Dose-response-time data analysis

R. Andersson. PhD thesis, University of Warwick. supervisors J. Gabrielsson, M. Jirstrand, M. J. Chappell, N. D. Evans, August 2017.


The traditional approach to pharmacodynamic modelling relies on knowledge about the pharmacokinetics. A prerequisite for obtaining kinetic information is reliable exposure data. However, in several therapeutic areas, exposure data are unavailable including when the drug response precedes the systemic exposure (for example pulmonary drug administration) and when the drug is locally administered (for example ophthalmics).

Dose-response-time (DRT) data analysis provides an alternative to exposure-driven pharmacodynamic modelling when exposure data are sparse or lacking. In DRT modelling, the response data are assumed to contain enough information about the drug kinetics, whereby a biophase model can be developed and act as the driver of the pharmacological response.

The following work presents the fundamental principles of DRT modelling. This include the entire procedure of identifying a DRT model, encompassing the assessment of the biophase function and the pharmacodynamic model, extensions to cover population variations, identifiability analysis, parameter estimation, and model validation. To demonstrate the utility of the technique, two extensive pre-clinical DRT studies of the interaction between nicotinic acid (NiAc) and free fatty acids (FFA) are presented. The first study covered the response behaviour following intravenous and oral NiAc dosing in both normal (lean) and diseased (obese) rats. The second study extended the models of the first study to incorporate insulin as a driver of the FFA response. Moreover, data from chronic trials were analysed with the aim to quantitatively understand the adaptive behaviours associated with long-term NiAc treatments.

The aim of this work is to answer the questions of when and how to use DRT data analysis, and what the limitations of the method are.

The DRT models of the first study were successfully fitted to all response-time courses in lean rats, with high precision in the parameter estimates (relative standard errors (RSE) < 25%), visual predictive check (VPC) and individual plots that captured the population and subject trends, and “-shrinkages of less than 10%. The model for the obese rats were less precise, with specific parameters being practically non-identifiable (with, for example, RSE 250%). The results for both lean and obese rats were generally consistent with those of an exposure-driven reference model, albeit with less precision and accuracy in the parameter estimates. Finally, the model was able to describe non-linear biophase kinetics, present at high oral dosages of NiAc.

The DRT models of the second study were able to capture the response-time courses for insulin and FFA on a population and individual level, and for both lean and obese rats. However, many parameters were uncertain (with RSE of, for example, 30-50%) and some were practically non-identifiable (with RSE of > 100%). The estimates were generally less precise and more inaccurate than those obtained in an exposure-driven reference model. Yet, most parameter estimates of the DRT models were within one standard deviation from those of the exposure-driven model. The final model was used to predict steady-state FFA exposures following repeated NiAc dosing for a range of different infusion protocols. The optimal dosing regimens consisted of infusions and wash-out periods were the wash-outs were 2h longer than the infusions. These predictions were consistent with those made by the exposure-driven model. Albeit, the DRT model predicted a slightly lower optimal reduction of FFA exposure.

It is important to recognise that DRT analyses introduce bias and variability in the parameter estimates. To obtain reliable results, it is advisable to have rich pharmacodynamic data, covering drug administration at different routes, rates, and schedules. With these issues taken into account, the technique still performed well in the two extensive studies presented in this work.

In conclusion, DRT data analysis is a modelling technique used in situations when exposure data are unavailable. The method is versatile and can describe a range of different pharmacological behaviours. Precision and accuracy is lost when comparing to an exposure driven pharmacodynamic modelling approach. Thus, DRT modelling is not to be considered as a replacement of the gold-standard pharmacokinetic-pharmacodynamic framework, but rather as a compliment when exposure data are unavailable.

Photo credits: Nic McPhee