Submodels statistical

STATISTICAL MECHANICS AS THE SECOND SUBMODEL. The interaction potential obtained via quantum mechanics constitutes the input necessary to obtain a statistical description of many water molecules interacting at a given pressure and temperature. 

Various methods are available to estimate population parameters, but today the nonlinear mixed effects modeling approach is the most common one employed. Population analyses have been performed for mAbs such as basiliximab, daclizu-mab and trastuzumab, as well as several others in development, including clenolixi-mab and sibrotuzumab. Population pharmacokinetic models comprise three submodels the structural the statistical and covariate submodels (Fig. 3.13). Their development and impact for mAbs will be discussed in the following section. 

The statistical submodel characterizes the pharmacokinetic variability of the mAb and includes the influence of random - that is, not quantifiable or uncontrollable factors. If multiple doses of the antibody are administered, then three hierarchical components of random variability can be defined inter-individual variability inter-occasional variability and residual variability. Inter-individual variability quantifies the unexplained difference of the pharmacokinetic parameters between individuals. If data are available from different administrations to one patient, inter-occasional variability can be estimated as random variation of a pharmacokinetic parameter (for example, CL) between the different administration periods. For mAbs, this was first introduced in sibrotuzumab data analysis. In order to individualize therapy based on concentration measurements, it is a prerequisite that inter-occasional variability (variability within one patient at multiple administrations) is lower than inter-individual variability (variability between patients). Residual variability accounts for model misspecification, errors in documentation of the dosage regimen or blood sampling time points, assay variability, and other sources of error. 

A second approach is, postulate a series of competing models and then use a more rigorous statistical criteria to choose which function best describes the data. For example, one could build different covariate submodels, one for each function to be tested, with the model having the smallest AIC taken forward for further development. More will be discussed on these approaches later in the chapter and elsewhere in the book. It should be noted that rarely do published PopPK models justify the choice of covariate submodel used. 

Wahlby, U., Bouw, M.R., Jonsson, E.N., and Karlsson, M.O. Assessment of Type I error rates for the statistical submodel in NONMEM. Journal of Pharmacokinetics and Pharmacodynamics 2002 29 251-269. 

We have developed a general template for construction of asymptotically efficient substitution estimators of /o fully respecting the statistical model. It works as follows. Firstly, one determines a representation of x /o as a function of a smaller parameter Qg instead of the whole P . Let f be the parameter space of Qq. For notational convenience, we will refer to this mapping as I again. Thus, )Ao = P(Qo)- r ow assume the existence of a loss function L(Q) (O) for Qg so that Qo = argminge EgL(Q)(0), and a corresponding submodel... 

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