Furthermore, the classical estimation methods known to provide highly reproducible values, and short run-times for simple PK models. Here, the model with higher number of random-effect parameters (IIVs) are referred as of high dimensions. These methods are known to perform well when models structure are simple and low in dimension. Therefore, it is important to understand the performance of different approach-based methods for handling data with a low number of subjects.Ĭlassical estimation methods like FOCE-I, including FO, FOCE and Laplace, approximate the likelihood by taking Laplace transformation and Taylor linearization. A list of estimation methods is available in NONMEM, including classical estimation methods and maximum likelihood expectation maximization (EM)-based estimation methods. It can also be useful for analyzing data obtained from a low number of subjects involved in a study.
NONMEM is the gold standard software for population analysis that allows for mixed-effect modeling of PK/pharmacodynamic data while accounting for both unexplained inter-subject, inter-occasion, and residual variability (random effects), as well as measured concomitant effects (fixed effects). Population analysis is a set of statistical techniques that can be used to study the average response (clinically measured event of any biomarker) in a population, as well as the IIVs in responses arising from different sources. As a result, it can be difficult to calculate and analyze the pharmacokinetic (PK) parameters, especially if the PK parameters show very high inter-individual variability (IIV). In addition, different aspects of the study design are not considered when calculating the number of subjects. This is because in the early stages of drug development, statistical approaches are difficult to apply, potentially leading to bias when predicting population mean and distribution of parameters and/or all sources of variability.
EM-based estimation methods can be considered for adapting to the specific needs of a modeling project at later steps of modeling.Įxploratory preclinical (as well as clinical) trials may involve a low number of subjects (around 6 subjects). The classical FOCE-I method appeared to estimate the PK parameters more reliably than the BAYES method when using a simple model and data containing only a few subjects. Similar performance of the estimation methods was observed with theophylline dataset. In general, estimates of random-effect parameters showed significant bias and imprecision, irrespective of the estimation method used and the level of IIV. The rRMSE and REE values of all parameter (fixed effect and random effect) estimates showed that all four methods performed equally at the lower IIV levels, while the FOCE-I method performed better than other EM-based methods at higher IIV levels (greater than 30%). NONMEM software assisted by Pirana, PsN, and Xpose was used to estimate population PK parameters, and R program was used to analyze and plot the results.
A case study was performed with a clinical data of theophylline available in NONMEM distribution media. Relative root mean squared error (rRMSE) and relative estimation error (REE) were used to analyze the differences between true and estimated values. A stochastic simulation and estimation (SSE) study was performed to simultaneously simulate data sets and estimate the parameters using four different methods: FOCE-I only, BAYES(C) (FOCE-I and BAYES composite method), BAYES(F) (BAYES with all true initial parameters and fixed ω 2), and BAYES only. In this study, 100 data sets were simulated with eight sampling points for each subject and with six different levels of IIV (5%, 10%, 20%, 30%, 50%, and 80%) in their PK parameter distribution. In this study, the performance of a classical first-order conditional estimation with interaction (FOCE-I) and expectation maximization (EM)-based Markov chain Monte Carlo Bayesian (BAYES) estimation methods were compared for estimating the population parameters and its distribution from data sets having a low number of subjects. Exploratory preclinical, as well as clinical trials, may involve a small number of patients, making it difficult to calculate and analyze the pharmacokinetic (PK) parameters, especially if the PK parameters show very high inter-individual variability (IIV).