Getting a Handle on PK Parameters

Helen Winsor

Thomas Jaki, lecturer at Lancaster University and an expert in the estimation of PK parameters, joins Pharma IQ to discuss the challenges and changes in this area.

Pharma IQ: Thomas, welcome. So, firstly, what are the key issues to overcome when it comes to improving the clinical trials process?

T Jaki: There are a couple of issues related to that. I think the most pressing at the moment is that there are a large number of unsuccessful Phase III trials, which basically means that a lot of money has been spent, a lot of time has been spent on developing a product that just doesn’t work. More importantly however, it’s actually exposing patients to ineffective and possibly even hazardous treatment while the time, of course, could have been spent on developing other treatments instead.

The main issue then is that most of the failures in these Phase III trials are actually due to mistakes or inaccuracies that have been made during the early phase trials. So during Phase I, Phase II trials related to determining the safety of our new treatment, maximum tolerated dose, minimum receptive dose, which patient populations would benefit best from the treatment. So it’s actually looking at the early phase trials that at the moment, in my opinion, the key issues are trying to improve the early phase trials so that in the long run the Phase III trials, the long running, the extensive trials are going to have better success rate and better products are going to come through.

Now, related to these early trials, I think the key issues, or the key points to be addressed, have to do with the fact that at the moment the entire development process is rather disjointed, meaning that there’s a Phase I trial, the first one for one question, then there’s a Phase II trial or maybe a Phase II A trial that’s trying to answer another question, a Phase II B trial that’s answering a different question. So rather than separating the process out, it would be better to answer questions simultaneously rather than answering them one after the other, which is going to mean that in order to answer multiple questions at the same time there’s going to be a larger sample size, there’s going to be more information that’s going to be available to answer those questions together.

The other improvement that can be made to address these issues is just to look at better statistical methods, how one can use the information that is available more optimally, and finally how one transfers information between the different stages of the development so that starts from in vitro studies already going all the way through the first studies and then going on to the later phase studies and the question there is how does one transfer the information that has been obtained in vitro, that had been obtained in animals and how does one use that in order to study the compound, study the treatment later on?

Throughout these all I think it’s also quite important that the patient’s perspective is included formally just to make sure that the trials that are running, that are developed, that are ongoing, are not just compromised by the fact that patients don’t comply to the treatment regiment, for example. So those, in my view, would be the main issues at the moment.

Pharma IQ: Thank you, Thomas. What are the key strategies currently at the forefront and how would you say that these different strategies differ?

T Jaki: I think it’s related to the previous point. On the one hand, there’s the improvement and one strategy is to improve the statistical methodology, basically making sure that the way this data is collected is so flexible that we then can use the methods to analyse the data that has been accumulated. That means using, say, adaptive designs, using seamless designs, using designs which have been developed over the last say 10 or 20 years, which is going to lead to a better product overall.

The second strategy is just to make sure that the interaction between the different stages of the development is going to be improved, so that means starting from the in vitro experiment all the way through to Phase III, Phase IV there’s just better communication on an investigator level, that the information is passed on and the knowledge about the treatment is passed on.

Finally, the third strategy is just to formally include the patient’s perspective, seek formal ways to ensure that the patient’s opinion is valued prior to even conducting any trials just to ensure that the recruitment grades are going to be desirable, are going to be met and that compliance is better than it is at the moment.

Pharma IQ: There are some good points there, and how do you assess whether the noncompartmental approach or modelling is the best option?

T Jaki: That’s quite a tricky question. On some level, I think, a lot of times it’s actually a philosophical question as the non-compartmental approach is in some sense a non-prometric method while a modelling approach is the prometric equivalent. So a lot of times it comes down to the fact of whether or not somebody believes in the models, somebody believes that the underlying model that I want to use in the modelling approach is appropriate, or if I don’t have trust in any models and therefore I want to avoid making any assumptions about certain structures, structure of data, certain behaviour of the data.

More formally, it really comes down to how well I understand the compound that is investigated, which means if there have been previous studies in similar populations and if there’s data available that tells me that a certain type of model is fitting well, then a modelling approach would be most appropriate; while if it’s an entirely new compound, something we don’t know anything about, generally speaking, people would be more uncomfortable with using any assumptions about the shape of the model.

The second question has to do with the purpose of the study. There are different approaches, different things can be achieved with modelling that can’t be achieved with a noncompartmental approach. Generally speaking, the more information one puts in, the more is possible, which means if I want to use a modelling approach I can do a few things that I can’t do with the non-compartmental approach, but at the added risk of having had a misspecification and therefore getting invalid or a questionable result at the end. But I think it’s a balance of those two points that makes the main decision of whether one goes with a nonprometric approach or a prometric approach, whether one uses non compartmental approach or modelling instead.

Pharma IQ: Yes. Thanks, Thomas. Looking specifically at non-compartmental estimation, what methods are available for non-compartmental estimation of PK parameters?

