1. Chance Correlation in QSAR studies Ahmadreza Mehdipour Medicinal & Natural Product Chemistry Research Center

2. Correlation or causation? Correlation is essential but not sufficient Correlation is meaningless unless its cause (or role) in the biological activity is interpreted A satisfactory QSAR correlation does not mean that a particular descriptor causes the efficient action of a compound

3. Chance Correlation Topliss Ratio (J. Med. Chem. 1972, 35, 1066) A misconception Ratio of variables in model to Sample Size Ratio of variables in Data Pool to Sample Size Revalidation of problem by Livingstone (J. Med. Chem. 2005, 48, 6661)

4. Topliss et al. demonstrated that the more independent variables (X) that are available for selection in a multiple linear regression model, the more likely a model will be found by chance. These authors recommended that in order to reduce the risk of chance correlations there should be a certain ratio of data points to the number of independent variables available. Unfortunately, this ratio was often misinterpreted as the number of data points to the number of independent variables in the final model, a practice that did very little if anything to reduce chance effects. D.W. Salt, S. Ajmani, R. Crichton, D.J. Livingstone, An improved approximation to the estimation of the critical F values in best subset regression. J. Chem. Inf. Model. 47 (2007) 143-149.

5. Chance Correlation How does it occur? A Trial Example with random data Characteristics: N (Sample Size)=20 K (Number of variables in data pool)=10, 20, 50, 75, 100

6. N=20 K=10

7. N=20 K=20

8. N=20 K=50

9. N=20 K=75

10. N=20 K=100

11. Avoiding chance correlation What should we do?

12. Solutions for detection of chance correlation F max critical Randomization of Y (input scrambling) Validation procedures

13. F max Critical Linvingstone Approach Normal tabulated F is significant ONLY WHEN K=P K= number of variables in data pool P= number of variables in model

14. F max Critical However, in most cases K>>P K= number of variables in data pool P= number of variables in model N=Sample Size

15. Introduction of F max Critical Simulated random data Run 1000 times Different N, K and P Obtain F max for each combination (for a significance level of 5%) Check for some Known data sets www.cmd.port.ac.uk

16. Randomization of Y Ys are randomly attributed to samples

17. Y-randomization However This method should also be performed during Variable selection process if, R 2 max and Q 2 max are low Then, the risk of chance correlation is low

18. Cross-validation Process Different N, K, P N=10, 20, 30, 40, 50, 80, 100 P=1-8 N=p, 10, 20, 30, 50, 100 Run 1000 times Evaluation factors R 2 of training set Q 2 1 = Q 2 for LOO CV Q 2 20% = Q 2 for Leave-20% of samples-Out CV Q 2 50% = Q 2 for Leave-50% of samples-Out CV R 2 P = R 2 of one random test set (25% of samples)

20. Cross-validation Process Leave-one-out Vs Leave-group-out Q 2 L50%O is independent of N, K, P Hemmateenejad B, Mehdipour AR, Bagheri L, Miri R, Judging the significance of the multiple linear regression-based QSAR models by cross-validation. To be submitted

21. Concluding Remarks Be aware of N to K ratio Not only N to P ratio Check different approaches for chance correlation

22. Models are not real but sometimes are helpful