Pharmacokinetic Parameters in Drug Development

A complex biochemical “dance” occurs between the body’s natural processes and the chemical composition of pharmaceutical drugs when taken by humans. These complicated interactions are measured and described using pharmacokinetic and pharmacodynamic parameters. Pharmacokinetics (PK) describes the absorption, distribution, metabolism, and excretion (also known as ADME) of drugs in the body. Pharmacodynamics (PD) describes how biological processes in the body respond to or are impacted by a drug. In drug development, PK and PD parameters are used to understand this complex interplay between drugs and the body to design, refine, and create safe and effective therapeutics.

What are PK Parameters?

PK parameters are used to translate and understand how a drug interacts with the body. PK parameters tell drug developers:

how the drug is absorbed after administration
how the body distributes the drug into different bodily compartments or tissues
how the body metabolizes or degrades the drug
how the body excretes or gets rid of the drug

Determining PK parameters for a drug starts with administering the drug to subjects in a clinical study. Then, samples of blood, urine, or other bodily material are collected from subjects at pre-specified time points. Each sample collected is analyzed to determine how much of the drug is present (drug concentration) at that specific timepoint. Drug concentrations are analyzed over time to determine the “concentration versus time” profile or CxT profile. An example of a typical concentration-time plot for an orally administered drug with key PK parameters including, Cmax, Tmax, AUC, and half-life is displayed below:

Cmax is the maximum observed concentration of the drug collected in bodily material from subjects in a clinical study
Tmax is the time it takes to reach the maximum concentration or time to Cmax
AUC stands for “Area Under the Curve” and represents the total exposure of the drug experienced by the subject in a clinical study
Half-life (t1/2) is the time it takes for half the drug concentration to be eliminated
A comprehensive list of PK parameters is provided here

How Are Pharmacokinetic Parameters Calculated?

PK parameters can be calculated using noncompartmental analysis (NCA) techniques in a series of steps including:

The preparation of concentration data obtained from a clinical study
Computational analysis of concentration versus time data to determine PK parameters

Drug concentrations in bodily matrices are determined by a bioanalytical laboratory and the raw concentration data are used in a computational noncompartmental analysis to generate the PK parameters. The methods used for calculating PK parameters generally apply to intravenous or extravascular administrations. PK parameters should be calculated only from individual subjects with sufficient concentration versus time data. The mathematics for NCA are straightforward but typically software is used to conduct this type of analysis.

PK Analysis Dataset

Prior to conducting the analysis to determine PK parameters, a dataset must be created that contains both concentration and time data. The data must be set up in an acceptable format for conducting an NCA. CDISC is the preferred structure/format for the dataset and should be created using standard programming languages (e.g., SAS or R).

Nominal vs. Actual PK Sampling Time

The “nominal time” of PK sample collection is the time that a sample was intended to be collected as described in the clinical protocol. The “actual time” of PK sample collection is the specific time that a sample was actually collected from the subject following dosing of an investigational drug in a clinical study. PK parameters should be determined using the actual PK sampling times relative to actual dosing times when possible.

What is Below the Limit of Quantification (BLQ)?

A bioanalytical lab uses a validated assay to determine the amount of drug in a biological sample and creates a standard curve of known drug concentrations to determine the reliable quantification range of the assay. There is a lower limit of quantification (LLOQ) and an upper limit of quantification (ULOQ) that defines the range. If a drug concentration falls below the LLOQ then the concentration is deemed to be below the limit of quantification (BLQ). Although the drug may be detected at a concentration value lower than the LLOQ, those concentrations should not be used in the calculation of PK parameters. There are multiple principles of PK analysis that relate to the handling of BLQ data. Typical rules for handling BLQ values in concentration versus time analysis following oral administration of a drug include:

If a BLQ value occurs in a profile before the first quantifiable concentration, it should be assigned a value of zero.
If a BLQ value occurs after a quantifiable concentration in a profile and is followed by a quantifiable concentration, then the BLQ value should be treated as missing and excluded from the PK analysis.
If a BLQ value occurs after the last quantifiable concentration, it should be treated as missing and excluded from the PK analysis.
If two BLQ values occur in succession after Cmax, the profile will be deemed to have terminated at the first BLQ value and any subsequent quantifiable concentrations should be treated as missing and excluded from the PK analysis.

When to Exclude PK Data from the Dataset

All PK data should be included in the calculation of PK parameters; however, there are some instances in which exclusion of PK data may be warranted when inclusion of such data in question would impact the interpretation of PK endpoints. In all instances, clear justification must be provided in the PK report for the exclusion of any data. Below are some examples of when PK data should be excluded from the dataset, however this is not an exhaustive list of reasons for data exclusion:

Exclusion of data due to insufficient absorption
Anomalous concentration value
Pre-dose quantifiable concentrations of drug (e.g., before first doses or following washout)
Lack of exposure when such exposure was expected
Certain BLQ values based on rules defined above
Dose or formulation failure

Calculating Area Under the Curve (AUC) Parameters

The standard method for calculating AUC parameters is the linear-up/log-down trapezoidal method. Alternative methods may be used for calculating AUC parameters, but justification for this change should be provided in the final clinical study report (CSR) or PK report. The following AUC parameters are calculated using the linear-up/log-down trapezoidal method (unless another interpolation method is justified in the CSR):

AUC versus time curve from time of dosing to the time of last quantifiable concentration (AUClast)
AUC versus time curve from time of dosing to a specified point post-dose (AUC0-t)
AUC versus time curve between two specified time points in a PK profile (AUCt1-t2)

The area from time of dosing extrapolated to infinity (AUCinf) should be calculated using λz and Clast. In some circumstances, it may be preferable to use the last predicted quantifiable concentration instead of the last observed quantifiable concentration for the extrapolation to infinity. Lastly, reporting of AUCinf values is contingent on the percent of the total area obtained by extrapolation (AUC%Extrap).

Parameters Dependent Upon AUCinf

The calculation of total body clearance following intravascular (CL) or extravascular (CL/F) administration and mean residence time extrapolated to infinity (MRTinf) are dependent based on AUCinf. The volume of distribution based on the terminal elimination phase following intravascular (Vz) or extravascular (Vz/F) administration and the volume of distribution at steady state following intravascular administration (Vss) are also dependent upon the calculation of AUCinf.

Software Used for NCA and PK Parameters

NCA is typically done using software designed for analyzing concentration versus time data to calculate PK parameters. However, it’s important to know that the FDA does not require you to use any one specific PK/NCA analysis software package over another. Software programs such as Microsoft Excel or other spreadsheet programs can be utilized to compute PK parameters. Similarly, statistical software such as SAS or R can be used by programmatically incorporating NCA mathematics in code and running the computations. The only requirement of the FDA is that your software system is validated as per FDA regulations (e.g., 21 CFR Part 11). There are multiple options to consider when determining which software solution is best for your needs and budget when conducting an NCA. Commercial off-the-shelf software solutions exist with NCA mathematics embedded in them that can be used to compute PK parameters for a fee. Also, there are free versions of NCA analysis software in R available on the comprehensive R archive network (CRAN).

Conclusions

The complex interactions between the human body’s natural processes and a pharmaceutical drug are interpreted using pharmacokinetics. In drug development, PK parameters are used to understand how a drug is absorbed, distributed, metabolized, and ultimately excreted (ADME) from the body. In other words, PK parameters describe how a drug gets into the body, moves around, and gets out of the body which is important information required by FDA and other regulatory bodies to approve drugs for public use. We can help make the most of your clinical studies involving PK data by planning for and conducting NCA to the highest standard. Contact us today for expert guidance on your PK analysis dataset and NCA analysis.