9 Frequently Misunderstood Concepts in PK/PD Modeling

In teaching pharmacometrics, I’ve noticed that scientists have difficulty with certain PK/PD modeling concepts. Maybe you’ve read about some of these terms in journal articles, but didn’t know what they meant? Or you’ve heard these terms bandied about by colleagues, but felt too shy to ask them what they meant? I’ll clarify some important concepts related to pharmacokinetic analysis, bioanalysis, and study designs.

High quality PK analysis requires great bioanalysis

The field of bioanalytical chemistry, or bioanalysis, is an important area of research. Bioanalysis has a direct impact on the work of pharmacokineticists. A blood sample (or other matrix)  is converted into a drug concentration using analytical equipment. Many bioanalysis topics should be of interest to individuals in the field of pharmacokinetics. After all, bioanalysis results are the starting materials for pharmacokinetic analysis. Any good cook wants to use the best ingredients to make a delicious meal. Likewise, the pharmacokineticist selects the best bioanalysis tools to ensure the highest quality pharmacokinetic analysis.

  • Bioanalytical calibration curves: The calibration curve is the keystone of bioanalysis. It is what links the instrument response to a specific concentration of drug. It is like the magic decoder ring that helps you decipher the hidden messages. If the ring isn’t right, then the resulting message is not interpretable. Calibration curves are important.  We should understand how they are built, and what techniques and challenges are involved. Read more
  • Bioanalytical method validation: The purpose of method validation is to demonstrate that a specific bioanalytical method can reliably determine the concentration of drug in a study sample with a high degree of confidence. Validation does not mean that a method is perfect, or even adequate for the study. Validation means that the method has met a set of criteria designed to ensure that it is reliable and consistent. Read more
  • Ligand binding assays: Large molecules, such as peptides, proteins, and macromolecules, are often called “biologics” because they are derived from endogenous biological molecules. But, in general, they are modified such that the body no longer recognizes them as an endogenous compound. Although some are identical to actual endogenous molecules, e.g., insulin. For some of these biologics, standard chromatographic methods may be adequate. But, these molecules are usually too large, too hydrophilic, and too difficult to detect using HPLC/UV or even LC/MS/MS. Read more

Key concepts in pharmacokinetic analysis

Non-compartmental pharmacokinetic analysis has been the mainstay of pharmacokinetic data analysis for over 50 years. Non-compartmental pharmacokinetic analysis, or NCA, was developed as a method to standardize pharmacokinetic data analysis before personal computers had adequate computing power to perform nonlinear model fitting. While developed as a surrogate for model fitting, NCA has the advantage of repeatability. Anyone can take a set of data and perform NCA using any software and arrive at the same answers. This was particularly important when modeling software was often “home-grown” and highly variable. NCA still plays an important role in pharmacokinetic data analysis. Further, the ability to automate NCA methods renders it amenable to rapid analysis of large and diverse data sets.

  • Calculating the elimination rate constant: The elimination rate constant is the rate at which drug is cleared from the body assuming first-order elimination. Various abbreviations represent the elimination rate constant including ke, kel, λ, and λz. The calculation of the elimination rate constant can be done using pharmacokinetic parameters. Or it can be done from a plot of concentration time data. Read more
  • Understanding steady state pharmacokinetics: “Steady state” is an important term in pharmacokinetics. But, it can often seem a bit abstract and confusing to many. Here is how I define steady state. When the rate of drug input is equal to the rate of drug elimination, steady state has been achieved. Read more

Study design tips

Just as you cannot make a silk purse out of a sow’s ear, great PK/PD analysis cannot salvage a poorly conceived study design. As a pharmacometrician, you can influence the conduct of studies. Likewise, the design of a study informs how you might go about performing your analysis. Over the years, I’ve worked with data from many pre-clinical and clinical studies. Here are some pointers for you that I’ve picked up.

  • The advantages and challenges of cassette dosing: Cassette dosing is a technique primarily used in drug discovery efforts in non-clinical studies to collect pharmacokinetic data from multiple drug candidates in a single experiment. A typical cassette dosing pharmacokinetic study involves simultaneous administration of 5-10 compounds to a set of animals. Serial blood samples are obtained and LC/MS/MS techniques are used to measure the concentration of each analyte in each sample. Thus, instead of running 5-10 separate PK studies, a similar amount of information can be obtained from a single study. This method can support rapid evaluation of many compounds with fewer animals. Read more
  • Using sampling “windows” for PK blood samples:  One of the most common questions posed by clinical operations experts when including pharmacokinetic sampling in a clinical trial is the following:“What is the time window we should allow for each blood sample?”My answer is always the same: “Don’t include any window.” I am almost always met with a confused look. The confusion is borne out of years of social programming for clinical operations staff by inexperienced clinical pharmacologists. I still see wording in protocols that say something like, “Because PK is the primary endpoint, the blood draws for PK samples should take priority over all other activities and should occur on the scheduled time point before any other procedure.” Unfortunately, statements and sentiments such as these are not supported by scientific data and actually can contribute to poor quality clinical data. I will demonstrate that sampling time does not affect PK parameter calculations. Read more

Troubleshooting modeling problems

So, you’ve got a firm grasp of the principles of bioanalysis. You know the concepts of pharmacokinetics forwards and backwards. Your study design is divine. Yet, you’re still having trouble building PK/PD models. Some modeling concepts that I find my students often have some confusion towards include:

  • What is identifiability? Developing models for pharmacokinetic or pharmacodynamic data requires creativity, patience, and hard work. Sometimes that creativity ends up violating mathematical principles which can lead to poorly fitting models and frustration for a modeler. One common area where mistakes are made is related to the analysis of parent and metabolite data. Because data are available for both analytes (parent drug and metabolite), it seems like it should be a piece of cake … and sometimes it is. But other times we forget about a key mathematical principle called identifiability. Read more
  • What is the -2LL or the log-likelihood ratio? If you have ever read the literature on pharmacokinetic modeling and simulation, you are likely to have run across the phrase  “-2LL” or “log-likelihood ratio”. These are statistical terms that are used when comparing two possible models. But what is the log-likelihood ratio? And how do you use it? Read more.

Learn more about Certara’s pharmacometric consulting services

To see some of these pharmacometric principles in action, read this recent case study of how my colleagues helped a sponsor bring a novel antibiotic from pre-clinical studies through market approval to treat adults with complicated infections. What concepts in PK/PD modeling are you having trouble with? Let me know in the comments!