Handling of time-varying covariates in population model building.
Ulrika Wählby(1), Alison H. Thomson(2), Peter A. Milligan(3) and Mats O. Karlsson(1)
(1)Division of Pharmacokinetics and Drug Therapy, Uppsala University, Uppsala, Sweden (2)University of Glasgow, Dept of Medicine & Therapeutics, Western Infirmary, Glasgow, UK (3)Department of Clinical Pharmacokinetics and Pharmacodynamics, Pfizer Global Research and Development, Sandwich, UK
Time-varying covariates contain more, and to some extent different, information than time-constant covariates. As information is linked to the magnitude or the frequency of change it is of value to document these changes, and also to properly account for the variation in population pharmacokinetic (PK) or pharmacodynamic (PD) modelling. Yet, covariate models seldom differentiate between time-constant and time-varying covariates as in (1), even if there are exceptions (e.g. Taright et al. PAGE 1997). Some examples of extended models which apply only to time-varying covariates are given in (2)-(5) below.
1) Standard covariate model:
P = THETA(1) *(1 + THETA(2) *(COV – medianCOV)) *exp(ETA(1))
2) Model for separate inter- and intra-subject variation in the covariate relationship:
P = THETA(1) *(1 + THETA(2) *(BCOV – medianBCOV) + THETA(3) *DCOV) *exp (ETA(1))
where BCOV and DCOV are the baseline and change from baseline covariate values, respectively
3) Interindividual variability in covariate relation:
P = THETA(1) *(1 + THETA(2) *exp(ETA(2)) *(COV – medianCOV)) *exp(ETA(1))
4) Model including predicted covariate values (CÔV) from a model for the covariate:
P = THETA(1) *(1 + THETA(2) *(CÔV – medianCÔV)) *exp(ETA(1))
5) Time-dissociation of covariate influence:
P = THETA(1) *(1 + f (THETA, COV, time))
In addition to the models above, there is a possibility that the interpretation of the change in a covariate over time is confounded, as it may be affecting drug disposition, or the change could be caused by the drug treatment itself, or the influence is bi-directional (e.g. a nephrotoxic (hepatotoxic) drug producing decreased creatinine clearance (increased liver enzyme levels) as well as a lowered CL).
In sequential PKPD modelling essentially all these models (apart from (2)) are regularly applied when associating PK (a time-varying covariate) to PD, however, usually not for associating “traditional” covariates (e.g. lab-values) to PK or PD relationships. How additional information in such time-varying covariates may be utilized in some of these models will be illustrated using real data sets.
Reference: Taright, N., Mentré F. and Mallet A., Non-stationarity of kinetic parameters in multi-occasion designs. Oral presentation PAGE, Glasgow 1997.