Extrapolations from QSAR

One of the major problems that arises with some QSAR studies is extrapolation from beyond spanned space. Predictive ability is sound when one has probed an adequate range in electronic, hydrophobic, and steric space. At the onset of the study, the training set should address these concerns. Lack of adequate attention to such issues can result in QSAR... 

The similarity in the sensitivity distributions derived from QSAR and experimental acute toxicity data results in only minor differences in the extrapolated phenol toxicity values for the most sensitive species about 4 mg/1 from the experimental data and 4.6 mg/1 from the QSAR estimates. 

Babich et al. (1986) described the relationship between the toxicity of 9 cations and a 50% reduction in uptake of neutral red dye by fish cell cultures. A QSAR was extrapolated from Figure 6 of Babich et al. (1986) (Table 5.1). Their fish cultures were BF-2 cells, an established fibroblastic cell line derived from the caudal fin of the blue-gill (Lepomis macrochirus). The 9 cations used to develop the Babich et al. (1986) QSAR are listed in Table 5.15. 

Extent of Extrapolation For a regression-like QSAR, a simple measure of a chemical being too far from the applicability domain of the model is its leverage, hi [36], which is defined as... 

The validity of a model is always limited to a certain domain in the parameter space. For example, if a quantitative structure-activity relationships (QSAR) model is specified for nonpolar organic chemicals in the log range from 2 to 6 and has a molecular weight below 700, then an application to substances outside this range is an improper extrapolation. Note that the parameter space may be difficult to discern for example, combinations of low values for one variable and high values for another could constitute an extrapolation if such combinations had been missing in the validation or specification of the model. Exceedence of model boundaries introduces additional uncertainty at best, but can also lead to completely incorrect outcomes. 

One of the most important problems in QSAR analysis is establishing the domain of applicability for each model. In the absence of the applicability domain restriction, each model can formally predict the activity of any compound, even with a completely different structure from those included in the training set. Thus, the absence of the model applicability domain as a mandatory component of any QSAR model would lead to the unjustified extrapolation of the model in the chemistry space and, as a result, a high likelihood of inaccurate predictions. In our research we have always paid particular attention to this issue (12, 20-27). A good overview of commonly used applicability domain definitions can be found in reference (28). 

The idea is to take apart some molecules of known activity from the dataset set to confront later the generated model with different compounds to those of the training set . In theory, this method brings an answer to the question, Can we extrapolate the predictions of the model to other different moleculesT and it is certainly legitimate that one asks this question if the model is to be further exploited. For 3D-QSAR models, a statistical metric (often termed tj,ref) similar to r2 [see Eq. (3.3)] can be calculated. 

The problem is that all these features are present or absent together. For this reason, the results of the QSAR analysis will assign the same importance to all these features and if only one of them is relevant for the activity, no model would be able to distinguish this single feature from the others, since all are present or absent simultaneously in the tested compounds. However, if these results are extrapolated to external compounds, in which maybe only some of the features are present, the predictions will be wrong. 

A9.6.3.1 Choosing an appropriate QSAR implies that the model will yield a reliable prediction for the toxicity or biological activity of an untested chemical. Generally speaking, reliability decreases with increasing complexity of chemical structure, unless a QSAR has been derived for a narrowly defined set of chemicals similar in structure to the candidate substance. QSAR models derived from narrowly defined classes of chemicals are commonly employed in the development of pharmaceuticals once a new lead compound is identified and there is a need to make minor structural modifications to optimize activity (and decrease toxicity). Overall, the objective is make estimates by interpolation rather than extrapolation. 

The first approach to applicability domain evaluation is the statistical analysis of the training set, trying to define the best conditions for interpolated prediction that is usually more reliable than extrapolation. Extrapolation is not a problem in principle, because extrapolated results from theoretically well-founded models can often be reliable. However, QSAR/QSPR models are usually based on empirical, and limited experimental evidence and/or are only locally valid therefore, extrapolation usually results in high uncertainty and not reliable predictions. 

Molar volume can be measured by determination of density of dilute solutions with extrapolation to infinite dilution or by estimation, using the neat liquid density. Edward has presented excellent data for alkanes. Hall and Kier have shown that these data, plus six compounds added by Edward (taken from Longworth), lead to the following QSAR relation ... 

The importance of QSAR in the prediction and design of biologically active compounds is now well recognized. There are quite a number of methods intended to determine QSAR. All of them are based on the concepts that there is a direct correlation between the molecular structure of the chemicals and their biological activity and that the QSAR obtained from a given set of compounds with known activity can be extrapolated to new compounds. 

Quantitative Structure-Activity Relationships (QSAR) express the biological potencies of a series of related compounds as a linear function of their physicochemical properties. A major reason for deriving a QSAR hypothesis is the hope that some aspect of the QSAR can be successfully extrapolated, to produce compounds of potency higher than any of those from which the QSAR was derived. Unfortunately, the QSAR literature does not contain many examples of successful extrapolation, or "predictive successes."(i) Even these few examples would be vulnerable to the following criticisms ... 

As stated, currently available QSARs are available only for permeabihty coefficients from aqueous vehicles. This limits their usefulness in terms of the assessment of mixtures and the like. Currently, little is known about the quantitative effect of penetration enhancers, formulations, and different solvents (Moss et al., 2002). This means that predictions from aqueous vehicles cannot be extrapolated to predict the effects of other solvents or formulations. This is a severe limitation in the applicability of QSARs in skin permeabihty. 

The differences in sensitivity of organisms and test systems, although a possible complication for interspecies extrapolations, do not affect the reliability of these correlations. Much more critical are the actual limitations of their validity stemming from the different modes of toxic action of environmental contaminants in various species. Chemicals (e.g. herbicides and AChE inhibitors) that have different toxicity mechanisms in fish and algae, respectively (Figure 8.4), reveal distinct QSARs the interspecies correlations thus break down (e.g. Gehring and Rao, 1977 Smissaert and Jansen, 1984 Wallace and Niemi, 1988 Nendza and Wenzel, 1993). 

For chemicals acting by a uniform mode in different organisms (e.g. nonspecific toxicants), interspecies extrapolations (Chapter 8) are a further means of obtaining toxicity data for environmental risk assessments. When experimental results are unavailable, they can be used with QSARs to fill data gaps. Biologists may prefer interspecies extrapolations, as they proceed from real (i.e. experimental) data. For mathematicians, chemists and statisticians, QSARs may be more reliable, as their input parameters, chemical structures and physico-chemical properties are usually considered to be subject to much less variability as compared to biological data. In practice, there mostly remains only the pragmatic point of view all available information should be collected, scrutinized expertly, and then used (or rejected) for hazard and risk assessments. 

In the final stage of the QSAR process, the activity of a drug candidate can be estimated from its molecular descriptors and the QSAR equation either by interpolation or extrapolation of the data. The predictions are more reliable when a large number of lead compounds and molecular descriptors are used to generate the QSAR equation. 

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