traditionally made simplifications of covariate-parameter relationships are often inadequate. Extensions to the covariate-parameter relationships that include time-varying covariates have been developed, and their appropriateness and benefits have been described.