Statistically sound model

Models can be generated using stepwise addition multiple linear regression as the descriptor selection criterion. Leaps-and-bounds regression [10] and simulated annealing (ANNUN) can be used to find a subset of descriptors that yield a statistically sound model. The best descriptor subset found with multiple linear regression can also be used to build a computational neural network model. The root mean square (rms) errors and the predictive power of the neural network model are usually improved due to the higher number of adjustable parameters and nonlinear behavior of the computational neural network model. 

Cronin and Schultz have in a recent article [14] quite nicely put forward some rather basic requirements to derive statistically sound models ... 

In this section, methods are described for obtaining a quantitative mathematical representation of the entire reaction-rate surface. In many cases these models will be entirely empirical, bearing no direct relationship to the underlying physical phenomena generating the data. An excellent empirical representation of the data will be obtained, however, since the data are statistically sound. In other cases, these empirical models will describe the characteristic shape of the kinetic surface and thus will provide suggestions about the nature of the reaction mechanism. For example, the empirical model may require a given reaction order or a maximum in the rate surface, each of which can eliminate broad classes of reaction mechanisms. 

Next, they applied the stepwise MLR to the training set providing TPSA, LA, and MW as the descriptors so as to take into account hydroaffinity, lipoaffinity, and molecular size effects. However, the calculation failed to generate a statistically sound linear equation using all three descriptors. Instead the following linear model was generated (Eq. 42) which was comparable to Clark s Eq. 31 ... 

The model includes the well-understood descriptor logP and a descriptor based on atomic charge (ATCH4), which is also readily interpretable. However, it also contains the hard-to-interpret descriptors ESDL3 and PEAX X. Thus, although the model is statistically sound, it does not promise to engage the chemist s imagination. 

This chapter will try to answer some of these questions and investigate various approaches to derive statistically sound, robust, and predictive in silico models. 

This section attempts to present some of the most common statistical techniques used today to derive statistically sound structure-activity or structure-property models with good predictive ability. 

The establishment of a statistically sound data-set on usage allows an evaluation of likely operator exposure, as realistic work rates can be derived from the data collected, such as average field size, area sprayed per operator per day, amount of pesticide handled per day, etc. All of these factors are vital in refining predicted operator exposure models, and are discussed at length by Hamey (2001). 

This chapter describes some of the approaches and techniques used currently to derive in silico models for the prediction of absorption, distribution, metabolism, elimination/excretion, and toxicity (ADMET) properties. The chapter also discusses some of the fundamental requirements for deriving statistically sound and predictive ADMET relationships as well as some of the pitfalls and problems encountered during these investigations. It is the intention of the authors to make the reader aware of some of the challenges involved in deriving useful in silico ADMET models for drug development. 

The system constants in Eqs. (1.6) and (1.7) are obtained by multiple linear regression analysis for a number of solute property determinations for solutes with known descriptors. The solutes used should be sufficient in number and variety to establish the statistical and chemical validity of the model [72-74]. In particular, there should be an absence of significant cross-correlation among the descriptors, clustering of either descriptor or dependent variable values should be avoided, and an exhaustive fit should be obtained. Table 1.4 illustrates part of a typical output. The overall correlation coefficient, standard error in the estimate, Fischer F-statistic, and the standard deviation in the individual system constants are used to judge whether the results are statistically sound. An exhaustive fit is obtained when small groups of solutes selected at random can be deleted from the model with minimal change in the system constants. 

Gaussian process modelling works by a similar functional transformation of the data and has also begun to be deployed by QSAR practitioners. It is thought to be particularly good at building models with little expert supervision, because it allows statistically sound alternatives to both model discovery and validation, therefore is well suited to automated QSAR model discovery and updating. 

Based on damage data from the field, it is feasible, by means of statistical distribution models, to describe product failure in a statistically sound way. The state of the art in industry is the application of WeibuU distribution models (Pfeifer, T. 2002). Using the WeibuU distribution function Fwd(1), cf equation (1), and the WeibuU density functionywo(t)> cf- equation (2), it is feasible to form the failure rate function X(t), cf. equation (3). The parameters are to (failure-free time), T (characteristic life time) and b (form parameter). The use of WeibuU distribution models allows to describe simple product failures and to inden-tify different damage phases or behaviors in a product Ufe cycle (Birolini, A. 2007). 

Using QSAR-methodology on basis GUSAR program statistically sound and thoroughly validated consensus model for thymidylate synthetase inhibitors, that are quinazoline derivatives, is obtained. The six parametric model has following statistical characteristics N=30, R2=0.926, F=34.093, SD=0.247, Q2=0.884, V=6. It was... 

As with troubleshooting, parameter estimation is not an exact science. The facade of statistical and mathematical routines coupled with sophisticated simulation models masks the underlying uncertainties in the measurements and the models. It must be understood that the resultant parameter values embody all of the uncertainties in the measurements, underlying database, and the model. The impact of these uncertainties can be minimized by exercising sound engineering judgment founded upon a famiharity with unit operation and engineering fundamentals. 

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