PK/PD Modeling Exercise


Hi. I’m Cody Peer, a clinical pharmacologist and
staff scientist in the National Cancer Institute’s clinical pharmacology program. Today, we’re going to be doing a follow-up
activity to Joe Rogaboru’s [spelled phonetically] PK/PD modeling, and we’ll be performing an
activity to demonstrate how to build a PK/PD model and explore the different ways that
these models can be used for clinical drug development and to gain a better understanding
of the pharmacology of whatever drug you’re studying. So, a PK/PD model is essentially an exposure-response
model describing the relation of the drug in terms of how much drug molecules are circulating
through your body and how that’s tied to whatever response that you’re looking at. So, all drugs have a desired effect on target
that they’re designed to hit, and also some side effects off target effects. And while the desired effects are studied,
obviously, we want to also study the off-target effects, because if the drug is too toxic
then patients can’t tolerate it, and then they go off-study and they don’t get the benefit
of the drug. So, during clinical drug development phase
ones, two, and three, a toxicity profile is generally developed and identified, and also
response models. So, we can gain a better understanding of
exposure-response relationships with these drugs throughout the clinical development,
and then we can use that data to build said models. The drug in question that we’ll be discussing
today is called beleodaq; the generic name is belinostat. It is a second-generation histone deacetylase
inhibitor. It is — because it is a second generation,
it has — all the HDAC inhibitors in this generation have a hydroximate molality on
the end of their molecule, and that makes it a good handle, so to speak, on the drug
metabolism for glucuronidation, and we’ll cover that shortly here. It was FDA-approved in 2014 for peripheral
T-cell lymphoma relapse to refractory at a dose of 1,000 milligrams per meter squared
as a 30-minute IV infusion. Its pharmacokinetic profile is best described
by a rapid distribution into the periphery and rapid elimination with a short half-life
ranging from 0.3 to three and a half hours in humans, in plasma. And, like other drugs in its class, hydroximate
histone deacetylase inhibitors, it is predominately glucuronidated by the polymorphic UGT1A1. And there are two particular sites where the
gene UGT1A1 is altered. One is the *28 genotype, where there’s an
extra region in the promoter that reduces its expression, hence reduces its activity. And patients with the *28 one or two copies
have a slower metabolism and slower clearance. So, they have overexposure of drug. And then same with UGT1A1*60, different site,
same effect. So, we built a PK/PD model that describes
the genotype effects along with every other kind of population characteristic that we
included. And this will also tie into Dr. Beezus’ [spelled
phonetically] population PK lecture, where he described how to build a population PK
model, which is what this is. And we noticed here that patients that were
carriers of the *28 and/or *60 had a slower rate of metabolism. And during this infusion, which was a 48-hour
infusion — this is a different study and a different disease setting, so in this case
the study was trying to get the drug approved in a different disease setting to ad on to
the FDA approval of peripheral T-cell lymphoma. And so, because it has a short half-life,
this study had a prolonged 48-hour infusion to prolong the drug’s effect. And, during the drug infusion, the black line
here represents the steady state of drugs exposure for impaired metabolizers. And, as you can see, it’s higher than people
with regular or extensive metabolism. So, this sort of proves our hypothesis that
patients with these genotypes do have a slower metabolism and a higher exposure. And the model did simulate a slower clearance
for the impaired metabolizers. In the lower left figure there, the red box
depicts a clearance for the impaired metabolizers, and it has a slower clearance rate than extensive
metabolizers. And so, in order to not overdoes impaired
metabolizers, we simulate a dose reduction that, when you do the does reduction in impaired
metabolizers, you get a more comparable exposure. So, you are helping those patients not have
too much toxicity. So, the purpose of this activity is to go
through the steps to build a PK/PD model. So, what we’re going to do first is, now that
we’ve described the PK model, we’re going to go through the process of putting that
model together in terms of text, so that we can understand how that PK model is built. So, the pharmacokinetics is essentially just
describing the kinetics of the drug over time. So, in order to do that, we use differential
equations and we’re describing the movement of the drug from the central compartment in
the plasma to the periphery and then back into the central compartment where it can
be metabolized and cleared. So, the top two lines there are the differential
equations of describing the drug movement in the first or second compartment, as well
as a variety of other lines of code that we will get to. So, this overall line of code here describes
everything that we would need for the Pop. PK model. The first section highlighted in red here
is the structural model. So, this is where you can code a two-compartment
model structure and also describing the rates into and out of each compartment. We have four parameters that the model is
estimating; the volume of each compartment — one and two — the clearance rates into
and out of — between the compartments, and then the overall systemic clearance rate out
of the body. And so, we have a variety of ways that we
can do that. So, the type of model this is is a mixed-effect
population model. So, the mixed-effects is a mix of the fixed
and random effects. And one other aspect to a structural model
here is the unexplained error. So, we try to explain as much error in the
model as possible, and the unexplained portion of error, we can still describe by a proportional
