Validation of QSAR Models - Strategies and Importance

Transcription

1 Ravichandran Veerasamy, et al : Validation of QSAR Models-Strategies and Importance 511 International Journal of Drug Design and Discovery Volume Issue 3 July September Validation of QSAR Models - Strategies and Importance Ravichandran Veerasamy 1*, Harish Rajak, Abhishek Jain 3, Shalini Sivadasan 1, Christapher P. Varghese 1 and Ram Kishore Agrawal 3 1 Faculty of Pharmacy, AIMST University, Semeling 08100, Kedah, Malaysia. Institute of Pharmaceutical Sciences, Guru Ghasidas University, Bilaspur (CG), India. 3 Department of Pharmaceutical Sciences, Dr. H. S. Gour University, Sagar, India ABSTRACT: Quantitative Structure-Activity Relationship (QSAR) is based on the hypothesis that changes in molecular structure reflect changes in the observed response or biological activity. The success of any quantitative structure activity relationship model depends on the accuracy of the input data, selection of appropriate descriptors, statistical tools and the validation of the developed model. Validation is a crucial aspect of QSAR modeling. Validation is the process by which the reliability and significance of a procedure are established for a specific purpose. Hence in this review we focus on the importance of validation of QSAR models and different methods of validation. KEYWORDS: QSAR; Internal validation; External validation; Randomization. Introduction A variety of in vitro and computational methods are being proposed for the toxicological assessment of chemicals owing to the increasing requirement for alternative methods to in vivo toxicity testing. More efforts will be given to include methods such as in vitro techniques and Quantitative Structure-Activity Relationship (QSAR) models in the regulatory decision-making process in Europe 1, under the new registration, evaluation, and authorization of chemicals (REACH) system 3. For reasons of practicality, cost effectiveness and animal welfare, it is envisaged that QSAR will play an important role in the assessment of existing chemicals for which further information may be required under the REACH system. Therefore, it will be essential that the QSAR models used will produce reliable estimates. QSAR is a widely accepted predictive and diagnostic process used for finding associations between chemical structures and biological activity. QSAR has emerged and has evolved trying to fulfill the medicinal chemist s need and desire to predict biological response 4. The quantitative structure-activity relationship paradigm first found its way into the practice of agro chemistry, pharmaceutical * For correspondence: Tel.: Ext. 109; Fax: phravi75@rediffmail.com chemistry, toxicology, and eventually most facets of chemistry. The overall goals of QSAR retain their original essence and remain focused on the predictive ability of the approach and its receptiveness to mechanistic interpretation. QSAR includes all statistical methods, by which biological activities (most often expressed by logarithms of equipotent molar activities) are related with structural elements (Free Wilson analysis), physicochemical properties (Hansch analysis), or fields (threedimensional QSAR). It is a technique that quantifies the relationship between structure and biological data and is useful for optimizing the groups that modulate the potency of the molecule 5. There are different types of computational methods in QSAR depends upon the data complexity. Those are twodimensional (D), three-dimensional (3D) and higher dimensional methods 6. D-QSAR is insensitive to the conformational arrangements of atoms in space, while 3D- QSAR needs information on the position of the atoms in three spatial dimensions 7. In 4D-QSAR for each molecule, a set of automatically docked orientations and conformations are developed by genetic algorithms 8-1. Induced-fit scenarios of ligands upon binding to the active site and solvation models can be thought of as the fifth (protein flexibility) and sixth (entropy) dimensions in 5Dand 6D-QSAR, respectively. 511

