Submodels covariate

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. 

Next, a three subpopulation mixture model is tried, whereby subjects could remain stable, gain, or lose weight. For this first mixture attempt, drug exposure is not included as a covariate. The three submodels and probability models are as follows (see C9. txt r9. txt). 

If the assumptions of point 5 hold, we can estimate the variances and the covariances of our estimates of the various parameters by a simple routine calculation. Note that among these assumptions is one that the model fitted is either the right model, or contains the right model as a submodel. 

When a model like this is written down for physical or chemical purposes, it will be rare that the experiment is so conducted as to make the covariances between u and the or the covariances among the x,— zero. If we were to submit u to least squares analysis, as if it were a response, with submodel B as the model, we would find... 

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. 

However, the use of interaction in covariate models is not common. (It is easy to see how these models could be expanded to three or more covariate or mixed and matched depending on the covariates). For example if age had a linear relationship with clearance, but weight followed a power model then one such covariate submodel might be... 

In summary, covariate submodels are limited by the imagination of the modeler and indeed, reviewing the literature one can find many strange covariate submodels. The covariate submodels described here are the most common and many problems can be handled using them. Regardless of the covariate submodel used, good practices dictate that the reason for choosing the model be indicated. 

An adequate covariate submodel building strategy was used. 

Obviously not all assumption tests can be applied at every stage of model development, although many should. At the least, many of these assumptions should be examined once a final covariate submodel or base model is developed. It should also be noted that many of these assumptions are tested by examination of the EBEs. As such, datasets that have few observations per subject will be of less value than datasets with many observations per subject since sparse data tend to produce EBEs that are more model dependent than data dependent. More will be said of the quality of the EBEs later in the chapter. 

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