hello and good morning afternoon or evening my name is Stacy tannin Bal and I am the lead of the pharmacometrics group in the US for Estell Pharma Global development and I'm really happy to be with you to continue the presentations on model informed drug development with module 2 I'll be doing a review of the various model types commonly used for Mid and I've split this presentation into two parts to control the length what I have here is my bio sketch I'm not going to read it to you it's here for you in the slides but I do want to point out that at the bottom of the slide is my email address if you have any comments or questions please don't hesitate to reach out and and send me an email I'd be very happy to hear from the folks who are watching this presentation to get your feedback so let me jump in and talk about why we do what we do and when I say we I mean modeling and simulation scientists or pharmacometricians when a patient goes to the doctor's office and they're sick or they're not feeling well or they have a disease and they get a drug all they really want to know is when will I feel better if I take this drug when am I going to get a response but the prescriber patient and regulator actually have many more questions one is what's the appropriate individual dose for a patient if a patient doesn't respond or have an adverse event how should the dose be adjusted what happens if a patient misses a dose or takes too much how soon will the effect start and that's certainly a a primary concern of patients and how long will it last in order for me and my teen to be able to answer these questions we have to understand all of the steps between dose and response and we need to understand them in a quantitative way we need to know what will happen if we change the dose if we miss a dose or if we take too much and we do that using pharmacometrics we do that using PK and pkpd modeling and I'll speak more about these Concepts as we go through this presentation but just in brief PK relates the drug dose to the drug concentration profile and when I say dose I mean dose and regimen dose and frequency as well as the formulation when I mention PD that is how the exposure of the drug whether it's the drug concentration the area under the curve the maximum Etc leads to a downstream response and that can happen either directly or that can happen after a series of steps and feedback loops PD can be much more heterogeneous and complicated than PK but we will touch on both of them today ultimately why we do what we do is to get the right dose of the right drug to the right patient at the right time and that can be as simple as this acetaminophen label which is take two caplet every 6 hours while symptoms last for children and Adolescent for the case of acetaminophen you have a fairly wide therapeutic range which means most people will be covered by the same dose however sometimes you need to dial in a little bit more closely to that therapeutic range and that's why in children for example children under 12 you might want a dose by body weight or by some other covariant that we will talk about later that helps you to dial in on getting the appropriate individualized dose to a patient but ultimately my team Works to help figure this out and make sure that we're getting the right dose and timing for each patient so that they get optimal efficacy and minimal safety issues and how do we do what we do we do it through the application of pharmacometrics this is the science which deals with quantitative description of disease drug effects and variability this is how we Implement mild informed drug development it requires Proficiency in a number of areas such as the biology of disease PK and PD as I mentioned before and Mathematics or statistics as well as computational techniques pharmacometrics lies at the heart of what drug companies do collecting data from animals normal volunteers and patients and I would also add we also collect data from literature on similar compounds and within that same indication and then we quantify those data we integrate it together together and we are able with that to determine what that data mean for optimizing drug efficacy and minimizing toxicity and we do that by getting the dose right I'm going to start with the simplest just to make sure that we're all on the same page when we talk about modeling and simulation and defining what are models so please indulge me if you are a mathematici if you're very comfortable with models just sit sit with me for a few minutes while we talk about this at the very simplest form models are mathematical relationships among relevant pieces of information what I like to think of a model is is a summary it's a conceptual tool for translating complex dirty very heterogeneous real world data into a simplified form and that's a mathematical model it's an equation yes it generalizes the detail so you're not going to see all of the small details that happen with within each individual but it gives us Trends and it allows us to summarize quite a lot of information into a succinct package by using this summarizing our information data and assumptions we can then use them to probe alternate designs and outcomes and that is simulation and I'm going to talk a little bit more about simulation in a few minutes so let's start with a model mathematical relationships among relevant pieces of information and I'm going to start with the simplest model that we have which is a linear regression and you see these all the time you see Scatter Plots and you try to draw the best straight line that you can through that plot and you end up with a dependent variable and an independent variable and I'll talk about what those mean in pharmacokinetics and pharmacodynamics in a moment but I just want to orient you to this this plant and you also have things like parameters so for a linear regression your parameters are the slope and The Intercept now let's talk about this in the context of PK or PD your plot will probably not look like this but hopefully you get the gist so in pharmacokinetics when we talk about a dependent variable that is the drug concentration the drug concentration is a function of the independent variables usually on the x- axis you'll see time but sometimes you see dose or regimen so these are the things that drive the dependent variable and when we do our pharmacokinetic models we get things like clearance and volume of distribution we're able to estimate the half-life we're able to determine the exposure the maximum concentration cmax as well as the time that that occurs T-Max so these are the parameters of our pharmacokinetic models and I'll be touching on all of these things again as I get into the modeling components a little bit later for pharmacodynamics the dependent variable variable may be something like a biomarker or a clinical endpoint a surrogate end point for example or blood pressure uh sometimes these are yes no uh pharmacodynamic variables tend to be much much more heterogeneous than pharmacokinetic our independent variables are things like time and Drug exposure and our parameters can vary as I said pharmacodynamic models are quite a bit more variable but generally we'll get some information on the minimum response the maximum response the