2 51 International Journal of Drug Design and Discovery Volume Issue 3 July September 011 The process of QSAR model development can be generally divided into three stages: data preparation, data analysis and model validation (Scheme 1). These steps represent a standard practice of any QSAR modeling and their implementations are often determined by the researcher s interests, experience and software availability. Acquiring a good quality QSAR model depends on many factors, such as the quality of biological data, the choice of descriptors, variable selection, statistical methods and validation Validation is a crucial aspect of any QSAR modeling. It is the process by which the reliability and relevance of a procedure are established for a specific purpose 19. Formal validation is one of the most overlooked steps in the model development at many times. In the QSAR community, the validation of a model is little more than an assessment of statistical fit and, occasionally, predictivity using crossvalidation techniques. However, it is now being accepted that validation is a more important process that includes assessment of issues such as data quality, applicability of the model and mechanistic interpretability in addition to statistical assessment 0. In this review, we discussed about the validation parameters for the QSAR models which are developed by multiple linear regression (MLR) and partial least square regression (PLS). Scheme 1 Various stages of QSAR model development

3 Ravichandran Veerasamy, et al : Validation of QSAR Models-Strategies and Importance 513 Importance of validation of QSAR models The QSAR models are useful for various purposes including the prediction of activities of untested chemicals. The success of drug discovery efforts depends heavily on the use of structure-activity relationship techniques 1. Over the years of development, many methods, algorithms and techniques have been discovered and applied in QSAR studies. Main challenge in QSAR is to select the group of descriptors which describe the most critical structural and physicochemical features associated with activity. Quality of biological data and effective descriptor or variable selection is an initial essential part of the QSAR modeling process 3. The application of QSAR models is depends on statistical significance and predictive ability of these models. The regulatory decisions, justification of usage and use of a particular QSAR model is depend on the model ability to predict unknown chemicals with some known degree of certainity 18,4. QSAR model can lead to false prediction of biological activity if the developed QSAR model is not validated. So validation of QSAR models, after model development, is most important part in QSAR studies. QSAR has clearly matured, although it still has a way to go. The estimation of accuracy of predictions is a critical problem in QSAR modeling 5. Only in this decade, validation of QSAR models has received considerable attention 14-17, Four tools of assessing validity of QSAR models 35 are (i) cross-validation, (ii) bootstrapping, (iii) randomization of the response data, and (iv) external validation. Several principles for assessing the validity of QSAR models were proposed at an International workshop held in Setubal (Portugal), which were subsequently modified in 004 by the OECD Work Programme on QSARs 1,3. Against this background, in this review we have discussed about the different validation methods of QSAR models. Validation Methods for QSAR Models Validation methods are needed to establish the predictiveness of a model on unseen data and to help determine the complexity of an equation that the amount of data justifies. Using the data that created the model (an internal method) or using a separate data set (an external method) can help validate the QSAR model (Scheme ). The methods of least squares fit (R ), crossvalidation (Q ) 36-38, adjusted R (R adj), chi-squared test ( ), rootmean-squared error (RMSE), bootstrapping and scrambling (Y-Randomization) 39,40 are internal methods of validating a model. The best method of validating a model is an external method, such as evaluating the QSAR model on a test set of compounds. These are statistical methodologies used to ensure the models created are sound and unbiased ( good model ). A poor model can do more harm than good, thus confirming the model as a good model is of utmost importance. Scheme Various stages of QSAR model validation

