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Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5571_Библиотеки_им_академика_М_И_Перельмана

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kernel (mostly used in image analysis) and the hyperbolic tangent kernel [318] (that often plays the role of proxy in neural networks).
Once the kernel has been chosen, the best hyperplane to separate the two groups has to be determined. In SVM, the maximum-margin hyperplane is chosen. This hyperplane is the best one with regard to the Vapnik–Chervonenkis theory. This is limiting overfitting (i.e., making a very precise definition of the lea rning sample but losing any ability to generalize to new data), which is a risk when involved with very high dimensional spaces.
A tolerance to misclassifications on either side of the hyperplane has to be introduced since it is rare to have perfectly linearly separable observations. This is performed through the introduction of an error penalty, which is chosen by the user and allows a trade-off between a large margin and a small number of errors. This is called the soft margin. The final optimization issue is a classical one solved by usual optimization algorithms.
Possible Extensions SVM can be extended to classify more than two groups. Generalizing a method designed to classify two groups consists in reducing the multiclass problem into several two-class problems. There are two approaches: the one-versus-one where each group is compared to each other and the one-versus-all comparing each group to the other ones. The former one is the most frequently used. In this approach, each comparison outputs a vote for one class and the majority class is assigned. SVM can also be used to perform regression. SVM principle has been used in several other contexts to perform nonlinear transformations before applying other methods (kernel-PCA, kernel-PLS, etc.).
2.6.4 Decision Trees
2.6.4.1 Aim A decision tree is a simple supervised model, which explains and predicts one response variable (discrete or continuous) taking into account numerous descriptors/features. DTs are based on tree diagrams where leaves or nodes represent classifications and branches represent conjunctions of features that lead to those classifications. DTs correspond to a binary recursive partitioning process since parent nodes are split into two child nodes and recursive because it can be repeated by treating each child node as a parent. The first step of DT is splitting each parent node in two children nodes using some split index, and then deciding when a tree is complete. A splitting rule showing maximal index value is regarded as the best rule among possible splittingrules. Each terminal node of the tree is assigned to a class outcome or predicted value. Pruning can be used to avoid overfitting. Pruning cuts deepest subtrees of the built decision tree according to their potential generalization performance.
Classification tree analysis is possible when the predicted outcome is the class to which the data belong (discrete outcome, e.g., active versus inactive compounds). Regression tree analysis is when the predicted outcome can be considered as a real number (continuous outcome as solubility, permeability values of drugs). Classifi­cation and regression tree (CART) analysis, first introduced by Breiman et al. [319], is used to refer to both the above procedures. Figure 2.32 represents an example of
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a diagram tree to predict molecules of three types Y ¼ (YA, YB, YC) using three descriptors (X
1
, X2, X3). DT creates a branching structure in which the branch at each intersection is determined by a rule relating to one of the three descriptors for the molecules and final leaves are assigned to the dominant type among the observations falling in each leaf. DT is a simple method, easy to understand and interpret.
2.6.4.2 Examples of ADME/Tox Application DT approach has been applied in combinatorial library design, prediction of “drug-likeness” as a general property, prediction of specific biological activities, and on some specific compound profiling.
With discrete outcome, decision trees are used for the identification of substruc­tures that discriminate activity from nonactivity within a given collection of com­pounds [320–323]. DT approach allows to estimate the conditional probability of activity given the combination of substructures present (or absent) in a given collection of compounds while accounting for the abundance of substructures within the library [323]. Once identified, each of these discriminating substructur es are tested statistically for enriched activity and compared to the privileged substructures reported in the literature. DTs are also used for the classification of chemical compounds into drug and nondrugs [111, 324]. In Schneider et al., DT interpretation suggested the main criteria for separating drugs from nondrugs. These were a molecule weight higher than 230 Da, a molar refractivity higher than 40, and the presence of ring(s) as well as one or more functional groups. This approach resulted in at least 39% of the nondrugs filtered out, while retaining more than 83% of the actual drugs.
Figure 2.32 DT example. Diagram tree predict molecules of three types Y ¼ (YA, YB, YC) using three descriptors (X
1
, X2, X3). First discriminant descriptor is X1, related to threshold t1; for
branch X
1
> t1: discriminant descriptor is X2, related to threshold t2, allowing to predict
Y
A(X2
> t2) else YC(X2 t2); for other branch (X1 t1): descriptor X3, related to t3, predict
Y
c(X3
> t3); and else (X3 t3), descriptor X1predict YA(X1> t12), either YB(X1 t12).