rate of change of response as your exposure changes and things like potency and I will touch on these Concepts in more detail further in the presentation so I mentioned modeling and simulation now let's talk about simulation and this is an application of modeling and I like this this quote in the bottom and I am afraid I don't know who to attribute it to but I really like this the ultimate goal of modeling is prediction not description description is useful it is important for us to be able to characterize our PK and PD that we've observed but in order for us to optim the dose we need to expand beyond that so what simulation is is entering different inputs into our model to see what the output would look like or how sensitive the output is to changes in certain inputs and we'll talk about this in a little bit more detail further in the presentation but you're really using a mathematical model to conduct in experiments and we call them in silico as opposed to initro or invivo we can use simulation to optimize the design of future studies and actually we often try to optimize the design of our current studies as well to estimate missing observations in the data and predicting observations outside of the data to examine the sensitivity of the model output to non-controllable inputs because that's very important we may find out that we need to adjust our study design or get additional information to handle non-controllable inputs and of course to explore situations that you cannot do in the clinic they would be e ethically financially or physically impossible but they provide valuable information and we'll talk about this a little bit more when we get into the concept of clinical trial simulation so during this presentation I'm going to mention pharmacometrics as a catchall term for several types of modeling starting with the simplest which is PK modeling and as I mentioned before that is how dose becomes concentration and what is the impact of dose on our concentrations and exposures we also have pkpd modeling this is really the simplest form where we look to see how the concentration either in the plasma or at the site of action begets the downstream response we can actually look at modeling and simulation without any Pharma involved at all so we can look at disease progression modeling and we can look at the disease and how it progresses over time without any kind of intervention we can do that at a very very simple level just look at the slope or we can look at it on a very very very micro level by looking at systems biology and this is looking at the pathways of disease feedback loops and other complications to really understand how the disease impacts the entire body but of course we're in Pharma and so we want to talk about how the drug impacts both of these things so we have the drug impacting these very simple disease progression models and that's drug disease modeling and quantitative systems pharmacology is how we link PK to these system biology uh systems biology models but let's start at the beginning we're going to start with PK and pkpd modeling and that's because pharmacokinetics and pharmacodynamics contribute to many sections of the ctd in the package insert and maybe I'm biased but we provide foundational quantitative understanding of drug disposition and drug effect both safety and efficacy and if you look through the ctd there AR in a lot of places where PK and PD don't touch we helped to support and inform key drug Discovery and development decisions with PK and pkpd modeling so that's really where I'm going to spend the bulk of my presentation I will touch on some of the other kinds of models that I'd mentioned in the previous slide but what I'm going to focus in on part one is exclusively PK and then during part two we'll talk about some of the other types of modeling so let us begin at the beginning and talk about pharmacokinetics and pharmacokinetics is how the dose regimen and formulation leads to a concentration time profile so let me start with the general principles of pharmaco kinetics it's often thought of as a mathematical process only but really PK itself is a physical chemical process the drug needs to get out of the dosage form into solution and be carried by active or passive measures from the site of administration to the systemic circulation so that's absorption it then needs to be distributed through the circulatory system to the site of action as well as to the rest of the body that's distribution and this is why you sometimes see of Target effects because the drug doesn't just go where we want it to go unfortunately the drug is then broken down by chemical processes generally into inactive components and then these inactive components or the unchanged drug needs to be excreted usually by the kidney by active or passive processes to summarize and understand all of these processes this is where the math comes in we can simplify these to a set of parameters which quantitates the adme of a drug it gives us important insights into how much drug gets in and how quickly how extensively the drug distributes out of the plasma and how efficiently and quickly the drug is eliminated and then other parameters which are derived from these give us useful information on how to optimally dose a drug what's the optimal dose what's the optimal frequency that's things like the half life of the drug the exposure metrics like the area under the curve the peak concentration or the minimum concentration C Min and of course the time of the peak concentration so now I'd like to spend a little bit of time talking about how PK is collected during the course of drug Discovery and development then we'll finally get to how we actually analy those data with models but let's start with phaco connects that's collected in pre-clinical studies PK and preclinical is very very useful because you can collect a really wide range of doses that you generally cannot do in humans and that really allows us understanding of the the edges of the PK processes so we get to understand whether or not there's going to be saturation in any of our atme processes it gives us an idea of dose linearity with au and cmax and potentially when that starts to deviate and the important part of PK in preclinical is that we can scale that to humans using a number of different ways we'll talk on both allometric scaling and pbpk later in the presentation pbpk is physiologically based pharmacokinetic modeling pkpd in preclinical is also quite useful in that we can get a really strong assessment of our exposure response profile due to the wide range of Doses and it gives us ideas of Target engagement during uh different at different exposures of the drug it allows us to assess the minimum anticipated biological effect level MB so the very lowest dose that we can give and see some kind of effect as well as the no adverse effect level and we can do that in order to help us identify exposure caps as well as exposure targets so this will help us S Suggest safe and effective starting doses once we get into our first and human studies speaking of first and human studies let's start there and we're going to start with healthy volunteer studies single and multiple ascending dose some companies call it sad mad studies for the most