4 514 International Journal of Drug Design and Discovery Volume Issue 3 July September 011 Internal Validation Least Squares Fit The most common internal method of validating the model is least squares fitting. This method of validation is similar to linear regression and is the R (squared correlation coefficient) for the comparison between the predicted and experimental activities. An improved method of determining R is the robust straight line fit, where data points are away from the central data points (essentially data points a specified standard deviation away from the model) are given less weight when calculating the R. An alternative to this method is the removal of outliers (compounds from the training set) from the dataset in an attempt to optimize the QSAR model and is only valid if strict statistical rules are followed. The difference between the R and R adj value is less than 0.3 indicates that the number of descriptors involved in the QSAR model is acceptable. The number of descriptors is not acceptable if the difference is more than 0.3. R = Fit of the Model NXY ( x) ( Y) ([NX ( X) ] [NY ( Y) ]) Fit of the QSAR models can be determined by the methods of chi-squared ( ) and root-mean squared error (RMSE). These methods are used to decide if the model possesses the predictive quality reflected in the R. The use of RMSE shows the error between the mean of the experimental values and predicted activities. The chi squared value exhibits the difference between the experimental and predicted bioactivities: n (y i y ˆ i) = i1 ŷ n RMSE = Sqrt i1 i (y ˆ i y m) n1 Where, y and ŷ are the experimental and predicted bioactivity for an individual compound in the training set, y m is the mean of the experimental bioactivities, and n is the number of molecules in the set of data being examined. Large chi-square or RMSE values ( 0.5 and 1.0, respectively) reflect the model s poor ability to accurately predict the bioactivities even the model is having large R value ( 0.7). For good predictive model the chi and RMSE values should be low (<0.5 and <0.3, respectively). These methods of error checking can also be used to aid in creating models and are especially useful in creating and validating models for nonlinear data sets, such as those created with Artificial Neural Network (ANN) 41. However, excellent values of R, and RMSE are not sufficient indicators of model validity. Thus, alternative parameters must be provided to indicate the predictive ability of models. In principle, two reasonable approaches of validation can be envisaged one based on prediction and the other based on the fit of the predictor variables to rearranged response variables. Cross-validation A common method for internally validating a QSAR model is cross-validation (CV, Q, q, or jack-knifing). CV process repeats the regression many times on subsets of data. Usually each molecule is left out once (only), in turn, and the R is computed using the predicted values of the missing molecule. Sometimes more than one molecule (leave many out, LMO) is left out at a time. CV is often used to determine how large a model can be used for a given data set. A cross-validated R is usually smaller than the overall R for a QSAR equation. It is used as a diagnostic tool to evaluate the predictive power of an equation. CV used to measure a model s predictive ability and draw attention to the possibility a model has been overfitted. Over-fitting refers to the phenomenon in which a predictive model may well describe the relationship between predictors and response, but may subsequently fail to provide valid predictions for new compounds. Overfitting of the model is usually suspected when the R value from the original model is significantly larger (5%) than the Q value (Difference between R and Q should not be more than 0.3) 36. CV values are considered more characteristic of the predictive ability of the model. Thus, CV is considered a measure of goodness of prediction and not fit in the case of R. The process of CV begins with the removal of one or a group of compounds, which becomes a temporary test set, from the training set. A CV model is created from the remaining data points using the descriptors from the original model, and tested on the removed molecules for its ability to correctly