1. Predictive Classifiers Based on High Dimensional Data Development & Use in Clinical Trial Design Richard Simon, D.Sc. Chief, Biometric Research Branch National Cancer Institute http://linus.nci.nih.gov/brb

2. “Biomarkers” Surrogate endpoints –A measurement made before and after treatment to determine whether the treatment is working –Surrogate for clinical benefit Predictive classifiers –A measurement made before treatment to select good patient candidates for the treatment

3. Predictive Biomarker Classifiers Many cancer treatments benefit only a small proportion of the patients to which they are administered Targeting treatment to the right patients can greatly improve the therapeutic ratio of benefit to adverse effects –Treated patients benefit –Treatment more cost-effective for society

4. Developmental Strategy (I) Develop a diagnostic classifier that identifies the patients likely to benefit from the new drug Develop a reproducible assay for the classifier Use the diagnostic to restrict eligibility to a prospectively planned evaluation of the new drug Demonstrate that the new drug is effective in the prospectively defined set of patients determined by the diagnostic

5. Using phase II data, develop predictor of response to new drug Develop Predictor of Response to New Drug Patient Predicted Responsive New Drug Control Patient Predicted Non-Responsive Off Study

6. Applicability of Design I Primarily for settings where the classifier is based on a single gene whose protein product is the target of the drug With substantial biological basis for the classifier, it may be unacceptable ethically to expose classifier negative patients to the new drug

7. Evaluating the Efficiency of Strategy (I) Simon R and Maitnourim A. Evaluating the efficiency of targeted designs for randomized clinical trials. Clinical Cancer Research 10:6759-63, 2004. Maitnourim A and Simon R. On the efficiency of targeted clinical trials. Statistics in Medicine 24:329-339, 2005. reprints and interactive sample size calculations at http://linus.nci.nih.gov/brb

8. Two Clinical Trial Designs Un-targeted design –Randomized comparison of T to C without screening for expression of molecular target Targeted design –Assay patients for expression of target –Randomize only patients expressing target

9. Relative efficiency depends on proportion of patients test positive, and effectiveness of drug (compared to control) for test negative patients When less than half of patients are test negative and the drug has little or no benefit for test negative patients, the targeted design requires dramatically fewer randomized patients. –May require fewer or more patients to be screened than randomized with untargeted design

10. Web Based Software for Comparing Sample Size Requirements http://linus.nci.nih.gov/brb/

14. Developmental Strategy (II) Develop Predictor of Response to New Rx Predicted Non- responsive to New Rx Predicted Responsive To New Rx Control New RXControl New RX

15. Developmental Strategy (II) Do not use the diagnostic to restrict eligibility, but to structure a prospective analysis plan. Compare the new drug to the control overall for all patients ignoring the classifier. –If p overall  0.04 claim effectiveness for the eligible population as a whole Otherwise perform a single subset analysis evaluating the new drug in the classifier + patients –If p subset  0.01 claim effectiveness for the classifier + patients.

16. The purpose of the RCT is to evaluate the new treatment overall and for the pre-defined subset The purpose is not to re-evaluate the components of the classifier, or to modify or refine the classifier The purpose is not to demonstrate that repeating the classifier development process on independent data results in the same classifier

17. Developmental Strategy III Do not use the diagnostic to restrict eligibility, but to structure a prospective analysis plan. Compare the new drug to the control for classifier positive patients –If p + >0.05 make no claim of effectiveness –If p +  0.05 claim effectiveness for the classifier positive patients and Continue accrual of classifier negative patients and eventually test treatment effect at 0.05 level

18. The Roadmap 1.Develop a completely specified genomic classifier of the patients likely to benefit from a new drug 2.Establish reproducibility of measurement of the classifier 3.Use the completely specified classifier to design and analyze a new clinical trial to evaluate effectiveness of the new treatment with a pre-defined analysis plan.