part I should take an aside to say that phase one studies are generally in healthy Volunteers in some therapeutic areas like oncology it's done in cancer patients and of course that makes PK very very difficult you're also attending to things like variability dose changes dose interruptions and other confounding factors like disease and standard of care so we're going to put those aside for now we're going to focus on the healthy volunteer part as this is the most common and informative information that we have when we collect these data we have very rich sampling for PK characterization and when I mentioned Rich samples I mean several samples per subject and generally covering the entire concentration time profile so we get a really nice assessment of the PK in these patients again just like in preclinical this allows us to assess dose linearity within the doses that are used in humans and if we in our MTH studies it allows us by looking at the PK let's say day one and day 14 or when we think we're getting to steady state gives us some idea of the steady state PK and the amount of accumulation that occurs with regular dosing we can compare our maximum concentration to that safety cap that we mentioned in the previous presentation or sorry in the previous slide and we can look at things like Au and other exposure metrics to make sure that we are getting suff ient exposure for efficacy this will help us in coming up with our later phase doses where we need to make sure that we're seeing appropriate efficacy helps us to understand the half-life of the drug in humans which will help us to impact dosing frequency as well as getting initial assessments of clearance in healthy volunteers which will give us an initial assessment also of our variability we'll plot clearance as a function of things like age and body weight to see whether or not we have very important covariates we need to investigate as we go into later phase studies the primary PD that we collect in these studies is safety and tolerability but sometimes efficacy biomarkers or other kinds of end points might be collected to help us with proof of pharmacology in some of the later studies let's talk about the clinical pharmacology studies and these are a suite of studies that are used to have preliminary understanding of external factors on drug PK usually in healthy volunteers again so these are things like the food effect study renal and hepatic impairment studies sometimes depending on the type of drug we might look at age and gender like elderly versus non-elderly or children versus adults uh for age just to be able to understand whether or not these are important covariants Downstream we do mass balance studies bioavailability is important if we're not going to be using an initial IV dosage form if we're going into oral dosing or subcutaneous you have to understand how much drug will get into the system of course there's a thorough QT study where we look at the QT as a function of drug concentration and then there's drug drug interaction studies and some of these studies due to the fact that we have things like physiologically based PK models some of these studies in well understood indications and well understood uh um Pathways can be supplemented or even replaced by pbpk and we'll speak on that when we get to the pbpk sections shortly now as we move into the later phase studies we start to look at the PK in our Target population the goals for PK in these particular studies are to understand and quantify the sources of inner subject and inner occasion variability in our Target population and to address whether or not this variability has an impact on dosing and exposure but PK characterization in later phase studies can be a lot more complex because it's generally very sparse sampling you may only have maybe one or two samples per subject and it's not necessarily going to be at the consistent times that you'll see in these sad mad studies and you have more missing data patients drop out patients discontinue or change their dosing and speaking of that we often have incomplete dosing information for the most part these later phase studies the patients are coming in for scheduled visits but they're taking their drug at home so we have to make some assumptions around the times and dates that they're taking the doses if these aren't things that are being rou keenly collected and and written down so there is some incomplete dosing information that we need to contend with and there's also a lot more intrinsic and extrinsic factors to consider there's a lot more heterogeneity in a patient population other medications for example and other standard of care as well as disease progression that we need to take into account for this patient population that maybe we didn't need to consider for healthy volunteers and so as a result there's going to be higher variability but we have methods to be able to assess all of these things and we often will pull our data if appropriate with some of our richer PK studies so that it can help to supplement the information that we're missing with these other patients so now finally we will get to the meat of this presentation which is to look at some of the methods and models that we use for PK analysis I just want to clarify you often hear people talk about PK analysis in two different ways ways uh the term is used both in bioanalysis as well as in pharmacometrics so what I'm going to be talking about today is not the extraction of the drug concentrations from blood samples but the quantitative methods for determining the PK parameters like we talked about before clearance volume and halflife so now let's proceed to talking about PK models and I'm going to start actually by not talking about modeling but talking about the quantitative analysis of PK data and that is non compartmental analysis so in a case like this uh it's usually done in in early phase studies with Rich PK so we have a few subjects but we have lots and lots of samples per subjects richly sampled data and in non-compartmental analysis you only need a piece of paper you need a piece of graph paper and a ruler and a pencil and a calculator so you don't actually need to have these really strong computational methods to be able to determine the PK and individual patients we extract their information directly from each individual's data so for example we get things like the area under the concentration time curve so this is a PK profile for an individual patient it's obviously simulated but the area under the curve is essentially we can calculate using something called the trapezoidal rule or we can calculate directly uh the area under that curve that gives us an estimate of the exposure of that patient in this case over 24 hours we can also get the cmax and the T-Max which we've already defined but it's the maximum concentration as well as the time at which that occurs and we can get things like the elimination rate constant which is the line that you see here on the plot that just appeared as well as to some extent the absorption rate constant if you do something that's called Curve stripping from those we can derive parameters like the halflife the clearance the volume of distribution and if we have both IV and oral or subcutaneous data or non IV