predict the bioactivities. In the leave-one-out (LOO) method of CV, the process of removing a molecule, and creating and validating the model against the individual molecules is performed for the entire training set. Once complete, the mean is taken of all the Q values and reported. The data utilized in obtaining Q is an augmented training set of the compounds (data points) used to determine R. The method of removing one molecule from the training set is considered to be an inconsistent method 37,38. A more correct method is leave-many-out (LMO), where a group of compounds is selected for validation of the CV model. This method of cross-validation is especially useful if the training set used to create the model is small ( 0

5 Ravichandran Veerasamy, et al : Validation of QSAR Models-Strategies and Importance 515 compounds) or if there is no test set. For good predictability R Q value should not exceed 0.3. The equation for CV is Q PRESS = 1 N (y y ) i1 i m PRESS = N (y pred,i y i ) i1 where the y i is the data value(s) not used to construct the CV model. PRESS is the predictive residual sum of the squares. Beware of Q To validate a QSAR model, most of researchers apply the LOO or LMO CV procedures. The outcome from this procedure is a cross-validated correlation coefficient R (Q ). Frequently, Q is used as a criterion of both robustness and predictive ability of the model. Many authors consider high Q (for instance, Q > 0.5) as an indicator or even as the ultimate proof of the high predictive power of, the QSAR model. They do not test the models for their ability to predict the activity of compounds of an external test set (i.e., compounds that have not been used in the QSAR model development). There are several examples of recent publications, in which the authors claim that their models have high predictive ability without validating them by use of an external test set Some authors validate their models by the use of only one or two compounds that were not used in QSAR model development 47,48 and still claim that their models are highly predictive. However, it has been found that if a test set with known values of biological activities is available for prediction, no correlation may exist between the predicted and observed activities for the test set 49,14. Bootstrapping Bootstrapping is another method of internal validation where samples are selected randomly from the data set. In the simplest form of bootstrapping, instead of repeatedly analyzing subsets of the data, sub samples of the data are repeatedly analyzed. Each sub sample is a random sample with replacement from the full sample. In a typical bootstrap validation, K groups of size n are generated by a repeated random selection of n objects from the original data set. Some of these objects can be included in the same random sample several times, whereas other objects may never be selected. The model obtained from n randomly selected objects is used to predict the target properties for the excluded samples. A high average Q in the bootstrap validation is a demonstration of the model robustness. Randomization test (Scrambling model) The predictive power of the equation is poor when the observations are not sufficiently independent of each other. One way to test for this is by randomization of the dependent variables. This procedure ensures that the model is not due to a chance. The set of activity values is reassigned randomly to different molecules, and repeating the entire modeling procedure. This process is repeated many times. If the random models activity prediction is comparable to the original equation, the set of observations is not sufficient to support the model. The creation of a Scrambled Model 39,40 is a unique method of checking the descriptors used in the model because the bioactivities are randomized ensuring the new model is created from a bogus data set. The basis for this method is to test the validity of the original QSAR model and to ensure that the selected descriptors are appropriate. These new models (Scram-models) are created using the same descriptors as the original model, yet the bioactivities are changed. After each Scram-model is created, validation is performed using the methods mentioned earlier. To ensure that the Scram-models