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With continuous outcome, decision trees are also used to predict ADME/Tox properties such as absorption properties [317, 325], solubility or permeability of drugs [326], distribution properties [327], P-glycoprotein [328] or BBB penetration [329], and metabolic stability [330]. For toxicity properties, DTs are used to predict hERG inhibition [202] and toxicity involving cytochrome P450 such as six CYP isoforms [331], 2D6 and 1A2 isoforms [193, 312], or the 3A4 isoform [332].
2.6.4.3 Usage Warning The main issue with DT is to choose the “best” appro­priate index to split parent node into two child nodes and to decide when a tree is complete. If the target is a classification outcome, different measures of node impurity for splitting nodes and pruning the tree can be used as misclassification errors. Gini index and cross-entropy or deviance are the most common measures of error [88]. For regression, the squared-error node impurity measure can be used.
The preferred strategy for pruning is to grow a large tree T0, stopping the splitting process only when some minimum node size is reached. The large tree is pruned using cost-complexity pruning. By using five- or ten-fold cross-validation, the subtree (obtained by pruning T0 that is collapsing any number of the internal nodes) is established, which minimizes the cost complexity.
One major problem with trees is their high variance. Often a small change in the data can result in a very different series of splits, complicating the interpretation. This instability is due to the hierarchical nature of the process: the effect of an error in the top split is propagated down to all the splits below.
DTs are valuable even with complex data or with a few observations (pruning). It is an appropriate choice from even a very large set of input descriptors due to the recursive partitioning strategy. It results in a descriptive means for calculating conditional probabilities and does not need any preselection of informative variables. To conclude, decision trees are conceptually simple yet powerful and, easy to understand. Classification scheme can be easily interpretable with the most significant descriptors usually appearing at early decision nodes.
2.6.4.4 Technical Description
Input Data Data come in records of the form (x, y) ¼ (x
1
, x2, x3, ..., xp, y): the
description of n individuals by p descriptors (x
1
, x2, x3, ..., xp) and the vector y of length n containing the data to be predicted (either discrete or any continuous variable).
Output The dependent variable, y, is the target variable to understand, classi fy, or predict. To follow the decision tree (with binary decisions obtained on most significant descriptors) allows assigning one y value to each leaf, indicating either the predicted group or the predicted value of the target variable. DT can describe or predict continuous output or discrete one (for two or more groups).
Description The goal is to create a model that predicts the value of a target variable based on several input variables. Each interior node is split according to a dichot-
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omous decision based on one of the input variables. There are two edges to children for each of the possible types of values of that input variable. Each leaf is assigned a value that is the predicted one for observations following the path leading to this leaf. A tree can be “learned” by splitting the source set into subsets based on an attribute value test.
A decision criterion based on maximal purity results in a mixture of classes in the children nodes that are lower than in the parent node. To construct the tree, the “best” division in term of purity criterion is chosen for the p descriptors x. The descriptor (associated to its best division), which results in the best decision in term of purity criterion among all descriptors, is chosen for the first branching. A splitting rule showing a maximal Gini index value is regarded as the best. This process is repeated on each derived subset or node in a recursive manner and is called recursive partitioning. The recursion is completed when the subset at a node has the same value as the target variable, or when splitting no longer adds value to the predictions. Each node of the tree is assigned to a class outcome or predicted value regression. To avoid excessive partitioning, there exist some techniques of pruning to optimize the tree. The pruning component of CART is analogous to the backward elimination approach in regression analysis. This idea provides a control for tree sizes, thus reducing the prediction error of the tree for new data not seen in the learning process. In the CART pruning process, Breiman et al. [333] use a linear combination of the expected loss of the decisions by the tree and the total number of the terminal nodes of the tree. A new observation follows the tree with a particular path and is affected to the corresponding final node.
Possible Extension The other popular methodology is C5.0, which uses a different scheme for deriving rule sets resulting in simpler trees [334]. A random forest combines many decision trees, in order to improve the classification rate. It is a relatively new technique introduced by Breiman in 2001 [335]. In random forest, training data are randomly selected for replacement from the original training data. The forest chooses the most popular class having most votes over all the trees in the forest.
