Model-Based Variable Importance

Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-ics. The network of signals and regulatory pathways, sources of variability, and multistep regulation that are involved in this problem is shown together with its main components. It is important to realize how between-subject and between-event variation must be addressed in a model of the system that is not purely structural, but also statistical. The power of model-based data analysis is to elucidate the (main) subsystems and their putative role in overall regulation, at a variety of life stages, species, and functional (cell to organismal) levels. Images have been selected for illustrative purposes only. See color plate.

The reduction of latent variables is an effective method to reduce the number of possible models, yet in PLS, variable reduction is not needed. The reduction of the number of variables in traditional regression techniques will lead to models with improved predictive ability and, in the case of PLS, a model that is easier to understand. The attempts to reduce the number of variables for PLS have only resulted in simpler models that fit the Training Set better yet do not have the predictive abilities of the complete PLS model (111). The reduction of latent variables with respect to the descriptors is possible with no apparent decrease in the model s ability to predict bioactivities, yet the remaining descriptor-based variables are considered to be more important before reduction and thus introduces bias (111). 

Rodent models thus provide opportunities to explore the relationship between dopaminergic function, attention and consciousness. Based upon the well designed study of Granon et al. (2000) showing a clear improvement of attentional performance after the infusion of a D1 agonist into the prefrontal cortex, further study of cortical arousal and variability of reaction times in these models may provide important information. The preliminary data indicating that D2 receptor antagonists may increase cortical arousal (Sebban et al., 1999) is contrary to expectation and requires confirmation... 

The mathematical model demonstrates the importance of sample collection (r/T), preconcentration (tjc), concentration (C), and detection (k) in a complete trace portal detection system. Of these three subsystems, the detector is the most understood. Considerable information is available that quantifies the sensitivity, specificity, and limits of detection (LOD) for a particular detection method when used for trace explosives detection [13-15], For trace detection portals, the selection of the detection method is based on performance, initial cost, and maintenance issues. The remaining subsystems (sample collection and preconcentration) are the most variable and least understood for their contribution to trace portal performance. Optimizing the explosive removal and transport in sample collection along with preconcentration will enhance the performance of the entire trace detection system. The sensitivity of the detector will help determine the performance needed from the sample collection and preconcentration. 

Brain endothelial cell culture requires a number of different factors that are supplied by the added serum. Therefore the selection of the adequate serum is of crucial importance in particular in coculture or tri-culture setup. The replacement of serum could be advantageous, and many factors (e.g., cAMP stimulants or glucocorticoids) have been used to supplement tissue culture media to support the tightness of the in vitro BBB without using serum or coculture with other brain cells. For example, a serum-free porcine BBB model based on primary cells using hydrocortisone-supplemented medium [27] has received much attention. However, each cell culture supplement introduces a new variable in a study which renders the interpretation of toxicity results difficult as the supplement may counteract the effects of the chemical on BBB function. 

Variables (measured properties and calculated descriptors) that were shown by these models not to correlate with the property of interest (human jejunal permeability) were dismissed as being of low relative importance, based on the method of variable importance (VIP). 

One way to identify important predictor variables in a multiple regression setting is to do all possible regressions and choose the model based on some criteria, usually the coefficient of determination, adjusted coefficient of determination, or Mallows Cp. With this approach, a few candidate models are identified and then further explored for residual analysis, collinearity diagnostics, leverage analysis, etc. While useful, this method is rarely seen in the literature and cannot be advocated because the method is a dummy-ing down of the modeling process—the method relies too much on blind usage of the computer to solve a problem that should be left up to the modeler to solve. 

An algebraic equation relating the fundamental state variables of a fluid P, V and T is known as an equation of state, abbreviated here by EOS. The simplest EOS is the ideal gas law PV=RT. The models based on equations of state are widespread in simulation because allow a comprehensive computation of both thermodynamic properties and phase equilibrium with a minimum of data. EOS models are applied not only to hydrocarbon mixtures, as traditionally, but also to mixtures containing species of the most various chemical structures, including water and polar components, or even to solutions of polymers. The most important equations of state are presented briefly below, but they will be examined in more detail in other sections. 

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