Interoccasion variability

PPK analyses provide an opportunity not only to estimate variability but also to identify its sources. Variability is usually characterized in terms of hxed and random effects. The hxed effects are the population average values of PK parameters, which may in turn be a function of patient characteristics discussed earlier. The random effects quantify the amount of PK variability, which is not explained by the hxed effects, and these random effects subsets are intersubject variability, interoccasion variability, and intraindividual and residual variability (12). Karlsson and Sheiner (13) have demonstrated that the lack of separation of interoccasion variability from residual intrasubject variability produced bias in estimation of PPK parameters. 

The variability in the observations made during clinical trials can be attributed to differences between patients (intersubject variability), differences occurring within a patient from day to day (interoccasion variability) and residual variability, which can be attributed to assay variability or other unknown sources. The pharmacosta-tistical model characterizes these sources of variability and estimates the magnitude of the different sources of variability. 

The interoccasion variability (IOV) or intraindividual variability [11] arises when a parameter of the model, e.g. CL, varies within a subject between study occasions. The term occasion can be defined arbitrarily, usually logical intervals for an occasion are chosen, e.g. each dosing interval in multiple dose studies or each treatment period of a cross-over study can be defined as an occasion. To assess the IOV of a specific parameter more than one measurement per individual has to be available per occasion. The IOV can be implemented in the random effect model as described in the following ... 

Karlsson, M. O., Sheiner, L. B. The importance of modeling interoccasion variability in population pharmacokinetic analyses. 

It recognizes variability such as intersubject, intrasubject, interoccasion variability as an important feature that should be identified and measured during drug development or evaluation. 

The objective for performing a population pharmacokinetic study should be taken into consideration in designing such a study. When designing a population pharmacokinetic study, the practical limitations of sampling times, number of samples/subject, and number of subjects should be considered. Also, the sampling of subjects at various periods (study days) should be considered if interoccasion variability is... 

A third possible source of variation, accounting for deviations in the PK parameters within subject from period to period, often referred to as interoccasion (lO) variability, may also be incorporated in the PK model. For example, we may define Vij = V exp(r]iy + rj jy), where rji v as before represents the intersubject random effect while represents the interoccasion random effect within subject, assumed independently distributed as N(0, cv-occ-V). 

Although the fixed effects have been well estimated, it is also of interest to examine how closely the estimated standard deviations of the random effects reflect the true variability in the simulated data. The dp2 data frame includes values of the generated subject random effects, interoccasion random effects, and measurement errors, from which sample variances can be obtained and compared to the model estimates. The intersubject sample standard deviations of log(ic ), og AUC), and log(T) are 0.33,0.41, and 0.23, respectively. The corresponding model estimates are 0.36, 0.39, and 0.26. For the lO random effects, the sample SDs are 0.17, 0.22, and 0.17, while the corresponding values obtained in the model fit are 0.20, 0.19, and 0.18, respectively. The sample and model SD for measurement error are both equal to 0.1, indicating a good agreement overall between sample and model estimates. 

D. J. Lunn and L. J. Aarons, Markov chain Monte Carlo techniques for studying interoccasion and intersubject variability application to pharmacokinetic data. Appl Stat IRSS Series C 46 73-91 (1997). 

There is a clear resemblance between the two figures although the one based on real data appears to be more variable. This may indicate that there are more covariate effects to be included in the model (based on the left panels) or that interoccasion variability would improve the model (based on the right panels) (4). 

Optimize the Random Effects Models. The random effects models— models for intersubject variability and residual error—should be optimized once the structural model has been optimized. This might mean including interoccasion variability if the data supports it. 

Nonlinear mixed effects models are similar to linear mixed effects models with the difference being that the function under consideration f(x, 0) is nonlinear in the model parameters 0. Population pharmacokinetics (PopPK) is the study of pharmacokinetics in the population of interest and instead of modeling data from each individual separately, data from all individuals are modeled simultaneously. To account for the different levels of variability (between-subject, within-subject, interoccasion, residual, etc.), nonlinear mixed effects models are used. For the remainder of the chapter, the term PopPK will be used synonymously with nonlinear mixed effects models, even though the latter covers a richer class of models and data types. Along with PopPK is population pharmacodynamics (PopPD), which is the study of a drug s effect in the population of interest. Often PopPK and PopPD are combined into a singular PopPK-PD analysis. 

In a population analysis, there are usually two sources of variability between-subject variability (BSV), sometimes called intersubject variability, and residual variability. Between-subject variability refers to the variance of a parameter across different individuals in the population. In this text, intersubject variability will be used interchangeably with between-subject variability. Residual variability refers to the unexplained variability in the observed data after controlling for other sources of variability. There are other sources of variability that are sometimes encountered in the pharmacokinetic literature interoccasion variability (IOV) and interstudy variability. Each of these sources of variability and how to model them will now be discussed. 

Variance model (between-subject, interoccasion, and residual variability) used and... 

Since some subjects were sampled on different occasions, the occasion on which each subject received their dose was determined so that BSV may be further partitioned into interoccasion variability (IOV). Once the data set was created, the first 19 subjects were removed and saved as a validation data set. This represented 20% of the total data. The remaining subjects were used for model development. Thus, the model development data set consisted of 250 observations from 78 patients, whereas the model validation data set consisted of 72 observations from 19 subjects. 

Figure 9.10 Goodness of fit plots, residual plots, and histograms of weighted residuals and random effects under the reduced 2-compartment model with tobramycin clearance modeled using a power function of CrCL and interoccasion variability on CL. Dashed line in observed versus predicted plot is the line of unity. Solid line in the weighted residual plot is an inverse square kernel smoother with 0.4 sampling proportion.

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