Concordance between criteria for covariate model building

When performing a population pharmacokinetic modelling analysis covariates are often added to the model. Such additions are often justified by improved goodness of fit and/or decreased in unexplained (random) parameter variability. Increased goodness of fit is most commonly measured by the decrease in the objective function value. Parameter variability can be defined as the sum of unexplained (random) and explained (predictable) variability. Increase in magnitude of explained parameter variability could be another possible criterion for judging improvement in the model. The agreement between these three criteria in diagnosing covariate-parameter relationships of different strengths and nature using stochastic simulations and estimations as well as assessing covariate-parameter relationships in four previously published real data examples were explored. Total estimated parameter variability was found to vary with the number of covariates introduced on the parameter. In the simulated examples and two real examples, the parameter variability increased with increasing number of included covariates. For the other real examples parameter variability decreased or did not change systematically with the addition of covariates. The three criteria were highly correlated, with the decrease in unexplained variability being more closely associated with changes in objective function values than increases in explained parameter variability were. The often used assumption that inclusion of covariates in models only shifts unexplained parameter variability to explained parameter variability appears not to be true, which may have implications for modelling decisions.