model, which is highlighted here in yellow. The fixed-effects is represented by the population
average of that parameter. So, for instance, let’s say one of these parameters
is body weight, for an easy example. So, if everyone in the world, a population,
weighed themselves, you’d have a population average. Let’s call it 70 kilograms. Some people weigh more, some people weigh
less. Trying to understand the reasons why certain
individuals weigh more or weigh less, you would have a population average weight and
then other covariates to explain why said individual might weigh more or less than the
population average. Are they taller? Are they older? Are they younger? What is their diet? Et cetera. So, in the parameter equation to calculate
each individual’s parameter estimate, you have a population average for that parameter,
and then other covariates or variables that help describe why that patient might have
a slightly different value for that parameter than the population average. So, again, the fixed effects are just the
population average. Then, we have the random effects, which are
those portions of the equation for each parameter that help describe why one patient has a different
value for that parameter than other patients. And, as we all know, not everyone reacts to
the drug the same, and there’s a variety of reasons why that is. It could be organ function, age, sex, gender,
race, a variety of things. So, in this study, we noticed that, in addition
to the base level between subject variability represented by the EDA [spelled phonetically]
values, we have a bunch of covariates. And we built a covariate model on top of our
base structural model, and in this particular drug in this particular study, with the study
data that we had available, such as albumin and renal function and obviously the UGT1A1
genotype status, those were the variables that significantly impacted the clearance. And the volume of the central compartment
body weight did explain some of the variability on that parameter. So, that is the population PK aspect of this
PK/PD model. So, now we want to talk about the PD aspect
of this PK/PD model. And first we’re going to do two parts to the
PK/OD analysis. First, we’re going to do the on-target desired
effects, which the HDAQ inhibitors inhibit histone deacetylases. And in histones, there is a regulated function
of relaxation and tightening of chromosomes around histones, the DNA around histones. So — and that’s regulated by histone acetylation
transferases and histone deacetylases. And so, the histone acetylases inhibitors
inhibit the deacetylation. So, knowing the mechanism of the drug is important
to develop this PK/PD model. So, with that said, we know that belinostat,
and other like drugs, histone deacetylase inhibitors, inhibit deacetylase activity at
certain histones on certain lysines. So, what we ultimately can measure as an indirect
marker of drug effect is global lysine acetylation. It’s an easy, validated way to assess the
reduction of the activity of the enzyme without actually measuring the enzyme’s activity directly. So, we indirectly measure just global lysine
acetylation. And as the drug works and inhibits deacetylation,
acetylation levels go up. And that’s how we can mark drug effect. So, building on top of our PK model, we’re
adding a PD response model, where knowing that our measured response is global lysine
acetylation, we have a regulation of the acetylation by acetylation and deacetylation in terms
of the model its modeled by. A K-in and a K-out rate, respectively. The drug effect for belinostat is on the deacetylation
aspect, or the K-out, because belinostat inhibits deacetylation enzymes. So — and we can mark — we can track our
response over time with the differential equation listed here. And because it’s a reversible mechanism,
the effect — the inhibitory effect, IMAX and IC50, are tied into the drug concentration. So, when the drug concentration’s zero, the
effect will be zero. And that captures the reversible aspect of
the mechanism. So, with the diagram of the model depicted
here, let’s next go through how to actually build that model in a — in an analysis software. So, we need the differential equations textually
to build that model. The PK model code here is the same as we just
discussed, in red, so we don’t need to cover that again. But the PD aspect of the model here is in
blue. And as we can see, if we want to track the
change in response over time, or the change in effect over time — so, we have the four
parameters here that we need to estimate for the model. The PD model is the K-in and the K-out rates,
the IMAX, and the IC50. So, the time component of this effect model
is tied indirectly to the drug concentration, which in itself is tracked by time. Drug concentration changes over time as a
drug is eliminated, and the drug concentration magnitude will change with dose. So, those all can be tied into the effect. So, after we can implement this code into
our whatever software we’re using — and, a side note: This model code here is in the
Phoenix modeling language, but it can easily be deciphered into NONMEM-Fortran or MATLAB
or any other comparable PK modeling software. The essence is the same; you’re having a differential
equation to describe the drug effect or drug concentration over time, and the nature of
that differential equation doesn’t change. Some syntax might change, but the essence
of the code depicted here will apply almost in every software. So, once we implement that code into our software
and implement the data set that has all the data variables that we need, we can simulate
what a exposure-response PK/PD relationship would look like. And in this diagram here, the blue lines are
represented — representing the drug concentration for this study, which was a 48-hour infusion. So, as drug levels increase up to a steady
state during the infusion, you can also see a correlated increase in the global acetylation
fold change, indicated by the red line. And on the right axis, the right Y axis there,
