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How PK Modeling Can Inform Sample Size Estimation and Dose Selection for Your Product

Drug development is an extremely cumbersome process, requiring the testing of an agent from in vitro studies to in vivo studies to in silico modeling. Given that it can take up to 20 years for a final product to be approved, it is unsurprising that drug attrition rates are very high.

Pharmacokinetics (PK) and bioequivalence (BE) studies serve as the foundation of determining the fate of drug products. Proper planning of PK assessments can accelerate the development of both novel drugs and new formulations of previously approved drugs developed via the 505(b)(2) pathway.

This blog post will discuss how PK modeling can contribute to sample size estimation, a key aspect of a clinical trial protocol. Modeling, using minimal data, can also support proper dose selection for bridging studies for new formulations, a technique that can significantly reduce the number of required studies. Minimizing the studies and sample size while allowing the detection of clinically important differences leads to cost-effective study designs, and the savings will be passed to patients in need of the medication.

Approaches to Pharmacokinetic Analysis

Classic Approach: Noncompartmental Analysis and Two One-Sided Tests

The classic approach to analyzing PK data in BE studies comparing two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). The NCA approach allows the area under the plasma concentration time curve (AUC) and the peak drug concentration (Cmax) to be derived for both treatment groups, which in turn allows their geometric mean ratios to be considered. This fundamental approach in PK can be used to analyze concentration time data to understand how the body handles the drug if there is insufficient sampling and mechanistic information. According to current FDA and EMA guidelines, the formulations are considered sufficiently similar if the 90%- confidence interval for these geometric mean ratios falls between 0.8 and 1.25. A failure to demonstrate BE may suggest that the test product should be reformulated, that the manufacturing method should be changed, that additional safety or efficacy data may be needed, or that the study was not properly powered for sample size.

In some cases, conclusions of BE between the test product and the reference product based on the Cmax and AUCs may not be sufficient. Differences in other parameters—for example, the shape of PK profiles such as Tmax—may be also important for safety or efficacy. Such differences could imply that the test product will not produce the same clinical response as the reference product. Additional data analysis, exposure-response evaluation, or clinical studies may be recommended to gain a more in-depth comparison.

Pharmacokinetic Modeling: Non-Linear Mixed Effects Modeling

When PK sampling is limited for any reason—such as to reduce burden in patients, particularly vulnerable populations like pediatrics or geriatrics—NCA may not be a reliable approach, and a model-based alternative can be used to estimate AUC and Cmax. Non-linear mixed effects modeling (NLMEM) is the most common statistical model used in population analysis.

There are several key advantages of NLMEM:

  • Improved accuracy of the estimates when dealing with sparse designs
  • Ability to determine power versus sample size curves with accuracy
  • Ability to handle cross-over, parallel, and mixed studies
  • Potential for dosing correction to allow the test product to achieve BE with a high power

An optimal structural model is found in a one-stage analysis that simultaneously estimates all parameters (fixed effect parameters, inter-individual variability, inter-occasion variability, measurement errors, etc.). Knowing the optimal PK model and its parameter characteristics allows for subsequent simulations to create new samples (PK profiles, optimal blood sample times, etc.) that could arise from that same population.

Test and reference PK profiles can be simulated using the developed PK model, followed by a BE test performed for each simulated dataset. Therefore, modeling with simulation strategies allows for the plotting of a power versus sample size curve and the proposal of new strategies to increase the probability of demonstrating BE.

Pharmacokinetic Analysis in Action

The typical modeling example for BE is the pilot cross-over 2×2 study between the reference product and the new formulation with a small sample size of fewer than 10 subjects. In the following hypothetical example, the data are too sparse to enable a classic BE analysis, so Camargo conducts a BE analysis using NLMEM. We estimate the PK parameters, including between-subject and within-subject variability as well as measurement error.

The results of the population analysis reveal the average relative bioavailability of the test to reference. Subsequent simulation procedures generate more than 1000 new data sets using the same study design as the original but with larger sample sizes using the population PK model. The comparison of relative bioavailability based on simulated data then indicates if BE can be achieved. The population PK analysis includes a covariate search to identify the PK parameters that are statistically different across the subjects.

If the bioavailability parameter appears to be significantly different statistically in the test group, the sponsor can use a corrected dose for the test product by dividing the reference dose by the average relative bioavailability. The new simulations with corrected dose are then used to assess a new power versus sample size curve and to propose a sufficient sample size for successful bridging using the optimized dose.

This example of BE analysis shows how using the population approach not only supports sample size estimation but also contributes to rational dosing selection. In this way, modeling can augment a sponsor’s ability to perform BE testing when the traditional NCA-based analysis fails or is not feasible.

Camargo’s worldwide expertise and extensive experience makes us your ideal partner for population PK and BE testing and analysis. Contact us to find out how we can help you choose the right sample size, dosing schedule, and dosing methodology for your product.


Galina Bernstein, PhD
Senior Director, Clinical Pharmacology

Uma Fogueri, PhD
Pharmacokinetics Scientist

Serge Guzy, PhD
President and CEO