Population pharmacokinetic models with time dependent covariates

We developed a two-step strategy to model the time-dependent pharmacokinetics (PK) of a drug, which was motivated by a study of Ditropan. At step one, we considered a spline-enhanced population pharmacokinetic model (SEPK) with time-dependent PK parameters. These time-depend PK parameters were modeled by natural cubic spline functions in the ordinary differential equations. Regression parameters, variance components and smoothing parameters were jointly estimated through maximizing a double penalized log-likelihood. Mean functions and their derivatives were obtained by the numerical solution of ordinary differential equations. Its flexibility in fitting and estimation with respect to model misspecification was discussed. At step two, some PK parameters were restricted as linear functions of time-dependent covariates which were modeled by spline functions, i.e. a spline-enhanced covariate population PK model (SECPK). A two-stage estimate was proposed and its consistency was proven. A modified two-stage estimate is proposed to reduce the bias of the two-stage estimate given the moderate sample size. Both models were applied to Ditropan data. The performance of these two models were evaluated through simulation, and their advantages were discussed.