Sparse sample and population pharmacokinetics

In drug development, it is necessary to understand the pharmacokinetics profiles (or time concentration profiles) of the experimental drug and calculate the pharmacokinetic (PK) parameters (Area Under the Curve – AUC, Clearance – CL, or Volume of distribution –Vd). These PK parameters can provide the estimate of the dose exposure and assist in the decision on dose timing and dose interval. In order to calculate the PK parameters, we typically need a serial of blood samples at multiple time points (usually more than 6) after the drug administration. In some situations, it is not feasible or not practical to obtain these many blood samples. The obvious example is in pediatric studies where it is not feasible to obtain multiple blood samples due to the blood volume restriction. The specimen may not just be blood samples. If the PK is conducted using other specimens, it is usually difficult to obtain multiple PK samples. For example, we could obtain middle ear fluid (MEF) sample to determine the antibiotic drug concentration in the ear and bronchoalveolar lavage (BAL) to determine the drug exposure in the lung. It is not practical to obtain multiple samples for these special specimens due to the safety concern.

When very few samples are available for each patient, we call it ‘sparse sampling’. With sparse data, we would need to employ a

Population PK

approach to estimate the PK parameters, describe the PK profile, or do PK/PD modeling. The use of population PK during the drug development has been steadily increasing. Regulatory agencies have issued several guidance on the use of population pharmacokinetics.

à        FDA guidance on Population Pharmacokinetics

à        FDA guidance General Considerations on Pediatric PK

à        FDA guidance Pharmacokinetics in Pregnancy

à        EMEA Guidance on the Role of Pharmacokinetics in the Development of Medicinal Products in the Paediatric Population

à        EMEA Guidance on Reporting the Results of Population Pharmacokinetic Analyses

There are different sparse sample designs. Below are some of the sparse sample designs I have seen.  

An example of sparse sampling at fixed time points is described in a paper by Vogelmeier et al. They used BAL fluid sample to study the intrapulmonary half-life of aerosolized product in Normal Volunteers”.

For BAL fluid samples, it is not feasible to obtain serial samples at all six time points (at screening, 0.5, 6, 12, 24, and 36 h). Therefore, in this study, “each volunteer underwent two BALs. The first lavage was done in the screening phase with an interval of between 3 and 7 d before inhalation of the drug. The volunteers were randomly assigned to one of five groups with the second lavage following 0.5, 6, 12, 24, or 36 h after aerosol administration. Each of the groups consisted of six individuals…”

Subjects in group 1 contributed two BAL samples at Screening and at 0.5 hours after inhalation.

Subjects in group 2 contributed two BAL samples at Screening and at 6 hours after inhalation.

Subjects in group 3 contributed two BAL samples at Screening and at 12 hours after inhalation.

Subjects in group 4 contributed two BAL samples at Screening and at 24 hours after inhalation.

Subjects in group 5 contributed two BAL samples at Screening and at 36 hours after inhalation.

With subjects from all five groups combined, a overall picture of the PK profiles over 24 hours after inhalation could be described. Original paper provided only the summary analysis. Nowadays, the data could be further analyzed using nonlinear mixed model from population PK model with software such as NONMEM.

In FDA guidance on Population Pharmacokinetics, an example was provided for estimating the AUC using sparse data (1-2 middle ear fluid samples per subject) in pediatric subjects.

“The penetration of drug X into middle ear fluid (MEF) was investigated using population PK analysis with sparse data (1-2 samples per subject) obtained from 36 pediatric patients (2 months to 2.0 years of age) who underwent clinical therapy with drug X. The estimated area under the concentration-time curve (AUC) that was above the minimum inhibitory concentration (MIC) (AUCMIC) and the half-life of drug X are 12.5 ug.hr/ml and 6.1 hours in MEF, respectively, vs. 23.7 ug.hr/ml and 3.2 hours in plasma, respectively….”

With this short description, we don’t know if MEF samples are taken from subjects at various times or fixed times. However, non-linear mixed model must have been used for analyzing the data.  

FDA’s guidance on population pharmacokinetics states, “the full population PK sampling design is sometimes called experimental population pharmacokinetic design or full pharmacokinetic screen. When using this design, blood samples should be drawn from subjects at various times (typically 1 to 6 time points) following drug administration. The objective is to obtain, where feasible, multiple drug levels per patient at different times to describe the population PK profile. This approach permits an estimation of pharmacokinetic parameters of the drug in the study population and an explanation of variability using the nonlinear mixed-effects modeling approach. “

If a full population PK sampling design is used, the sampling scheme will be something like below. The different subject could contribute different number of samples at various times.  

Subject number	Blood sampling time (t)	concentration at time t  Ct
001	Predose	xxx
001	24 hours post dose	xxx
002	Predose	xxx
002	8 hours post dose	xxx
002	12 hour post dose	xxx
003	Immediately postdose	xxx
003	5 hour post dose	xxx
004	4 hour post dose	xxx
…

Then when non-linear mixed model such as NONMEM is used to fit the data to characterize the PK profile with PK parameter (such as AUC) = function of concentration (Ct) at time t.

In multiple dose studies, if the purpose is to characterize the PK profile at steady state, one could implement a strategy of splitting the number of samples into different dose intervals.

Suppose we need 8 serial blood samples (t1 to t8) to calculate AUC and the dose interval is weekly, we can have these 8 samples split into 4 dose cycles. For each subject, we would only take two samples for each dose cycle. At steady state, for each subject, we expect PK profile after each repeat dose is not much different; the concentration at day 1 after repeat dose #1 would be similar to the concentration at day 1 after repeat dose #4, and so on. In this case, we would be able to calculate AUC for each subject with 8 samples from four dose intervals (instead of 8 samples from one dose interval over 7 days). The drawback is that the study period would be longer.