EM algorithms consist of an expectation (E) and a maximization step (M), where these methods differed in the way step E was performed, which involves the approximation of likelihood. In this study, the other estimation methods such as ITS, IMP, IMPMAP, and SAEM were not tested because these methods were expected to perform similar or below the performance of BAYES as these methods are based on EM algorithms. The BAYES method is a newly introduced method in NONMEM and is more suitable for estimation of population mean and distribution for complex PK/PD models. The FOCE-I method is a classical estimation method that is applied by most users and has a short run-time for estimation of population mean and distribution for simple models. Therefore, the objective of this study was to compare precision and accuracy of estimation methods for estimating population mean and distribution of PK parameters from a small number of subjects and explore options to minimize bias with a classical method and a maximum likelihood EM-based method. However, no previous study has compared estimation methods for estimating population PK parameters from a small number of subjects. Other expected features of the estimation methods are low sensitivity to priors and short runtime. The most desirable property of a given estimation method is its precision and accuracy as they are the basis of the reliability of the obtained estimates. Some previous studies have compared available estimation methods with different objectives, identifying various desirable traits of estimation methods. In case of complex PK/PD problems, EM based methods are faster than FOCE-I due to their efficient maximization step. It is due to this sampling step EM based methods have longer run-time compared to the classical methods for simple PK models. The EM based methods calculate the exact likelihood (with approximation) by sampling and summing through the probability density function space, which is theoretically expected to approach the true likelihood as the sampling reaches infinity. However, these linearization methods fail to converge and estimate parameters precisely with significant bias with increase in model complexity. 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. Exploratory preclinical (as well as clinical) trials may involve a low number of subjects (around 6 subjects).