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Although one of the basic principles implemented in NONMEM is that each ETA (η, the discrepancy of an individual parameter from the typical population value) is normally distributed with a mean of 0, a modeler may describe a parameter distribution with various types of distribution by defining an appropriate parameter submodel. Thus, the IE for the between-subject variability (BSV) of each parameter should be defined separately: this value is ω 2, defined in the $OMEGA block. However, the θ value contains no information on the variability or dispersion of corresponding parameters between individuals, which is another essential component to describe a specific distribution. The IE values for θs are given in the $THETA block. This value may be similar to the mean or median of the individual parameter values included in the dataset, and indicates the general extent or the central tendency of the corresponding parameter. As all pharmacometricians are aware, typical population values of PK and/or PD parameters are defined using THETA (θ). There are two levels of consideration for the IE designation in terms of describing the 'distribution.' The first level is the parameter distribution. Meaning of THETA, OMEGA and SIGMA and the IE their initial estimates By focusing only on the IE, which is typically discussed as a subtopic, this tutorial may serve as a practical guide for modeling efforts related to IE designation. This tutorial seeks to provide comprehensive knowledge of the IE at a beginner's level, which has not been cohesively presented in a single article or learning material. Nevertheless, a modeler may avoid spending unnecessary time investigating FPEs that are not valid by determining appropriate IE values with a basic understanding of the IE. Because the IE is not a simple set of values but an essential starting point for estimations based on the model structure, knowledge of the NONMEM estimation algorithm and of concepts of pharmacokinetics (PK) and pharmacodynamics (PD) is essential. Indeed, it is almost impossible for beginners to thoroughly understand the various aspects of the IE. In this context, it is important to have precise information and knowledge regarding the IE to achieve an acceptable model fit. This problem should not be overlooked because a modeler may obtain irrelevant FPEs if the IE values of model parameters are selected without a complete understanding. In particular, beginners in the field of pharmacometric modeling and simulation typically have an inadequate understanding as to how NONMEM works and the meaning of the control stream components therefore, knowledge regarding the concept, role, and specific value of the IE may be lacking. A single experience with pharmacometric modeling is sufficient for one to realize that the determination of specific IE values is not a simple task and that the final parameter estimates (FPE) and/or NONMEM run time may vary according to the IE values. The initial estimate (IE) is an essential component of a NONMEM control stream.
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The understandings on the roles, meanings and implications of IEs even help modelers in troubleshooting situations which frequently occur over the whole modeling process. NONMEM may fail to converge when too small IEs are provided for residual error parameters thus, it is recommended to give sufficiently large values for them. Because it is almost impossible for a modeler to give a precise IE for OMEGAs at the beginning, it may be a good practice to start at relatively small IEs for them. In practice, problems related to the value of the IE are more likely to occur for THETAs rather than the random-effect terms. To provide NONMEM with acceptable IEs, modelers should understand the exact meaning of THETA, OMEGA and SIGMA based on physiology.
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A 'good' set of IEs rather than arbitrary values is required because the IEs where NONMEM kicks off its estimation may influence the subsequent objective function minimization.
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By focusing on the IE, this tutorial may serve as a practical guide for beginners in pharmacometrics. The importance of precise information and knowledge on the initial estimates (IEs) in modeling has not been paid its due attention so far.