are truly random, the process of changing the bioactivities can be repeated and as each new Scram-model is created its R and Q values. Each time the R and Q values of the Scram-models are substantially lower further enforces that the true QSAR model is sound. The basis of using this method is to validate the original QSAR model because the Scrammodels are created using the original descriptors and bogus bioactivities. The model would be in question if there was a strong correlation (R > 0.50) 50 between the randomized bioactivities and the predicted bioactivities, specifically that the model is not responsive to the bioactivities. External validation Several authors have suggested that the only way to estimate the true predictive power of a QSAR model is to compare the predicted and observed activities of an (sufficiently large) external test set of compounds that were not used in the model development 49,50, The problem in external validation is how can we select the training and test set? Roy et al. clearly discussed that how we can solve this problem in one of their article. To estimate the predictive power of a QSAR model, Golbraikh and Tropsha recommended use of the following statistical characteristics of the test set 14 : (i) correlation coefficient R between the predicted and observed activities; (ii) coefficients of determination (R ) [54] (predicted vs. observed activities r 0, and observed vs. predicted activities r 0 '); (iii) slopes k and k' of the regression lines through the origin. They consider a QSAR

6 516 International Journal of Drug Design and Discovery Volume Issue 3 July September 011 model is predictive, if the following conditions are satisfied 14 : R pred > 0.6, r r 0 / r < 0.1, r, r 0 / r < 0.1 and 0.85 < k < 1.15 or 0.85 < k < The predictive ability of the selected model was also confirmed by external R pred. A value of R pred is greater than 0.6 may be taken as an indicator of good external predictability. test i1 Pr ed test R 1 i1 (y y ) exp exp pred (y y ) Where y tr is the average value for the dependent variable for the training set. The lack of the correlation between Q and R was noted in, Kubinyi et al. 49, Novellino et al. 51, Norinder 5, and Golbraikh and Tropsha 14, publication, where they demonstrated that all of the above-mentioned criteria are necessary to adequately assess the predictive ability of a QSAR model. Norinder suggest 5 that the external test set must contain at least five compounds, representing the whole range of both descriptor and activities of compounds included into the training set. Recently the use of internal versus external validation has been a matter of great debate 55. One group of QSAR workers supports internal validation, while the other group considers that internal validation is not a sufficient test for checking robustness of the models and external validation must be done. Hawkins et al., the major group of supporters of internal validation, are of the opinion that cross-validation is able to assess the model fit and to check whether the predictions will carry over to fresh data not used in the model fitting exercise. They have argued that when the sample size is small, holding a portion of it back for testing is wasteful and it is much better to use computationally more burdensome leave-one-out crossvalidation 56,57. Recent term to check the external predictability of the selected model is r m, which was proposed by Roy and Paul (008) [58] and it was calculated by the following formula m 0 r r 1 r r Where r is squared correlation coefficient between observed and predicted values and r 0 is squared correlation coefficient between observed and predicted tr values with intercept value set to zero. A value of r m is greater than 0.5 may be taken as an indicator of good external predictability. Unlike external validation parameters (R pred etc.), the r m (overall) statistic is not based only on limited number of test set compounds. It includes prediction for both test set and training set (using LOO predictions) compounds. Thus, this statistic is based on prediction of comparably large number of compounds. The r m (overall) statistic may be advantageous when the test set size is considerably small and regression based external validation