+31 623 118 438 jeroen@pd-value.com

Smooth PK-PD with IMPRES-M®

Development of pharmacokinetic-pharmacodynamic (PK-PD) models can be a time-consuming hands-on process. At PD-value, we have invented a novel approach that combines powerful tools in neighboring fields to improve PK-PD modeling. We are very proud to present you the result: IMPRES-M®!

Figure 1: PK curve smoothed with P-splines. Individual B-splines are drawn in different colors.

What is IMPRES-M®?

IMPRES-M® is impulse-response modeling where the core representation of a PK curve is a smoothed version of observations. The smooth (black curve in the figure) consists of P-splines, a method that represents data by cubic splines (the colored components in the figure) which are estimated by putting a penalty on differences between neighboring splines. Typically, a curve is all you get from smoothing, and that is not very useful in PK-PD. We need to interpolate and extrapolate to different doses and dose schedules.

The idea of IMPRES-M® now is to have the smooth curve represent the RESponse to a single dose, the IMPulse. The responses to different doses are folded back to one P-spline curve that is regressed through mathematical procedures of convolution and deconvolution. The curve then can be combined with any dose schedule to produce intra- and extrapolations at will.

Read some potential use cases of IMPRES-M® here.

Why has IMPRES-M® not been invented earlier?

The idea behind IMPRES-M® is simple and elegant. Just connect the dots while keeping track of doses. Splines are quite new to our field but are straightforward: the height of splines represent the curve at that point, with the benefit that the transition between them is seamless. You may ask yourself at this point, why have we not heard about this already? The answer is that PK curves are notoriously difficult to work with, they have sharp peaks at the start and slow tails. We had to combine a bag of statistical tricks to get useful PK smooths reliably. Patent pending.

What is the status of IMPRES-M®?

IMPRES-M® is currently under active development on 3 separate tracks: single-subject PK, PK-TTE, and population PK; see current status for details. The single-subject PK functionality is the track most progressed and will be available for testing in July 2024. Please register via the form at the bottom of this page if you would like to participate. Population modeling is an approach where we want to follow the curve for a whole population at once instead of only for single subjects. PK-TTE addresses the modeling of continuous exposure over time as it changes discrete endpoints, such as survival in oncology trials. We are especially excited about PK-TTE as it has the potential to avoid bias in estimating the impact of drug exposure. The first implementations are in R, but we are working on interfaces to NONMEM and nlmixr. Inclusion of IMPRESS-M into other software is also possible.

Take-home messages

IMPRES-M® is a novel method to perform PK-PD modeling. Its simple and elegant approach allows the user to obtain a smooth representation of a PK-curve without the hassle of developing a compartmental model step-by-step. A single-subject smoother is currently undergoing alpha testing and is expected to enter beta testing this summer. Modeling of exposure-to-survival events and population PK modeling will be presented at PAGE and enter testing phases at a later time. Are you inspired? How would you apply IMPRES-M® in your pharmacology projects? Let us know at impresm@pd-value.com.

Register for beta testing

Beta testing


15 + 4 =

Want to know more?

For further introductions or to explore avenues of collaboration, please send an e-mail to jeroen@pd-value.com or see the contact page for other communication options.