Identification of continuous covariate relationships

Objective: The objective of this presentation was to demonstrate a new method to identify continuous covariates. The investigation of time after kidney transplant as a covariate on tacrolimus bioavailability was used as an example.

Methods: A total of 3100 tacrolimus concentration-time points were obtained from 242 patients who underwent kidney transplantation at Oslo University Hospital (Oslo, Norway) [1] or Princess Alexandra Hospital (Brisbane, Australia) [2]. Population pharmacokinetic modeling was performed using NONMEM v 7.2. The effect of continuous covariates (age, total body weight, fat free mass, hematocrit, albumin, liver function test, corticosteroid dose and time after transplant) on pharmacokinetic parameters were initially investigated by categorizing subjects according to covariate value (e.g. time categories of post-transplant day 1-2, 3-4 and so on). Categories were selected to obtain approximately the same number of observations in each category. Separate relative values for clearance (CL) and bioavailability (F) were estimated for each category and these values were plotted as a function of the mean covariate value in each category. Empirical continuous parametric models (linear, power, exponential, sigmoid) were subsequently used to match the discrete distribution of category parameter values. The fit was evaluated using a prediction-corrected visual predictive check (pcVPC) as function of the continuous covariate.

Results: A pcVPC using time after transplant versus concentration revealed a systematic prediction error during the first 70 days. Estimation of 12 time category-specific values for CL and F led to decrease in objective function values (ΔOFV) of -196 and -228, respectively, which suggested changes in F were more important than changes in CL. The observed shape of time after transplantation on bioavailability was describable by two separate sigmoid functions (ΔOFV -217 for 6 parameters). The parametric model fit was similar to the categorical method fit with fewer parameters. The parametric model allows a continuous prediction of changes in F with respect to time after transplant. A pcVPC for this model indicated that the systematic prediction error during the first 70 days was no longer present.

Conclusions: When there is little or no prior knowledge about the expected shape of a covariate relationship, it can be useful to initially investigate the shape by categorizing subjects by covariate value and estimate a pharmacokinetic parameter for each category. The categories can subsequently be replaced by a parametric function. This method can help identify covariate relationships not easily identified using traditional methods.

[1] Storset, E. et al. Population pharmakokinetics of tacrolimus to aid individualized dosing in kidney transplant recipients. PAGE 2012, abstract II-252012. Available from: Accessed January 2013
[2] Bergmann, T. et al. Prediction correction: quick fix for VPC misdiagnosis in a tacrolimus popPK model. PAGANZ 2012. Available from: Accessed January 2013

Elisabet Storset

  • University of Oslo / University of Queensland