Evaluation of extrapolation potential of IMPRES-M, a non-parametric Impulse-Response Modeling framework when applied to pharmacokinetic profiles of different dosing frequencies
Zeyar Mohammed Ali, Lorenzo Cifelli, Jeroen Elassaiss-Schaap
PD-value, Utrecht, the Netherlands
Introduction: Effective utilization of smoothing in pharmacokinetic (PK) and pharmacodynamic (PK-PD) modeling is limited as currently available approaches [1-4] cannot be used to extrapolate across different dosing schemes such as single, intermittent dosing, different dose levels and/or dosing frequencies. A related limitation is application of data from variable, intermittent or sparse sampling schemes. When smoothing without explicit utilization of the underlying dosing schedule, such data are described in a strictly ad-hoc approach.
With the presentation of IMPRES-M, an impulse-response non-parametric regression framework (patent pending), a smoothing approach becomes available that in theory overcomes these limitations [5].
Objectives: The objective therefore is to assess the whether the IMPRES-M framework can successfully extrapolate data from pharmacokinetic simulations beyond the observed range, through comparison of extrapolations to simulated values.
Methods: PK profiles were simulated in R 4.3.2 using the rxode2 package using 1-, 2- and 3-compartmental pharmacokinetic models with intravenous dosing. The same models were also applied as per-oral versions by the addition of a first-order absorption compartment. For each model, 20 subjects were randomly drawn from a population with parameters according to a log-normal distribution with a s.d. of 0.1 to 0.3 (0.1 for Ka, 0.2 for Vc, 0.3 for CL, 0.2 for V2 and 0.3 for Q, if available). The random seed was kept the same for each model/iteration. Model parameters were selected to provide distinct compartmental profiles and accumulation beyond day 3. Samples were drawn during a 3-day q.d. dosing period, with 6 samples at day 1, 3 samples at day 2, and at 48 and 72h after the first dose. Log-normal residual error with an s.d. of 0.05, 0.10, 0.15, 0.25, 0.30 and 0.50. The same sampled subjects were used to simulate one week of b.i.d. dosing, at one tenth of the q.d. dose, i.e. the average daily dose during b.i.d. was 5 times lower compared to the simulated q.d. regimen. 6 samples were taken at the last day without residual error as the reference value (‘truth’). The 3-day samples were subjected to IMPRES-M analysis where the amount of smoothing was selected on the basis of leave-one-out crossvalidation (LOOCV), after which the model was executed in simulation mode to produce projected b.i.d. profiles at day 7. Differences between extrapolated results and simulated ‘true’ values were calculated as weighted root mean squared error per subject, where the error was weighted by the square of the simulated values: WMSE = (extrapolated – simulated)^2/simulated^2 and RWMSE = sqrt(WMSE).
Results:
The IMPRES-M captured the individual profiles mostly adequately on the basis of LOOCV-selected smoothing. The simulation was set up in such a way that perfect extrapolation was not possible, but nevertheless reasonable results were obtained. The RWMSE at a residual s.d. of 0.05 was about 7-15% increasing to about 24-28% for a s.d. of 25% except for two outliers at p.o. 1-compartmental models. Results at an s.d. of 0.30 were at or beyond the border of acceptable with a range of 28-93%. Similar results were obtained when simulating with iv-type profiles, where the results at higher s.d. were more in line with the residual error going up to 36-42% with the highest residual error tested.
Conclusions: In contrast to unstructured smoothing approaches, the IMPRES-M framework (patent pending) is shown to be able to extrapolate beyond the data domain it is fitted to. With a limited sampling scheme and incomplete capture of a PK profile, adequate extrapolation of a different dosing regimen at a different accumulation was achieved. Depending on the simulation setting, increasing residual error was associated with a proportional or strong reduction in quality of extrapolation.
References:
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[4] Park, K., Verotta, D., Blaschke, T. F., & Sheiner, L. B. (1997). A semiparametric method for describing noisy population pharmacokinetic data. Journal of pharmacokinetics and biopharmaceutics, 25, 615-642.
[5] Elassaiss-Schaap J et al., PAGE 2024, Abstract title: “Construction of IMPRES-M, a non-parametric impulse-response modeling method, in the context of varying pharmacokinetic profiles”