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- 1. On the Road to Predictive Oncology Challenges for Statistics and for Clinical Investigation Richard Simon, D.Sc. Chief, Biometric Research Branch National Cancer Institute http://brb.nci.nih.gov
- 2. Biometric Research Branch Website http://brb.nci.nih.gov • Powerpoint presentations • Reprints • BRB-ArrayTools software • Web based tools for clinical trial design with predictive biomarkers
- 3. Prediction Tools for Informing Treatment Selection • Most cancer treatments benefit only a minority of patients to whom they are administered • Being able to predict which patients are likely or unlikely to benefit from a treatment might – Save patients from unnecessary complications and enhance their chance of receiving a more appropriate treatment – Help control medical costs – Improve the success rate of clinical drug development
- 4. Types of Biomarkers • Predictive biomarkers – Measured before treatment to identify who is likely or unlikely to benefit from a particular treatment • Prognostic biomarkers – Measured before treatment to indicate long- term outcome for patients untreated or receiving standard treatment
- 5. • Surrogate endpoints – Measured longitudinally to measure the pace of disease and how it is effected by treatment for use as an early indication of clinical effectiveness of treatment
- 6. Prognostic & Predictive Biomarkers • Single gene or protein measurement – ER protein expression – HER2 amplification – EGFR mutation – KRAS mutation • Index or classifier that summarizes expression levels of multiple genes – OncotypeDx recurrence score
- 7. Validation = Fit for Intended Use • Analytical validation – Accuracy, reproducibility, robustness • Clinical validation – Does the biomarker predict a clinical endpoint or phenotype • Clinical utility – Does use of the biomarker result in patient benefit • By informing treatment decisions • Is it actionable
- 8. Pusztai et al. The Oncologist 8:252-8, 2003 • 939 articles on “prognostic markers” or “prognostic factors” in breast cancer in past 20 years • ASCO guidelines only recommended routine testing for ER, PR and HER-2 in breast cancer
- 9. • Most prognostic markers or prognostic models are not used because although they correlate with a clinical endpoint, they do not facilitate therapeutic decision making; • Most prognostic marker studies are based on a “convenience sample” of heterogeneous patients, often not limited by stage or treatment. • The studies are not planned or analyzed with clear focus on an intended use of the marker • Retrospective studies of prognostic markers should be planned and analyzed with specific focus on intended use of the marker • Prospective studies should address medical utility for a specific intended use of the biomarker – Treatment options and practice guidelines – Other prognostic factors
- 10. Potential Uses of Prognostic Biomarkers • Identify patients who have very good prognosis on standard treatment and do not require more intensive regimens • Identify patients who have poor prognosis on standard chemotherapy who are good candidates for experimental regimens
- 11. Predictive Biomarkers
- 12. Major Changes in Oncology • Recognition of the heterogeneity of tumors of the same primary site with regard to molecular oncogenesis • Availability of the tools of genomics for characterizing tumors • Focus on molecularly targeted drugs • Have resulted in – Increased interest in prediction problems – Need for new clinical trial designs – Increased pace of innovation
- 13. • p>n prediction problems in which number of variables is much greater than the number of cases – Many of the methods of statistics are based on inference problems – Standard model building and evaluation strategies are not effective for p>n prediction problems
- 14. Model Evaluation for p>n Prediction Problems • Goodness of fit is not a proper measure of predictive accuracy • Importance of Separating Training Data from Testing Data for p>n Prediction Problems
- 15. Simulation Training Validation 1 2 3 4 5 6 7 8 9 10 p=7.0e-05 p=0.70 p=4.2e-07 p=0.54 p=2.4e-13 p=0.60 p=1.3e-10 p=0.89 p=1.8e-13 p=0.36 p=5.5e-11 p=0.81 p=3.2e-09 p=0.46 p=1.8e-07 p=0.61 p=1.1e-07 p=0.49 p=4.3e-09 p=0.09
- 16. Separating Training Data from Testing Data • Split-sample method • Re-sampling methods – Leave one out cross validation – K-fold cross validation – Replicated split-sample – Bootstrap re-sampling
- 17. • “Prediction is very difficult; especially about the future.”