data should be able to also determine the bioavailability of the drug now non-compartmental analysis is easy as I mentioned you don't even need a computer and it makes very few assumptions because there's no underlying model we just take each subject's data as it comes and we take that as the whole truth um so it it doesn't really help us to understand the variability in those patients but we take each patient as the whole data set uh automation is still possible using appropriate software so you don't have to do it with graph paper and a pen um and the nice thing about non-compartmental analysis is because it's easy it'll also give us some assessment of variability and accumulation so this is the situation that I mentioned before where if you have day one PK compared to let's say day 14 or some steady state PK it'll give us an idea of the accumulation uh in patients and variability across patients the disadvantages though is that it does require many samples because you're really counting on the data to give you back those variables that you need so it's highly dependent on things like sampling time because you're pulling cmax and T-Max right off of the plot um you need to make sure that you're collecting them at the appropriate time if you miss it by an hour on either side your cmax and your T-Max pulled off the plot will not be the true cmax and T-Max and you have to have sufficient samples to define the terminal phase as well generally you want to have three to five samples in the terminal phase to get a true assessment of the halflife and tells you nothing about the mechanism uh you can't determine if there is nonlinearities or complex absorption you really just have to to take the data at face value and you have little predictive value you can't interpolate or extrapolate from non-compartmental analysis because you're taking each individual's PK as it is so in order to be able to circumvent some of these disadvantages generally we turn to compartmental PK and I'm going to start talking about compartmental PK applied to individuals so this would be a situation where you still have few subjects with lots of samples per subject and you're fitting each subject one at a time now unlike with non-compartmental analysis where you got things like Au the elimination rate constant uh and cmax and T-Max off the plot in this case they're derived variables so we start with our parameters from the model so in the model we calculate we estimate the clearance volume of distribution the elimination rate constant and then again depending on whether or not we have IV and oral data the bioavailability and the absorption rate constant and then we derive the parameters that we would normally take off of the plot um in non-compartmental analysis like Au cmax and TMax so let's talk a little bit about the advantages of doing compartmental analys analysis versus non-compartmental I alluded to these before uh one advantage is that you do get more weight to understand PK you have more parameters like absorption that you can actually put functional forms in and understand the absorption a little bit more deeply uh you don't have to do curve stripping assuming a very specific kind of absorption um it can fill in sampling gaps because you have a model for each subject you can do interpolation and sometimes extrapolation which I'll speak to on a future slide it gives us again the initial assessment of variability similarly to the way that it's done with NCA where you can look at clearance for each patient as a function of things like age and body weight and determine the variability across those patients and if you do have nonlinearity it's okay uh if the functional form is understood and we often do have a functional form for saturation and things like that we can work those into our models uh and so that helps us to assess the nonlinearity as well the problem with compartmental PK is it is modeling so it requires specialist software and training and sometimes as you're starting to add more parameters because you're starting to to try to assess more things um some parameters might not be identifiable if you don't have enough data to be able to determine some of these parameters you may not be able to to assess them properly and it's model dependent obviously it's compartmental modeling so you are assuming that the same model is applied to all individuals one size fits all and for the most part that's generally true but there are always exceptions to the rule that make it difficult for us to work around that and just like in non-compartmental analysis there is some dependence on sampling for example if you want to get cmax and T-Max it is important to try to sample around the time that that normally would happen so let's talk about a couple of different compartmental models that you will see very commonly and one is the one compartment model so one compartment model is essentially a bucket with a hole in it uh so you administer the drug to the patient it is immediately mixed and all over the body uh and then you have elimination from that bucket from the person and so it's very very simple if you plot the concentration time profile on a semi log plot so the y- AIS is on a log plot one compartment model is just a straight line and you'll see the same thing when you have oral dosing where once the drug is is absorbed so there is an absorption uh component you'll see this straight line surprisingly uh actually not surprisingly this is a fairly common way of of understanding PK in patients and it works in a lot of different cases but probably what's going to be more pable to most people and and more understandable to most people is the two compartment model because this gives the drug some time to distribute amongst the the circulatory system you know and into the tissues and the organs so before Administration what you can see on the left side there's no drug after Administration it goes into the central compartment which generally contains the heart the lungs and the eliminating organs like the liver and the kidney and then after a Time the drug it's distributed throughout the system and what you'll see is this by exponential plot you'll see this sort of L-shaped curve for lack of a better term where you have in the beginning a very very fast drop in the drug uh in the concentration in the plasma because you have distribution happening at the same time as elimination so a drug is leaving the plasma into this second compartment uh into the tissues and then over time only elimination is occurring because there's no more distribution your body's in equilibrium so these are fairly simple models but they are really quite useful and really quite common we do occasionally move to a third compartment um but generally the one in the two compartment models are the most common models that we look at in PK now what can we do with these well the utility of compartmental models is that we can do things like interpolation and extrapolation so if this is one subject and that line represents this individual's model and I took a PD sample at 4 and 16 hours and I want to know what was the concentration at that time we can pick those off the curve and similarly for extrapolation if I have this curve for this patient I can extend that curve