Adding a Placebo Component to Your PK/PD Model in Phoenix

PK/PD modeling is an exciting are of research in clinical pharmacology. Most often we try to model the effect of a drug by drawing relationships between the concentration and effect. This usually entails subsetting the data to exclude information from subject that received placebo during the trial. But statistical comparisons in clinical studies are most often performed by comparing active treatment to placebo treatment. This is because we have to correct for disease progression and the psychological effects of the placebo treatment. This is a tip on how to code for a placebo effect in Phoenix when building a PK/PD model.

A general PK/PD model has a form like the following:

C(t) = function(PK parameters, covariates, time)
E(t) = function(PD parameters, covariates, concentration)

The E(t) model may take a form such as the following “Emax” model:

E = (Emax * C)/(EC50 + C)

But often times there is a placebo or disease effect. For example, patients on placebo may get progressively worse over time. Or patients that receive placebo might actually improve slightly over time. Conceptually, we can build a PK/PD model that looks like the following:

E = Baseline + Placebo effect + Drug effect

But how do you create that model in Phoenix? First you write the code for the effect

E = Baseline + Placebo + Drug effect

Then you code your variables. Baseline is normally a single variable. You can either use the term “Baseline” as your variable, or recode it with something like the following:

E0 = Baseline

Then you code your placebo model. These can take many forms, but the simplest model is a linear increase (or decrease) over time. This would be coded as follows:

Placebo = Slope * t

Where “t” is time in the Phoenix model. Note that your time variable might be coded to a specific column in your dataset (e.g., Actual_Time) that has a different name. It doesn’t matter. Time is always “t” in Phoenix code.

The last thing is to code the drug effect model. The code for this is shown below:

E = (Emax * C)/(EC50 + C)

Obviously, more complex models for placebo effects and drug effects can be included. You can also add a disease effect if the disease changes over time in the study. I hope this helps you build your own models with placebo and disease effects in Phoenix.

To learn about how we’ve improved Phoenix to make performing NCA and PK/PD modeling even easier, please watch this webinar I gave on the latest enhancements to Phoenix.