2.6.5 Neural Networks
2.6.5.1 Aim Neural network (NN) attempts to mimic a network or circuit of biological neurons [336]. Each unit represents a neuron, and the connections represent synapses. The modern usage of the term often refers to artificial neural networks, which are composed of interconnecting artificial neurons or nodes (programming constructs that mimic the properties of biological neurons). NN result in powerful nonlinear statistical models. The central idea of NN is to extract linear combinations of the inputs as derived features, and then model the target as a nonlinear function of these features. An NN is a two-stage regression or classification model, typically represented by a network diagram (Figure 2.33). Derived features Z
m
are created from
linear combinations of the inputs, and then the target Y
q
is modeled as a nonlinear
function of Z
m
, using an activation function. This function performs a linear
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transformation for small coefficients but progressively implies nonlinear transfor­mation when the coefficient values increase. The units in the middle of the networks, computing the derived features Z
m
, are called hidden units because the values Zmare not directly observed. In general there can be more than one hidden layer. The result is a powerful learning method with widespread applications in many fields. It is often difficult to decode the final model to identify the changes to molecular structure needed to obtain a desired property. NNs also have a tendency to “memorize” rather than learn and are particularly susceptible to overfitting, especially if the training data are noisy.
2.6.5.2 Examples of ADME/Tox Applications The application of NNs in the field of ADME/Tox predictions was initiated in the 1990s to predict physicochemical properties of molecules such as aqueous solubility [337] and lipophilicity [338]. In the early 2000s, more sophisticated NN techniques have gradually emerged and been applied to this area [339]. With discrete outcome, filter programs have been established that use large databases of drug and nondrugs [111, 340]. These programs used NN approaches together with topological descriptors to encode the molecular structures.In these papers, the NN classificationmethod has been found to discriminate between drug-like chemical matter (represented by databases such as CMC, MDDR, WDI) and nondrug-like chemical matter (represented by dataset such as ACD). The result was 80–90% of the compounds were correctly classified as drugs or nondrugs.
With continuous outcome, NNs are used for prediction of lipophilicity and aqueous solubility of chemical compounds [341]. The ALOGPS 2.1 package, based on associative neural networks, combines k-nearest-neighbor and ANN methods on several datasets to careful ly analyze the associative neural network parameters. The predictive ability of associative neural network for the training sets was estimated using the leave-one-out method.
For ADME/Tox properties, NN have been used to predict solubility, distribu­tion [327], P-glycoprotein [183], for QSAR modeling of human serum protein binding [342], or absorption [343, 344]. For Toxicity properties, NN have been
Figure 2.33 Left: Schematic representation of a single hidden layer, feed-forward neural network. Right: The sigmoid function, the red zone shows that for x values near from 0, the sigmoid function is approximately linear.
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used to predict P450 1A2 inhib ition [312], P450 2D6 [345], P450 3A4 inhibi­tion [346, 347], and to predict whenever a compound might be cytotoxic [348].
2.6.5.3 Usage Warning Training neural networks is quite an art. As NNs are iterative processes, initialization of the coefficients is required. Usually, small coefficients are initially provided leading to a model that is not far from the linear one. It aims at providing a simple model that is not overfitting the training data. More complex transformations are derived during the training process if regularization is well controlled. In order to facilitate the coefficient initialization, a prior scaling of inputs (leading to zero mean and unit variance) is recommended (see PCA for more details about data scaling). In addition, the objective function often possesses many local minima. Different initializations can lead to different solutions. Several initial parameter sets to obtain a more reliable final solution should be attempted.
The number of hidden layers and of units generally has to be provided by the user. With too few hidden units, the model might not have enough flexibility to capture the nonlinearities in the data. Too many hidden layers are likely to produce overfitting models. However if regularization is well controlled, useless layers will simply reproduce the results obtained in the previous ones. Choosing a high number of hidden layers should not be a problem if the required work on regularization has been performed (see Section 2.6.5.4 for more details). Typically the number of hidden units is in the range of 5–100, with the number increasing with the number of inputs and number of training cases. Choice of the number of hidden layers is guided by background knowledge and experimentation.
Finally, neural networks are complex models but they are likely to be very efficient if well tuned. The model is generally overparameterized, and the optimization problem is nonconvex and unstable unless certain guidelines are followed. Similar to SVMs, NN models cannot be interpreted in terms of relationships between input and output variables.
These tools are especially effective in problems with a high signal-to-noise ratio and settings where prediction without interpretation is the goal. They are not effective to describe a process and the roles of individual inputs. Each input enters the model in many places in a nonlinear fashion.
2.6.5.4 Technical Description
Input Data This method is based on the description of n individuals by p descriptors collected in a matrix having n rows and p columns, called X, and of the values of q response variables measured on the same n individuals and collected in Y.
Output The predicted values of Y are provided. The final coefficients applied to each input variable and internal node are generally given.