out to understand what happens after I've stopped Ling so interpolation and extrapolation are both these are forms of simulation and they're very very very useful for us to be able to fill in gaps and in particular like in the interpolation component that I mentioned you know to be able to match our PK and PD at the same times is always quite useful so if we take the same patient PK profile and we want to know instead of interpolating or extrapolating we want to know what would happen if we half the dose or doubled the dose or gave it half as often or twice as often we can do that because this purple line that's going through these points is actually representative of an equation that represents this patient's PK profile as a function of dose in time so if we wanted to see what this patient would look like at half the dose at 50 milligrams instead of 100 or at two times the dose we can do that by plugging in different doses into the equation and and similarly let's say that we're concerned about this patient's maximum concentration they're doing well on efficacy we want to get the same exposure we want to get the same dose into these patients over the course of a day but maybe we want to lower this patient's cmax so we can do that by dividing the dose or by giving it let's say four times a day where you can see that the maximum concentration is reducing whereas the overall amount of drug the patient is getting in a day doesn't change so these are some of the things that you can do with these compartmental models that allow us to really help to optimize the dose in patients so in the case of compartmental PK applied to individuals I think you can see the utility of it but when we're applying compartmental PK to one subject at a time you really need to be in a situation where you have few subjects and many samples per subject when we talk about compartmental PK applied to a population and its individuals that's a situation where you often have many subjects sometimes many many subjects so we're talking about as we're getting into some of our late phase studies and we can have hundreds if not thousands of subjects and very few samples per subject see a very sparse data parameters that you get from the model are the same as that you would get from the compartmental model applied to individuals except one of the really useful things that you can get is understanding the impact of covariant and Quant quantifying the impact of those covariates and I'll I'll describe what I mean by covariates in just a moment why is this important well we know that if you give different patients the same dose of a drug you're going to get some slightly different if not fundamentally different PK profiles and that is because patients in particular as you get into the later phase studies and you have much more heterogen heterogeneity you have a lot of subject char characteristics that could impact the PK and I've alluded to some of these before age sex and body size but as you move into patients as well you'll have things like concominant medications you'll have different markers of Health uh could be disease status or Ral or hepatic function um you could have pharmacogenomics uh for example I am a very very slow metabolizer of 2d6 I can drink an entire bottle of Codine and nothing will happen to me I will feel no effect at all whereas I remember a friend of mine said she once drank uh one one dose of Codine and ended up on the floor for six hours very very fast metabolizer so we can incorporate those things into our models other things like Diet smoking exercise and standard of care can also impact the PK some of these things we can measure some of these things we can't but why is this important is that different exposure can be get different responses so it's really up to us to be able to quantify why patients have different exposures and if they are so different do we need to modify the dose and ultimately that is the ultimate question that we have to try to answer so unsurprisingly we answer the questions using modeling and in this case it's nonlinear mixed effects modeling otherwise known as population PK sometimes pop PK this is a model-based approach of analyzing data from all the individual subjects together that helps us account for how individuals differ from each other and how the overall population behaves so we're using the same compartment models that we talked about before the one compartment model the two compartment model but we're adding on a variance model that helps us to quantify the inter subject and the inter occasion variability and I'll speak to both of those let's talk a little bit about population PK and what are its advantages and disadvantages well what's nice about pop p K is that you can use rich and or sparse sampling from subjects subjects borrow information from each other because you look at the population as a whole you pull all the data together if you will to get a trend for the entire population so that helps us to get a feel for what the overall underlying model looks like and then we can start applying that model to subjects who only have sparse data and as a result we also have methods within population PK for handling missing data Within subjects it gives us both individual information so you might hear them called post talks or ebees but all these are individual PK parameters so an individual's clearance and volume as well as population parameters which sometimes we call typical values of things like clearance and volume and of course there's more parameters so it helps us to quantify variability and the impact of co-variates on our PK but it is complicated and so it requires even more specialist training and software than even the regular compartmental modeling does and because we have even more parameters to fit just like with compartment modeling we're now adding on even more so if you don't have sufficient data you might have some parameters that are not identifiable similar to what I spoke about before it is dependent on the model uh generally you are applying the same model to all individuals although within nonmem which is the software that most of us use for population PK there are ways around this such as mixture models where you can propose two different models and let the software decide which model each individual belongs to and to some extent it's sampling dependent so if you you can borrow information from other people but if you've sampled all of your patients in the initial stage of your PK profile and you don't have anything in the terminal phase you're not going to be able to get good model characterization as I mentioned in a previous slide we often will pull together our rich and our sparse PK in order to to have more support for the characterization of PK in our Target population to orient you a little bit to how population PK works and this is really as technical as it's going to get these are two different subjects you have the subject that's in Gray and you have the subject that's in black and the solid line that goes through the middle is the population mean so if we didn't have those two small lines going through the individual patient this is the best straight line that you can fit through these two patients and so this is the a straight line fit similar