is the global lysine fold change acetylation. And as the drug infusion is stopped at 48
hours, and the drug is quickly cleared due to the quick half-life of the belinostat,
the global acetylation levels quickly fall back to one-fold, which is baseline. So, this model can adequately capture the
reversible mechanism between belinostat drug concentrations and the histone deacetylase
inhibition. So, while that was the relationship with the
desired effect, we also have to understand the off-target undesirable adverse effects. And in this case, many of the drugs in this
class, including panobinostat, romidepsin, and belinostat, all have links to thrombocytopenia,
which is a decrease in platelets. The mechanism of this drug effect on platelets
is a delated maturation of the platelet precursor, which is a megakaryocyte, and if the drug
can delay the maturation of the precursor into the mature thrombocyte, then you’re eventually
going to deplete your thrombocyte, your mature thrombocyte count, over time, especially with
repeated cycles of drug, and it’s going to take your body longer to recuperate and replenish
your mature thrombocyte levels. So, with repeated dosing of panobinostat,
romidepsin, and belinostat, eventually patients have grade two or grade three or worse thrombocytopenia,
which can be resolved with platelet infusions, but it’s still a — it can be a dose-limiting
toxicity for a time, which will require the patient to dose-reduce or delay a dose, but
then they’re just not getting the desired effect that they need. So, we need to understand this relationship
a little bit better. It’s been published for panobinostat and several
other drugs in this class, but never for belinostat. And that is something that was recently published
by our group. So, as I said, this effect on this drug class
has been published before. So, what we can do is take what’s been published
into literature in terms of a PD response model for megakaryocyte maturation and drug
effect on it and apply that to our study here. So, we have our same PK two-compartment model
here, where the drug concentration is now linked to a drug effect in the yellow box
there, where it delays the maturation of the megakaryocytes. And so, this is a semi-mechanistic representation
of a drug effect on thrombocytes. And the code for this — the PK aspect, again,
is the same, in red, and the PD aspect here is in blue. And we’ll go through each section of code
one by one, describing this figure here. So, there are several aspects to this figure
that the code will represent. So, the first section is understanding the
proliferating compartment. And we have a differential equation here to
measure the amount of proliferator cells or megakaryocytes based on the rate going to
make them and the rate going to mature them. And that’s where the drug effect is. And our drug effect, which is described by
the caption there, “E drug,” is actually a linear effect on the effect with concentration. So, we have a slope parameter that we’re measuring
that is tied to the drug concentration. So, the drug concentration is linearly related
to the drug effect. And that relationship is described by the
slope parameter. The next section is the maturation section,
where the megakaryocytes are sequentially matured in these transit compartments, and
these transit compartments can be described with differential equations, as depicted here. And then the last section here is the circulating
compartment of mature thrombocytes, or mature platelets, which is what we are measuring
clinically. We’re measuring — when we take samples from
patients, we’re measuring their circulating platelet count. And this is where we can use this observe
data to build our model around and to — and to estimate each of the parameters that we
need to estimate in this model code. And so, what we can do is build a model, estimate
our parameters — it gives us the predicted number of circulating platelets, and we can
compare that to our observed or measured amount of platelets, and see how far off we are. And that will help us to optimize our parameter
estimates and come up with the best model. And we’ve done that, and with our optimal
model, with our optimal parameter estimates, which are listed here below, in the fixed
effects there, then we can simulate a PK/PD response in terms of platelets. So, the left Y axis is, again, depicting the
drug concentrations during a 48-hour infusion. And you see, as you increase dose from 250
in green to 600 mgs per meter squared in red, obviously your steady-state concentration
increases accordingly, and correspondingly, so does the delayed rebound effect of the
platelets. So, on the lowest dose there, in green, on
the right Y axis, is a circulating platelet count measure. And, as you can see, the green line kind of
rebounds the fastest, which makes sense; you have the lowest concentration of drug. And the highest concentration of drug, the
highest dose of drug, you actually rebound the slowest, and you don’t actually fully
recover by the end of the 21-day cycle. So, by the start of the next cycle on day
22, you aren’t really at the highest does level, at least, in this simulation. You’re not fully rebounded yet. So, any subsequent doses, your NADR [spelled
phonetically] is just going to go lower and lower, and eventually that dose is going to
cause, in most people, a at least grade two thrombocyte count, thrombocytopenia event. So, what this model is useful for is, if you
know someone is a UGT variant, and they’re going to clear the drug slower, even with
the same dose as everybody else, they may have a higher exposure. And we can correlate their higher exposure
with how slowly they’re going to rebound in their platelet count. So, you can try to predict when and how severe
their thrombocytopenia event will occur, and you can try to back down their dose early
enough to avoid this situation. And that reduction in dose can be optimized
by simulations. Personalized. So, that is all I have. I hope this activity was helpful for you and
thank you for your time.

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