- 18. Prediction on Simulated Null Data Simon et al. J Nat Cancer Inst 95:14, 2003 Generation of Gene Expression Profiles • 20 specimens (Pi is the expression profile for specimen i) • Log-ratio measurements on 6000 genes • Pi ~ MVN(0, I6000) • Can we distinguish between the first 10 specimens (Class 1) and the last 10 (Class 2)? Prediction Method • Compound covariate predictor built from the log-ratios of the 10 most differentially expressed genes.
- 19. Number of misclassifications 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
- 20. 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 the model developed by applying the specified algorithm to the full dataset
- 21. Permutation Distribution of Cross-validated Misclassification Rate of a Multivariate Classifier Radmacher, McShane & Simon J Comp Biol 9:505, 2002 • 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 cross-validated misclassifications as in the real data
- 22. Model Evaluation for p>n Prediction Problems • Odds ratios and hazards ratios are not proper measures of prediction accuracy • Statistical significance of regression coefficients are not proper measures of predictive accuracy
- 23. Evaluation of Prediction Accuracy • For binary outcome – Cross-validated prediction error – Cross-validated sensitivity & specificity – Cross-validated ROC curve • For survival outcome – Cross-validated Kaplan-Meier curves for predicted high and low risk groups • Cross-validated K-M curves within levels of standard prognostic staging system – Cross-validated time-dependent ROC curves
- 24. i -i p dimensional vector of expression levels for case i y =binary {0,1} class indicator for case i p dimensional weights for linear classifier computed for training set with case i omitted; ix β = = ) ( ) -i i component j is zero if variable j is not selected in feature selection step for training set -i score for case i computed from model developed with case i omitted y c ixβ = = ) ) { } { } { } { } -i i 1 i i 1 i i 1 predicted class mis-classification error y (c)=y sensitivity(c) y (c)=y specificity(c) (1 ) y (c)=y ROC curve sensitivity(c) vs 1-specificity(c) i n i n i i n i i I x c I y I y I β = = = > = = = = − ∑ ∑ ∑ ) ) ) ) LOOCV Error Estimates for Linear Classifiers
- 25. Cross-validated Kaplan-Meier Curves for Predicted High and Low Risk Groups 0 ( ; ) ( ; ) ( )exp( ) 1 ( ; ) estimate of weights based on algorithm applied to training set with case i omitted Algorithm may involve feature selection, i f t x t x t x F t x λ λ β β− ≡ = − = ) penalized regression, ... Classify case i as high risk if i ix cβ− > )
- 26. Cross-Validated Time Dependent ROC Curve -i * landmark time of interest sensitivity(c)=Pr[ x>c|t t*] Pr[t<t*| x>c]Pr[ x>c] = Pr[t t*] Estimate 1st term in numerator using KM estimator for cases with . Estimate 2nd tei t x c β β β β = ≤ ≤ > ) -i rm as proportion of n cases with . Estimate denominator using KM estimator for all n cases. specificity(c)=Pr[ x c|t>t*] Pr[t>t*| x c]Pr[ x c] = Pr[t>t*] Time-dependent ix cβ β β β > ≤ ≤ ≤ ) ROC is sensitivity(c) vs 1-specificity(c)
- 27. Is Accurate Prediction Possible For p>n? • Yes, in many cases, but standard statistical methods for model building and evaluation are often not effective • Standard methods may over-fit the data and lead to poor predictions • With p>n, unless data is inconsistent, a linear model can always be found that classifies the training data perfectly
- 28. Is Accurate Prediction Possible For p>>n? • Some problems are easy; real problems are often difficult • Simple methods like DLDA, nearest neighbor classifiers and shrunken centroid classifiers are at least as effective as more complex methods for many datasets • Because of correlated variables, there are often many very distinct models that predict about equally well
- 29. • p>n prediction problems are not multiple testing problems • The objective of prediction problems is accurate prediction, not controlling the false discovery rate – Parameters that control feature selection in prediction problems are tuning parameters to be optimized for prediction accuracy • Optimizaton by cross-validation nested within the cross- validation used for evaluating prediction accuracy • Biological understanding is often a career objective; accurate prediction can sometimes be achieved in less time
- 30. Model Instability Does Not Mean Prediction Inaccuracy • Validation of a predictive model means that the model predicts accurately for independent data • Validation does not mean that the model is stable or that using the same algorithm on independent data will give a similar model • With p>n and many genes with correlated expression, the classifier will not be stable.