to what you have before we have a slope and an intercept and so you have these typical values for the intercept and the slope which are going to be your population values of inter intercept and slope then when you look at each of the individuals what you get is an intercept for each subject and a slope for each subject but rather than fitting them individually you use that population model the population values of intercept and slope and you just adjust them so you have these little U parameters that you see here that are the adjustment for the intercept and the slope for each individual patient so then you have these indiv that's how you get the individual patient values or those post hop values that I mentioned before so this is where we talk about inter subject variability and remember these values when I when I talk about these uis um we're going to talk about them again in a minute on how it helps us to assess the impact of covariant on our PK and last but not least we always look for each individual and how far they Veer from their predicted line and so that's residual variability and so we add on this variability for each of our patients now I don't expect you to remember all of this but just generally to get the principle of this is we start with the population we get the best model for the population and then for each individual use us that population model as a foundation we then find the individual parameters that will make them fit appropriately hopefully that was clear that's as much technical stuff as I'm going to go into but if it's not clear please feel free to send me an email and I can try to explain this a little further or provide you some references that will help you understand po PK better the important part of Pop PK is one of the things that it gives us is the ability to quantify covariate effects so those uis that I was talking about before those are sometimes called Adas um these are the differences from in this case the typical value of clearance and what you can see is that when we plot these versus two different covariant in this case it's alpha 1 glycoprotein which is a plasma protein and on the right side is fat-free mass and what you can see here is that there is a relationship people with a high AGP tend to have a lower clearance people with a low AGP tend to have a higher clearance so because we know this we can then put these components into the models so if you take a look at the model on the right side if somebody were to walk into the clinic I would assign everybody the same clearance which is why you're going to see these errors however if I put AGP and fat-free Mass into the model then when someone walks in based on their AGP and based on their fat-free Mass I can get a much better assessment of their individual values of clearance so I start to reduce that error um and that helps us to refine each individual's needs so if you have someone who has a very high clearance that means they're getting rid of the drug faster we may need to give them a higher dose uh if you have someone with a very low clearance they're getting rid of the drug slower we might need to give them a lower dose and so by understanding the impact of covariates and understanding how extensive these relationships are that can help us decide whether or not we need to put covariants into the label and I already showed you a label in the beginning for acetaminophen where we had weight in the label for children because weight is such an important covariant and similarly covariates can impact dosing uh this southwest oncology group is is quite old it's from 2001 but you will often see milligram per kilogram dosing or milligram per meter squar dosing particularly in onc ology um and on the right hand side is the Zol dosing table and in this case it actually is dependent upon two covariates your IG level when you enter the clinic as well as your body weight so in these particular cases they may have a narrow therpeutic range or we need to make sure that we are dosing in order to make sure that the patient is getting the optimal safety and efficacy and as a result we'll put the covariates into the label so up until now most of the models I've been talking about like the one and two compartment models have implied that we have linear pharmacokinetics or first order pharmacokinetics I've alluded to the concepts of nonlinearity and saturation but I just like to spend a little bit of time talking about that because we have to incorporate those things into our models you'll sometimes hear linear pharmacokinetics referred to as dose independent dose proportional or firstorder pharmaco kinetics but these three components that the PK parameters are dose independent that if you divide your concentration by dose and then you plot concentration time profiles on the same plot they should be superimposable or that the exposure like the Au or the cmax is proportional to the amount of available drug linear pharmacokinetics essentially means if you double the dose you double the concentration and you double the exposure so generally if we're going to change the dosing regimen change the amount change the frequency this leads to predictable concentration profiles and the interpolation and extrapolation figures that I showed you before all assumed linear pharmacokinetics however particularly at high doses it is possible to saturate one or more of the PK processes so for example if you have active transport such as transport into the gut or pgp which is sort of the goalie to keep drugs from passing into the system or you have active secre active reabsorption in the kidney these things can be saturated at high doses because it's capacity limited similarly to protein binding you only have a certain amount of protein so when the doses are very high you've saturated all of your available protein for binding this can also happen um when you have time dependent PK uh such as up or down regulation of an enzyme as well as Target mediated drug disposition and if you if you haven't seen this episode of I Love Lucy I think this does a very nice job of explaining how saturation works but what happens with nonlinear PK is that changes in dose or dose regimen can lead to a disproportionate increase or decrease in the plasma drug concentration or the exposure and it's not always predictable so it can be a concern if a drug has a narrow therapeutic window if you think about this if you've just shifted the dose a little and you expect then the concentration to shift a little but it shifts a a lot it goes up quite a bit higher that can push you outside of the therapeutic window so we have to be aware of the nonlinearities in PK and be prepared to account for them and of course the way that we account for them is through modeling there is an equation called the michelis Menton equation and I'm I'm showing this to you to familiar familiarize you with this functional form because you're probably going to see it as a way to capture potentially saturable processes so what this is is the rate of some kind of process and generally we use it for clearance the rate of elimination is Vmax which is the maximum rate time C which is the concentration over km plus C and km is the concentration at which the rate of the process is half Vmax if