19. Guiding Principle The data used to develop the classifier must be distinct from the data used to test hypotheses about treatment effect in subsets determined by the classifier –Developmental studies are exploratory And not closely regulated by FDA FDA should not regulate classifier development –Studies on which treatment effectiveness claims are to be based should be definitive studies that test a treatment hypothesis in a patient population completely pre-specified by the classifier

20. Adaptive Signature Design An adaptive design for generating and prospectively testing a gene expression signature for sensitive patients Boris Freidlin and Richard Simon Clinical Cancer Research 11:7872-8, 2005

21. Adaptive Signature Design End of Trial Analysis Compare E to C for all patients at significance level 0.04 –If overall H 0 is rejected, then claim effectiveness of E for eligible patients –Otherwise

22. Otherwise: –Using only the first half of patients accrued during the trial, develop a binary classifier that predicts the subset of patients most likely to benefit from the new treatment E compared to control C –Compare E to C for patients accrued in second stage who are predicted responsive to E based on classifier Perform test at significance level 0.01 If H 0 is rejected, claim effectiveness of E for subset defined by classifier

23. Classifier Development Using data from stage 1 patients, fit all single gene logistic models (j=1,…,M) Select genes with interaction significant at level 

24. Classification of Stage 2 Patients For i’th stage 2 patient, selected gene j votes to classify patient as preferentially sensitive to T if

25. Classification of Stage 2 Patients Classify i’th stage 2 patient as differentially sensitive to T relative to C if at least G selected genes vote for differential sensitivity of that patient

26. Treatment effect restricted to subset. 10% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients. TestPower Overall.05 level test46.7 Overall.04 level test43.1 Sensitive subset.01 level test (performed only when overall.04 level test is negative) 42.2 Overall adaptive signature design85.3

27. Overall treatment effect, no subset effect. 10% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients. TestPower Overall.05 level test74.2 Overall.04 level test70.9 Sensitive subset.01 level test1.0 Overall adaptive signature design70.9

28. Development of Classifiers Based on High Dimensional Data

29. Good Microarray Studies Have Clear Objectives Class Comparison –For predetermined classes, identify differentially expressed genes Class Prediction –Prediction of predetermined class (e.g. response) using information from gene expression profile Class Discovery –Discover clusters among specimens or among genes

30. Components of Class Prediction Feature (gene) selection –Which genes will be included in the model Select model type –E.g. Diagonal linear discriminant analysis, Nearest-Neighbor, … Fitting parameters (regression coefficients) for model –Selecting value of tuning parameters

31. Simple Feature Selection Genes that are differentially expressed among the classes at a significance level  (e.g. 0.01) –The  level is selected only to control the number of genes in the model

32. Complex Feature Selection Small subset of genes which together give most accurate predictions –Combinatorial optimization algorithms –Decision trees, Random forest –Top scoring pairs, Greedy pairs Little evidence that complex feature selection is useful in microarray problems –Many published complex methods for selecting combinations of features do not appear to have been properly evaluated –Wessels et al. (Bioinformatics 21:3755, 2005) –Lai et al (BMC Bioinformatics 7:235, 2006) –Lecocke & Hess (Cancer Informatics 2:313,2006)

33. Linear Classifiers for Two Classes

34. Fisher linear discriminant analysis Diagonal linear discriminant analysis (DLDA) assumes features are uncorrelated Compound covariate predictor Weighted voting classifier Support vector machines with inner product kernel Perceptrons Naïve Bayes classifier

35. Other Simple Methods Nearest neighbor classification Nearest centroid classification Shrunken centroid classification

36. When p>>n It is always possible to find a set of features and a weight vector for which the classification error on the training set is zero. There is generally not sufficient information in p>>n training sets to effectively use complex methods

37. Myth: Complex classification algorithms perform better than simpler methods for class prediction. Comparative studies indicate that simpler methods usually work as well or better for microarray problems because they avoid overfitting the data.

38. Internal Validation of a Classifier Split-sample validation –Split data into training and test sets –Test single fully specified model on the test set –Often applied invalidly with tuning parameter optimized on test set Cross-validation or bootstrap resampling –Repeated training-test partitions –Average errors over repetitions

39. training set test set specimens log-expression ratios specimensspecimens Cross-Validated Prediction (Leave-One-Out Method) 1. Full data set is divided into training and test sets (test set contains 1 specimen). 2. Prediction rule is built from scratch using the training set. 3. Rule is applied to the specimen in the test set for class prediction. 4. Process is repeated until each specimen has appeared once in the test set.

