For example, a number of studies can be pooled into one analysis while accounting for differences between study sites, and all fixed-effect covariate relationships and any interindividual or residual error structure can be investigated.ĭisadvantages arise mainly from the complexity of the statistical algorithms and the fact that fitting models to data is time consuming. The models are also much more flexible than when the other methods are used. Since allowance can be made for individual differences, this method can be used with routine data, sparse data, and unbalanced number of data points per patient. The advantages of the one-stage analysis are that interindividual variability of the parameters can be estimated, random residual error can be estimated, covariates can be included in the model, parameters for individuals can be estimated, and pharmacokinetic–pharmacodynamic models can be used. Therefore, inclusion of additional variables in the model is warranted only if it is accompanied by a decrease in the estimates of the intersubject variance, and under certain circumstances intrasubject variance. This means that such differences were not explained by the model prior to adding the variable and were part of random interindividual variability. The purpose of adding independent variables to the model, such as CL CR in Equation 10.7, is usually to explain kinetic differences between individuals. Any improvement in the model would be reflected by a decrease in the objective function. A global measure of goodness of fit is provided by the objective function value based on the final parameter estimates, which, in the case of NONMEM, is minus twice the log likelihood of the data. The fitting routine makes use of the ELS method. NONMEM is a one-stage analysis that simultaneously estimates mean parameters, fixed-effect parameters, interindividual variability, and residual random effects. A covariance between two elements of η is a measure of statistical association between these two random variables. Each pair of elements in η has a covariance which can be estimated. Each ε variable is assumed to have a mean zero and a variance denoted by σ 2. The second level represents a random error (ε ij), familiar from classical pharmacokinetic analysis, which expresses the deviation of the expected plasma concentration in subject j from the measured value. The first level, described previously, is needed in the parameter model to help model unexplained interindividual differences in the parameters. There are, however, two levels of random effects. These equations can be applied to subject k by substituting a k for j in the equations, and so on for each subject. The understandings on the roles, meanings and implications of IEs even help modelers in troubleshooting situations which frequently occur over the whole modeling process.Where C L ¯ and V d ¯ are the population mean of the elimination clearance and volume of distribution, respectively, and η CL and η j V d are the differences between the population mean and the clearance ( CL j) and volume of distribution ( V dj) of subject j.
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. 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. 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.
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