you've ever seen emac models before this is going to look very familiar to you and you'll see emac models a little bit later it has the same functional form but what's important to look at is not so much the curvy part but really the two ends most drugs undergo saturable PK at high enough doses you just might not see it at clinical doses where you're more likely to see saturation is when you are in the preclinical stage when you are pushing the doses as high as possible and that's really important for us to start to understand these and see whether or not we have to be concerned about this as we get into the clinical dosing more likely what you're going to see at clinical doses is where your drug concentrations are quite low and much lower than km and what you can see is that red line that's inside the box is a pretty straight line so what you see is a proportional uh first order PK there so it reduces to first order PK when you have a linear relationship between the elimination rate and the concentration so it's not that you don't have saturable PK at all it's just more likely at the clinical Doses and the clinical exposures that we're seeing we are not actually seeing the saturable processes but the reason I'm showing this to you is just to make you aware that we do have functional forms to help us account for these nonlinearities in PK that you might see one of the places where you're very likely to see nonlinearities as well as other complex modeling challenges is when it comes to absorption modeling you know I mentioned on several occasions that that one compartment and two compartment models for the most part represent the distribution of the drug Within the system so the DME of adme but the absorption piece can be incredibly complicated and that's because there's so many formulations and so many ways to get the drug into the body intravenus is obviously going to be the most simple that goes straight into your systemic circulation where you don't have to worry about absorption but even with oral dosing it can be extremely complicated part of the reason that drug absorption particularly oral absorption is so complex is that it's dependent upon not just the dosage form itself and the physical chemical characteristics but also the anatomy and physiology of the drug absorption site so many potential complexities including gut pH which can impact how the drug goes into solution and how it dissolves um gut motility and carrying it to the site of absorption we also have active and passive transport passive transport just goes through a gradi so that's not really dose dependent but active transport such as being pulled by Transporters across the gut wall into the portal vein or into the system or pgp mediated efux can be saturated as I mentioned on a previous slide and then of course there's metabolic complications we often will lose drug from our dosage form due to gut wall metabolism as well as first past metabolism which can cause all kinds of complexities so a lot of times what you're going to to see if you're reviewing uh modeling reports you may see that the PK looks pretty good after the absorption phase but what you're going to see is a lot of model misspecification during the absorption phase um and that's just because of these complexities so we have a lot of different models that we can use for absorption and I'm not going to go through them in this presentation but we have first order absorption zero order absorption a combination of the two we have complex models that can handle lag times that handle gradual absorption which is called the transit model and other nonlinearities and many of these are good enough they're empirical they suit our purposes and they do good enough for us to be able to characterize the PK well enough but if we really need to fully understand the absorption process because there is so much physical and chemical and anatomical components to it and we want to ensure that we're getting adequate drug exposure in the systemic circulation it may be necessary to turn to a slightly more complex but physiologically realistic type of modeling and that's called pbpk or physiologically based PK so the next section I'm going to talk about focuses on pbpk so when we talk about the one and the two compartment models that we talked about before we tend to call those empirical models each of the compartments is not necessarily representative of organs and tissues unlike PBP K so in pbpk this is a concept that provides a mechanistic approach to study and predict the pharmacokinetics of drugs and it's really based more on physiologic and anatomic characteristics like some of the ones I talked about on the previous slide as well as the physical and chemical properties of a given drug so I'll go into those in a little bit more detail but because of the fact that it is physiologically chemically and anatomically based it's really quite ubiquit is it's really used probably the most across the mid3 landscape so it's used in formulation development to help to predict the absorption of a compound and can also include the food effect studies and other studies in the GI tract there's preclinical to clinical scaling you can develop a pbpk model in a rat and scale it up to humans for example there's drug drug interaction studies this is extremely common use of pbpk uh particularly in the cytochrome system where we really understand the mechanism of action and we really understand the impact of certain medications on cytochromes uh so we can predict ddis in many many drugs also in healthy to disease scaling so you can go from healthy uh adults to for example renal insufficiency or hepatic insufficiency and it's used very commonly also in adults to Pediatric patients so pbpk is worth understanding and knowing a little bit about because you're going to see it in a lot of different places in the ctd and in making some of the drug development and Discovery decisions so this is a pbpk model I know it looks scary but really it's actually much more palatable to people than usually uh the these more empirical models that I showed you before because each of these boxes represents an organ and each of these lines these arrows represent a blood flow so these are the organism specific parameters there's things you can weigh there things you can measure each of these boxes represents a real thing um and you have things like organ volumes blood flows hematocrite levels the composition of organs gastric emptying time these are things that are specific to an organism and usually you can measure or you can weigh then there's the drug specific parameters but when I say drug I don't mean this drug I mean this I mean the chemical compound and these are things like lipophilicity molecular weight acid Base Class PKA I I mentioned a couple others previously and so those aren't going to change when you go between different organisms the the chemical compound is the same what you do need to try to make sure you assess is the drag and organism specific parameters so what is the Unbound fraction of the drug in the plasma and that's going to depend on plasma protein levels you know and and um how tightly it binds to the plasma proteins for example things like blood to plasma ratio of the drug tissue plasma partition