T Jaki: There are quite a few different methods that are available, but the general idea of all of them is essentially the same. It’s saying, ‘if I have measurements at certain time points, I’ll take the average of those measurements and then I’ll interpolate linearly or somehow else between the time points that I have measured’. Our work specifically focuses on what’s called incomplete data designs, which basically means that rather than having observations for every subject in my study, for any participant in my study, I have observations on some of the time points, but not all of them. So it is, in some sense, a missing data problem that we’re working on. The second strategy that we’re working on is looking at merging somemodelling aspects with non-compartmental.

The idea behind that is quite simply saying you use non-compartmental approach for the area in the concentration versus time profile that one doesn’t feel one understands well. Generally speaking, those are the early time points in the study while for the later time points a fairly simple model is used. Often it’s going to be an experimental decay, for example, and that is for the parts of the concentration versus time profile that one does understand very well.

Now, the advantage of that is basically one gets the benefits from both ends. One gets the benefit from the non-compartmental approach together with the modelling approach. One gets more parameters that one can estimate than by non-compartmental alone. So, for example, one can estimate the area of the concentration curve up to infinity using such an approach. One can estimate half-life and so on and so forth but all that without having to rely too much on any parametric assumption which again merges the advantages of both of the approaches with limited or very small drawbacks.

Pharma IQ: Can you elaborate, please, on the methodology for testing for bioequivalence using the AUC?

T Jaki: The main issue there is that standard statistical methodology isn’t geared towards testing for equivalents. So from a statistical point of view, hypotheses are generally set up so that one tests for can we show that there exist no equivalents. So the general statistical methods for hypotheses testing don’t fit directly into the framework for showing that something is in fact equivalent.

Now, to overcome that problem a so-called confidence interval inclusion approach can be taken which is basically saying you find a confidence interval for the parameter of interest and if the parameter of interest falls within pre specified margins... usually these margins are determined by regulatory bodies and by considerations such as part one error so one finds this interval, we see if this interval falls within these pre-specified margins and if it does then it is said that the parameter of interest is equivalent.

Now, in the context of bioequivalence using the AUC basically the parameter of interest is the ratio of the AUCs. So it’s just the AUCs from the one compound, over the AUC of the other compound and that’s going to be my point estimate. One finds the confidence to afford this ratio of the two AUCs and see whether this confidence interval falls between, usually, 0.8 to 1.25, and if that is the case then the AUCs are set to be bioequivalent.

Specifically, what we are doing in this context is we are going to use the same ideas to estimate the individual AUCs. So again we’ve developed methods that they have to do or that can cater for incomplete data design of various sorts of different sampling schemes that have been used, find the ratio of those estimates and then find the associated confidence intervals.

The confidence interval, again, there are a lot of approaches that one can take in this context which are going to depend on various assumptions. So, for example, one can make assumptions about normality or an abnormality. One can make assumptions about the ratio having a certain distribution and so on. What we tend to use in this context is we’re using type confidence interval which has been shown to work fairly well, independent of any distributional assumption or any assumptions about what a typical AUC is going to look like.

The only tricky bit really once the decisions have been made on how one estimates the AUCs and which confidence interval is going to be used, is how to incorporate a possible correlation between the AUCs. So if the AUC in the first compound is somehow related to what we see in the second compound. Again in this case there are certain ways that one can overcome this problem, but unfortunately generic solutions so very flexible solutions have not yet been developed. So it’s a case-by-case situation in this instance, about how one can address that.

Pharma IQ: Thanks for your insight into this area, Thomas. Now, just to round us off, why do you think that a conference on this topic is useful at this time?

T Jaki: I think it’s useful to strengthen the efforts to develop a more coherent treatment development process, i.e. remove any traditional boundaries that have been set. In other words, that once the animal studies have been completed, essentially half the information is lost about what one learned about the drug in animals and things are going to be scaled up to be tested in humans. So the conference is going to help to remove those boundaries and it’s going to bring together a more coherent process overall really, starting from first experiment, the in vitro experiment, all the way through to Phase III and marketing studies.

The other particularly useful feature of this conference is that it’s aiming to get together those practical aspects as well as theoretical aspects that are involved in the issue of developing good treatments. So it’s a good mix of practical and theoretical insights that one is going to hopefully get at this conference.

Pharma IQ: Yes, and finally what do you personally hope to gain from taking part in the event?

T Jaki: I hope that I can get three particular things out of this conference. The first one is, being a statistician, I know a little bit about the practical limitations when a trial is running that are involved in the day-to-day running of such studies. So I want to learn more about what the practical limitations are and what is possible, what is not possible, because from a statistical point of view there’s a lot of flexibility in many cases. But what’s the point in developing statistical methods that then are not going to be used because of practical limitations.

The second thing I’d like to get out of the conference is just to learn about alternative approaches to same or similar problems that I’m involved in, to basically listen to other presenters and have discussions with the participants and see which routes they have taken in order to overcome a specific issue. Generally speaking, there’s more than one solution to a problem and sooner or later, hopefully, the best solution will emerge which, of course, only can happen through interaction between the people involved. Finally, of course, I want to promote some of the work that we have developed.

Pharma IQ: Thank you so much for your time today, Thomas. It’s been great to speak to you in advance of the event and we look forward to hearing more in your presentation.

T Jaki: Thank you


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