Description NNs are a wide category of methods aiming at performing nonlinear regression and classification. In general, they tend to imitate biological neurons behavior. Simple units receive information and produce other information in order to achieve a given goal.
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Figure 2.33 outlines the main features of a very simple NN. Input variables are combined in one layer of hidden units via linear combinations. Inside these hidden nodes, an activation function is applied to the result of the linear combination producing one value. This activation function is typically a sigmoid one (or sometimes radical basis function). As shown in Figure 2.33 (right), the sigmoid function is approximately linear at approximately zero. If the norm of the vectors containing the coefficients applied in the linear combination is not far from zero (i.e., if all the coefficients are small), the corresponding hidden unit can be considered as only performing linear transformation. To the contrary, higher coefficients imply a nonlinear transformation. The values provided by the hidden layers are linearly combined in each output variable and the obtained value is transformed by the output function. This function is usually the identity function for regression (the value remains unchanged) and the softmax function for classification (allowing one to obtain a probability for each class). There may be several hidden layers performing successive transformations.
In order to train a neural network an objective function is required. For regression, the sum of squared differences between the true and predicted values is used. The same method can be applied in classification as well as other functions such as cross­entropy (which measures the quantity of disagreement between true and predicted values). In order to minimize these objective functions, back propagation (also called gradient descent) is used. It consists in adapting the coefficients applied to each hidden unit (to obtain the output values) according to their contribution to the global error. It is possible to propagate these contributions to the linear combinations implying the input variables and to perform similar coefficient corrections. This process is repeated until convergence (there are no more changes in the coefficients) or a user-defined maximum number of iterations is reached. In this correction step, a penalty is applied to control regularization (the ability to generalize to new observations). This consists in penalizing high coefficients, which lead to highly nonlinear functions and thus to potential overfitting. This tuning parameter is often chosen through cross-validation.
Possible Extensions Many extensions have been proposed. They generally rely on changes concerning topology of connections between units (cycles can be allowed), using combination functions (weighted linear combinations, for example), activation and output functions, and learning algorithm.
2.7 CONCLUSIONS
In summary, although many currently developed molecules tend to challenge known rules, the alliance of medicinal chemistry and drug-metabolism pharmacokinetics­ADME/Tox has made a substantial impact on quality of drug candidates [125]. As new regions of the chemical space are explored, there will be a need to continue to explore the boundaries of the drug-like chemical space in order to be able to rationally design and balance the physicochemical properties of a drug candidate. Here, in silico tools greatly assist the decision-making process [198, 349, 350]. A major challenge is
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to forge a comparable partnership with preclinical pharmacology such that concen­tration–effect relationships equal the pharmacokinetic structure–activity relation­ships in lead optimization. Many other obstacles await such as designing better drugs for children and the elderly using ADME/Tox issues [351–353] and better assessment of interindividual variability [354, 355]. Pharmacogenomics, genotyping, toxicoge­nomics, proteomics, metabonimics and metabolomics, chemogenomics, structural biology, chemical systems biology, mapping adverse drug reactions in chemical space, integration and annot ation of the data, merging chemical and biological space, generation of drug–target networks, new algorithms, will all play a key role in understanding drug responses in different patients relative to their genetic constitution and in improving the predictive character of in silico methods [151, 356–362]. New experimental approaches and computer technologies will contribute to this process [67, 191, 363]. Better understanding of serious adverse drug reactions (SADRs) already allows for the development of the web-hosted tool such as SePreSA [364] http://sepresa.bio-x.cn/. SADRs are caused by unexpected drug–human protein interactions, and some polymorphisms within binding pockets make these popula­tions more susceptible to drug attack (e.g., Vioxx, 2004 or Avandia, 2007). While automating every modeling task, it will be important to not transform the in silico processes into black boxes. Ultimately, new predictive methods will be developed in the coming years integrating new experimental data and theoretical concepts. Mutations or single nucleotide polymorphisms in drug-metabolizing enzymes and for other ADME/Tox involved proteins, age, pathology-dependent variations will be considered. From a patient and clinician perspective, it is imperative that new predictive methods are pursued to administer inherently less toxic drugs coupled to the identification of genetically susceptible patient groups. All these will take time and require important financial investment. Further, this should be accomplished while limiting as much as possible animal experimentations. We do hope that this chapter provides the readers with a global picture of different concepts currently used or emerging in the field of in silico ADME/Toxpredictions. Definitively, this area will remain a challenge for at least the next 20–50 years.
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