parameter may be less reliable and highly dependent on individual test set observations. The r m (overall) statistic may be used for selection of the best predictive models from among comparable models are obtained, where some models show comparatively better internal validation parameters and some other models show comparatively superior external validation parameters. Other validation parameter named as R p to check the acceptability of the selected model has been reported by Roy (007) 55. The parameter R p, which penalize the model R for the difference between squared mean correlation coefficient (R r) of the randomized models and squared correlation coefficient (R ) of the non-randomized model. A value of R p should be greater than 0.5 may be taken as an indicator of model acceptability. R R * 1 R R p r The value of r m (overall) determines whether the range of predicted activity values for the whole dataset of molecules are really close to the observed activity or not (best predictive model or not). The value of R p, on the divergent, determines whether the model obtained is really robust or obtained as a result of chance only. Hence it can be inferred that a QSAR model can be considered acceptable if the values of r m (overall) and R p are equal to or above 0.5 (or at least near 0.5). The selection of robust and well predictive QSAR models on the basis of R, Q and R pred may mislead the search for the ideally predictive model so it may also be done on the basis of few other parameters, such as R CVext, r - r 0 / r, r - r 0 / r, k, k, r m (overall) and R p. When can we accept the developed QSAR model as reliable and predictive one? A developed QSAR model can be accepted generally in QSAR (MLR and PLS) studies when it can satisfy the following criterion (The following values are the minimum recommended values for significant QSAR model

7 Ravichandran Veerasamy, et al : Validation of QSAR Models-Strategies and Importance 517 meanwhile these evaluation measures are depend on the response measure scale or measure unit): If correlation coefficient R 0.8 (for in vivo data). If coefficient of determination R 0.6 If the standard deviation s is not much larger than standard deviation of the biological data. If its F value indicate that overall significance level is better than 95%. If its confidence interval of all individual regression coefficients proves that they are justified at the 95% significance level. If cross-validated R (Q ) > 0.5 If R for external test set, R pred > 0.6 Randomized R value should be as low as to R. Randomized Q value should be as low as to Q. (r r 0)/r < 0.1 and 0.85 < = k < = 1.15, or (r r' 0) / r < 0.1 and 0.85 < = k' < = 1.15 (for test set). r m (overall) and R p are 0.5 (or at least near 0.5). In addition, the biological data should cover a range of at least one, two or even more logarithmic units: they should be well distributed over whole distance. Also, physicochemical parameter should be spread over a certain range and should be more or less evenly distributed. Equation has to be rejected If the above mentioned statistical measures are not satisfied If the number of the variables in the regression equation is unreasonably large. If standard deviation is smaller than error in the biological data. Applicability domain Activity of the entire universe of chemicals can not be predicted even by a robust and validated QSAR model. The prediction of a modeled response using QSAR is valid only if the compound being predicted is within the applicability domain of the model. The applicability domain is a theoretical region of the chemical space, defined by the model descriptors and modeled response and, thus, by the nature of the training set molecules 59. It is possible to check whether a new chemical lies within applicability domain using the leverage approach. A compound will be considered outside the applicability domain when the leverage value is higher than the critical value of 3p/n, where p is the number of model variables plus 1 and n is the number of objects used to develop the model. Recently Jaworska et al. 60 reviewed the methods and criteria for estimating applicability domain through training set interpolation based on range, distance, geometrical and probability density distribution