coefficients intestinal permeability Etc so these are things that you would have to be able to assess for your particular organism and for the compound now what's neat about pbpk is that it can kind of expand or contract depending on the level of granularity that you need so in this particular case here's a model that looks at absorption on a very very micro level you can see each of the components of the small intestine the dadum the junim ETC all the way through the colon and you actually have different compartments for drug that is released drug that is dissolved and then drug that goes into the systemic absorption so if you need to understand it on a granular level like that you can do that but at the same time you can also contract so this is a situation where you have a rest of body compartment so you have organs and tissues that are of interest for the particular drug or things that you can measure or things that you can weigh but sometimes it doesn't really matter where the rest of the drug goes it's like in a mass balance where that's essentially all the remainder of the mass balance so I think what's nice about pbpk is that you can expand it or contract it based upon your needs so I'm going to walk you through a pbpk workflow and and these slides are courtesy of Andrea Edenton at the University of waterl she's really an excellent lecture on pbpk and I borrowed this schematic from her and in schematic we're talking about building an adult pbpk model and then scaling it to children but this could really be the same if you were building a rat model and scaling it to humans or building a healthy volunteer model and scaling it to disease patients so we're going to use adult as our reference population and what you do in pbpk is you build the model and then you predict or you simulate the adult plasma PK profile one thing that's important to note about pbpk okay is that there's no human data yet this entire model is built on first principles it's called bottom up so we have chemistry physiology pharmacology invitro data um these are things that you use to build the model and then on top so once you have collected some data you overlay The observed data on top of our prediction and we look to see does the model adequately reflect the observed data if it doesn't and in this this case it doesn't we optimize parameters to match the observed and simulated profile so this is called Model calibration now I want to be clear that when we talk about optimizing the parameters this is not just hey let's double the intrinsic clearance and see what happens it has to be built on rational physiological pharmacological and realistic assumptions and so you have to justify these changes when you make them to ensure that you're properly characterizing what's really going on in the system at least to the best of your knowledge so you're you're basing this on your understanding of the pharmacology and physiology of this drug and then once the model is calibrated to your satisfaction you then have your final model and adult and this is where the beauty of pbpk really comes in because now that you have the final model in this population you can then scale it to another population and that's what we're going to talk about now so as I mentioned before we're using adults as our reference population and children as our scaled or our our new population but again the principles I'm about to talk about will apply whether you're scaling from a healthy volunteer to a sick patient from rats to humans Etc to scale adults to children so we'll use that as an example you would scale things like protein binding children have different levels of protein available to bind to the drug you scale clearance children have smaller kidneys smaller liers and they're also just not as mature in their pharmacokinetic processes and there's actually an entire field of study called ontogeny that looks to understand how children from birth all the way through generally 2 years old were they're considered to be roughly equivalent to adults in terms of the maturity of their pharmacokinetic processes but a lot of these uh equations are based on age or body weight and so they will change as a function of time and of course scale anatomy and physiology children are smaller so they will have smaller kidneys smaller livers smaller organs their volumes and blood flows will change accordingly so when you scale this adult model to children or from your test or your reference population to your test population if you have data then you can evaluate your predictions against it if you don't then that would be a situation where you just put a lot of uncertainty around your predictions but in a lot of cases a lot of these scaling parameters are well understood if you have data though you can calibrate or optimize as appropriate to come to your final model in children or in your test population and this will give you an opportunity then to probe that model for different questions that you have to answer in terms of let's say dosing um for particular uh in particular for Pediatric patients we'll often use pbpk modeling to do exposure matching so that we can come up with the pediatric dose to come up to have the same exposure as you do in adults now as I mentioned going from adults to Pediatric patients there are ways to do this without pbpk the most common way to do so is allometric scaling uh it has been found that many many processes and and rates scale across and within species uh usually to the power of 75 for clearance and the power of one for volum of distribution uh so if you plot the rate of elimination versus body weight on a log log scale you will actually see that all the way from a very very small to a very very large population you roughly get a straight line and so allometric scaling is often used when you have you're going from adults to peeds or when you have a very very wide range of body weights within your adult population in order to be able to address the fact that larger people have larger organs and therefore have larger clearances so we account for for these using allometric scaling this isn't a pbpk principle but I did want to make this point uh before we leave the the topic of pharmacokinetics so part one today uh focused on PK principles and modeling so we really focused on the PK components because that's foundational to understanding the pkpd if we don't understand the disposition of the drug and the exposure to the drug then everything Downstream is going to be difficult for us to quanti and to optimize so what you have to look forward to in the next session is an expansion Beyond PK first thing we're going to talk about is no PK and the disease progression and systems biology modeling that I spoke about earlier which actually are understanding the disease without any intervention then we'll look at how the drug impacts disease progression how the drug impacts pharmacodynamics on a rather macro level and how the drug impacts pharmacodynamics on a micro level by talking about quantitative systems pharmacology so I hope that this has been useful for you thank you so much for joining me this is going to be now the end of part one and with that I invite you to please keep in touch if you have any questions and please join me for part two