40. Cross validation is only valid if the test set is not used in any way in the development of the model. Using the complete set of samples to select genes violates this assumption and invalidates cross-validation. With proper cross-validation, the model must be developed from scratch for each leave-one-out training set. This means that feature selection must be repeated for each leave-one-out training set. The cross-validated estimate of misclassification error is an estimate of the prediction error for model fit using specified algorithm to full dataset

41. Prediction on Simulated Null Data Generation of Gene Expression Profiles 14 specimens (P i is the expression profile for specimen i) Log-ratio measurements on 6000 genes P i ~ MVN(0, I 6000 ) Can we distinguish between the first 7 specimens (Class 1) and the last 7 (Class 2)? Prediction Method Compound covariate prediction Compound covariate built from the log-ratios of the 10 most differentially expressed genes.

43. For small studies, cross-validation, if performed correctly, can be preferable to split-sample validation –Cross-validation can only be used when there is a well specified algorithm for classifier development

46. Simulated Data 40 cases, 10 genes selected from 5000 MethodEstimateStd Deviation True.078 Resubstitution.007.016 LOOCV.092.115 10-fold CV.118.120 5-fold CV.161.127 Split sample 1-1.345.185 Split sample 2-1.205.184.632+ bootstrap.274.084

47. Simulated Data 40 cases MethodEstimateStd Deviation True.078 10-fold.118.120 Repeated 10-fold.116.109 5-fold.161.127 Repeated 5-fold.159.114 Split 1-1.345.185 Repeated split 1-1.371.065

48. Permutation Distribution of Cross- validated Misclassification Rate of a Multivariate Classifier Randomly permute class labels and repeat the entire cross-validation Re-do for all (or 1000) random permutations of class labels Permutation p value is fraction of random permutations that gave as few misclassifications as e in the real data

49. Validation of Predictive Classifier Does Not Involve Measuring overlap of gene sets used in classifier developed from independent data Statistical significance of gene expression levels or summary signatures in multivariate analysis Confirmation of gene expression measurements on other platforms Demonstrating that the classifier or any of its components are “validated biomarkers of disease status”

53. Publications Reviewed Searched Medline Hand screening of abstracts & papers Original study on human cancer patients Published in English before December 31, 2004 Analyzed gene expression of more than 1000 probes Related gene expression to clinical outcome

54. Types of Clinical Outcome Survival or disease-free survival Response to therapy

55. 90 publications identified that met criteria –Abstracted information for all 90 Performed detailed review of statistical analysis for the 42 papers published in 2004

56. Major Flaws Found in 40 Studies Published in 2004 Inadequate control of multiple comparisons in gene finding –9/23 studies had unclear or inadequate methods to deal with false positives 10,000 genes x.05 significance level = 500 false positives Misleading report of prediction accuracy –12/28 reports based on incomplete cross-validation Misleading use of cluster analysis –13/28 studies invalidly claimed that expression clusters based on differentially expressed genes could help distinguish clinical outcomes 50% of studies contained one or more major flaws

57. Class Comparison and Class Prediction Not clustering problems –Global similarity measures generally used for clustering arrays may not distinguish classes –Don’t control multiplicity or for distinguishing data used for classifier development from data used for classifier evaluation Supervised methods Requires multiple biological samples from each class

60. Sample Size Planning References K Dobbin, R Simon. Sample size determination in microarray experiments for class comparison and prognostic classification. Biostatistics 6:27- 38, 2005 K Dobbin, R Simon. Sample size planning for developing classifiers using high dimensional DNA microarray data. Biostatistics 8:101-117, 2007 K Dobbin, Y Zhao, R Simon. How large a training set is needed to develop a classifier for microarray data, (Clinical Cancer Research, in press)

61. Predictive Classifiers in BRB-ArrayTools Classifiers –Diagonal linear discriminant –Compound covariate –Bayesian compound covariate –Support vector machine with inner product kernel –K-nearest neighbor –Nearest centroid –Shrunken centroid (PAM) –Random forest –Tree of binary classifiers for k- classes Survival risk-group –Supervised pc’s Feature selection options –Univariate t/F statistic –Hierarchical variance option –Restricted by fold effect –Univariate classification power –Recursive feature elimination –Top-scoring pairs Validation methods –Split-sample –LOOCV –Repeated k-fold CV –.632+ bootstrap

62. Acknowledgements Kevin Dobbin Alain Dupuy Boris Freidlin Aboubakar Maitournam Michael Radmacher Sudhir Varma Yingdong Zhao BRB-ArrayTools Development Team