based approaches. A cluster-based approach have been proposed by Stanforth et al. 61 to modeling the domain of applicability by applying an intelligent version of the K- means clustering algorithm, modeling the training set as a collection of clusters in the descriptors space, assigning a test compound fuzzy membership of each individual cluster from which an overall distance may be calculated. Guha and Jurs 50 have used a classification method that divides the regression residuals from a previously generated model into a good class and a bad class and builds a classifier based on the division. The trained classifier is then used to determine the class of the residual of a new compound. Dispute on QSAR Validation Hawkins et al., the major group of supporters of internal validation, are of the opinion that cross-validation is able to assess the model fit and to check whether the predictions will carry over to fresh data not used in the model fitting exercise. They have argued that when the sample size is small, holding a portion of it back for testing is wasteful and it is much better to use computationally more burdensome leave-one-out cross-validation 56,57. An inconsistency between internal and external predictivity was reported in a few QSAR studies 51,5,6. It was reported that, in general, there is no relationship between internal and external predictivity 63,64 : high internal predictivity may result in low external predictivity and vice versa. In many cases, comparable models are obtained where some models show comparatively better internal validation parameters and some other models show comparatively superior external validation parameters. This may create a problem in selecting the final model. So it is must to develop some good validation techniques to overcome the entire above mentioned disputes. Conclusion Validation of QSAR models is a very important aspect to understand reliability of model for prediction of a new compound not present in the data set. If we consider 1000 reported QSAR models, out of which only 50 to 60 models are really predictive but its not sure that these 60 models have been obeyed all the conditions and validation parameters discussed in this articles. Our opinion is, both internal and external validation strategies are important and, in fact, one should adopt all available validation strategies to check robustness of the model. Only few

8 518 International Journal of Drug Design and Discovery Volume Issue 3 July September 011 reported QSAR models were following all the validation characteristics mentioned in this article 65,66. As a conclusion, not only the above recommendations for validation of QSAR models by different scientist and researcher should be followed, also the chemical space of training and test sets has to be analyzed; real outliers, with respect to congeneric character and structural similarity, have to be discovered and eliminated. Even then, predictions by QSAR models are remains as a risky procedure. So, still we need proper validation techniques to select a good predictive QSAR models. References [1] Von, P.C.; Kuhne, R.; Ebert, R.U.; Altenburger, R.; Liess, M.; Schuurmann, G. Chem. Res. Toxicol. 005, 18, [] enterprise/reach/overview.htm [3] Combes, R.; Balls, M.; Bansil, L. ATLA. 1991, 30, [4] Seidel, J.K.; Schaper, K.J. Chemical structure and biological activity, Verlag Chemie Weinheim: New York, 1979, [5] Hansch, C. In Comprehensive Medicinal Chemistry, Ramsden, C. A. Ed.; Pergamon Press: New York, 1990; Vol. 4, pp 5-8. [6] Livingstone, D.J. Predicting Chemical Toxicity and Fate. CRC Press LLC: Boca Raton, FL, 004, [7] Winkler, D.A. Briefing Bioinformat. 00, 3, [8] Albuquerque, M.G.; Hopfinger, A.J.; Barreiro, E.J.; De Alencastro, R.B. J. Chem. Inf. Comput. Sci. 1998, 38, [9] Santos-Filho, O.; Hopfinger, A.; J. Comput-Aided Mol. Des. 001, 15, 1-1. [10] Ravi, M.; Hopfinger, A.; Hormann, R.; Dinan, L. J. Chem. Inf. Comput. Sci. 001, 41, [11] Krasowski, X. Hong, A. Hopfinger, N. Harrison. J. Med. Chem. 45 (00) [1] Hong, M. X.; Hopfinger, A. J. Chem. Inf. Comput. Sci. 003, 43, [13] Tetko, I.V.; Sushko, I.; Pandey, A.K.; Zhu, H.; Tropsha, A.; Papa, E.; Oberg, T.; Todeschini, R.; Fourches, D.; Varnek, A. J. Chem. Inf. Model. 008, 48, [14] Golbraikh, A.; Tropsha, A. J. Mol. Graphics Mod. 00, 0, [15] Tropsha, A.; Gramatica, P.; Gombar, V.K. QSAR Comb. Sci. 003,, [16] Tong, W.; Xie, Q.; Hong, H.; Shi, L.; Fang, H.; Perkins, R. Environ. Health Perspect. 004, 11, [17] Aptula, A.O.; Jeliazkova, N.G.; Schultz, T.W.; Cronin, M.T.D. QSAR Comb.Sci. 005, 4, [18] He, L.; Jurs, P.C. J. Mol. Graphics Mod. 005, 3, [19] Ghafourian, T.; Cronin, M.T.D. SAR QSAR Environ. Res. 005, 16, [0] Roy, K.; Leonard, J.T. QSAR Comb. Sci. 006, 5, [1] Kolossov, E.; Stanforth, R. SAR and QSAR Environ. Res. 007, 18, [] Roy, P.P.; Roy, K. QSAR Comb. Sci. 008, 7, [3] Walker, J.D.; Jawrska, J.; Comber, J.H.I.; Schultz, T.W.; Dearden, J.C. Environ. Toxicol. Chem. 003,, [4] Roy, P.P.; Leonard, J.T.; Roy, K. Chemom. Intell. Lab. Sys. 008, 90, [5] Tong, W.; Hong, H.; Xie, Q.; Shi, L.; Fang, H.; Perkins, R. Curr. Comput. Aided Drug Des. 005, 1, [6] He, L.; Jurs, P.C. J. Mol. Graph. Mod. 005, 3, [7] Ghafourian, T.; Cronin, M.T.D. SAR QSAR Environ. Res. 005, 16, [8] Balls, M. ; Blaauboer, B.J. ; Fentem, J.H. ATLA. 1995, 3, [9] McKinney, J.D.; Richard, A.; Waller, C.; Newman, M.C.; Gerberick, F. Toxicol. Sci. 000, 56, [30] Tong, W.; Welsh, W.J.; Shi, L.; Fang, H.; Perkins, R. Environ. Toxicol. Chem. 003,, [31] Worth, A.P.; Cronin, M.T.D. ATLA. 004, 3, [3] Cronin, M.T.D.; Jaworska, J.S.; Walker, J.D.; Comber, M.H.I. Watts, C.D.; Worth, A.P. Environ. Health Perspect. 003, 111, [33] M.T.D. Cronin, J.S. Jaworska, J.D. Walker, M.H.I. Comber, C.D. Watts, A.P. Worth. Environ. Health Persp. 111 (003) [34] Worth, A.P.; Leeuwen, C.J.; Hartung, T. SAR QSAR Environ. Res. 15 (004) [35] A.P. Worth, T. Hartung, C.J. Leeuwen. SAR QSAR Environ. Res. 15 (004)

9 Ravichandran Veerasamy, et al : Validation of QSAR Models-Strategies and Importance 519 [36] A.R. Leach. Molecular modeling: Principles and applications. Pearson Education Ltd. Harlow, England, 001. [37] Shao, J. J. Am. Stat. Assoc. 1993, 88, [38] Besal, E. J. Math. Chem. 001, 9, [39] Wold, S.; Ericksson, L. Partial least squares projections to latent structures (PLS) in chemistry. In Encyclopedia of computationalchemistry, Ragu & Schleyer, P. (ed.), John Wiley & Sons, Chichester, 1998, Vol. 3, [40] Yasri, A.; Hartsough, D. J. Chem. Inf. Comput. Sci. 001, 41, [41] Schneider, G.; Wrede, P. Prog. Biophys. Mol. Biol. 1998, 70, 175. [4] Gironbs, X.; Gallegos, A.; Ramon, C.D. J. Chem Inf Comput. Sci. 000, 46, [43] Bordhs, B.; Kijmives, T.; Szant, Z.; Lopata, A. J. Agric. Food Chem. 000, 48, [44] Fan, Y.; Shi, L.M.; Kohn, K. W.; Pommier, Y.; Weinstein, J.N. J. Med. Chem. 001, 44, [45] Randic, M.; Basak, S.C. J. Chem. Inf. Comput.Sci. 000, 40, [46] Suzuki, T.; Ide, K.; Ishida, M.; Shapiro, S. J. Chem. Inf. Comput. Sci. 001, 41, [47] Recanatini, M.; Cavalli, A.; Belluti, F.; Piazzi, L.; Rarnpa, A.; Bisi, A.; Gobbi, S.; Valenti, P.; Andrisano, V. ; Bartolini, M.; Cavrini, V. J. Med. Chem. 000, 43, [48] Morbn, J. A.; Campillo, M.; Perez, V.; Unzeta, M.; Pardo, L. J. Med. Chem. 000, 43, [49] Kubinyi, H.; Hamprecht, F.A.; Mietzner, T. J. Med. Chem. 1998, 41, [50] Guha, R.; Jurs, P.C. J. Chem. Inf. Model. 005, 45, [51] Novellino, E.; Fattorusso, C.; Greco, G. Pharm. Acta Helv. 1995, 70, [5] Norinder, U. J. Chemom. 1996, 10, [53] Zefirov, N.S.; Palyulin, V.A. J. Chem. Inf.Comput. Sci. 001, 41, [54] Sachs, L. Applied Statistics: A Handbook of Techniques, Springer-Verlag, BerlirdNew York, [55] Roy, K. Expert Opin. Drug Discov. 007,, [56] Hawkins, D.M.; Basak, S.C.; Mills, D. J. Chem. Inf.Comput. Sci. 003, 43, [57] Hawkins, D.M. J. Chem. Inf. Comput. Sci. 004, 44, 1-1. [58] Roy, K.; Paul, S. QSAR Comb. Sci. 008, 8, [59] Atkinson, A.C. Plots, Transformations and Regression. Clarendon Press, Oxford, UK (1985). [60] Jaworska, J.; Nikolovzjeliazkova, N.; Aldenberg, T. Altern. Lab. Anim. 005, 33, [61] Stanforth, R.W.; Kolossov, E.; Mirkin, B. QSAR Comb. Sci. 007, 6, [6] Kubinyi, H. A general view on similarity and QSAR studies. In: Computer-Assisted [63] Lead Finding and Optimization, van de Waterbeemd H, Testa B, Folkers G (Eds), VHChA and VCH, Basel, Weinheim. 1997, 9-8. [64] Kubinyi, H.; Hamprecht, F.A.; Mietzner, T. J. Med. Chem. 1998, 41, [65] Ravichandran, V.; Shalini, S.; Sundram, K.M.; Dhanaraj, S.A. Eurp. J. Med. Chem. 010, 45, [66] Roy, P.P.; Paul, S.; Indrani, M.; Roy, K. Molecules. 009, 14,