- 31. Traditional Approach to Oncology Clinical Drug Development • Phase III trials with broad eligibility to test the null hypothesis that a regimen containing the new drug is on average not better than the control treatment for all patients who might be treated by the new regimen • Perform exploratory subset analyses but regard results as hypotheses to be tested on independent data
- 32. Traditional Clinical Trial Approaches • Have protected us from false claims resulting from post-hoc data dredging not based on pre- defined biologically based hypotheses • Have led to widespread over-treatment of patients with drugs from which many don’t benefit • Are less suitable for evaluation of new molecularly targeted drugs which are expected to benefit only the patients whose tumors are driven by de-regulation of the target of the drug
- 33. Molecular Heterogeneity of Human Cancer • Cancers of a primary site in many cases appear to represent a heterogeneous group of diverse molecular diseases which vary fundamentally with regard to – their oncogenecis and pathogenesis – their responsiveness to specific drugs • The established molecular heterogeneity of human cancer requires the use new approaches to the development and evaluation of therapeutics
- 34. How Can We Develop New Drugs in a Manner More Consistent With Modern Tumor Biology and Obtain Reliable Information About What Regimens Work for What Kinds of Patients?
- 35. Using phase II data, develop predictor of response to new drugDevelop Predictor of Response to New Drug Patient Predicted Responsive New Drug Control Patient Predicted Non-Responsive Off Study
- 36. Evaluating the Efficiency of Enrichment and Stratification Clinical Trial Designs With Predictive Biomarkers • Simon R and Maitnournam A. Evaluating the efficiency of targeted designs for randomized clinical trials. Clinical Cancer Research 10:6759-63, 2004; Correction and supplement 12:3229, 2006 • Maitnournam A and Simon R. On the efficiency of targeted clinical trials. Statistics in Medicine 24:329-339, 2005.
- 37. Model for Two Treatments With Binary Response •New treatment T •Control treatment C •1-γ proportion marker + •pc control response probability •response probability for T: –Marker + (pc + δ1) –Marker - (pc + δ0)
- 38. Randomized Ratio (normal approximation) • RandRat = nuntargeted/ntargeted ∀ δ1= rx effect in marker + patients ∀ δ0= rx effect in marker - patients ∀ γ =proportion of marker - patients • If δ0=0, RandRat = 1/ (1-γ) 2 • If δ0= δ1/2, RandRat = 1/(1- γ/2)2 2 1 1 0(1 ) RandRat δ γ δ γδ ≈ ÷ − +
- 39. Randomized Ratio nuntargeted/ntargeted 1-γ Express target δ0=0 δ0= δ1/2 0.75 1.78 1.31 0.5 4 1.78 0.25 16 2.56
- 40. • Relative efficiency of targeted design depends on – proportion of patients test positive – effectiveness of new drug (compared to control) for test negative patients • When less than half of patients are test positive and the drug has little or no benefit for test negative patients, the targeted design requires dramatically fewer randomized patients
- 41. Trastuzumab Herceptin • Metastatic breast cancer • 234 randomized patients per arm • 90% power for 13.5% improvement in 1-year survival over 67% baseline at 2-sided .05 level • If benefit were limited to the 25% assay + patients, overall improvement in survival would have been 3.375% – 4025 patients/arm would have been required
- 42. Developmental Strategy (II) Develop Predictor of Response to New Rx Predicted Non- responsive to New Rx Predicted Responsive To New Rx Control New RX Control New RX
- 43. Developmental Strategy (II) • Do not use the diagnostic to restrict eligibility, but to structure a prospective analysis plan • Having a prospective analysis plan is essential • “Stratifying” (balancing) the randomization is useful to ensure that all randomized patients have tissue available but is not a substitute for a prospective analysis plan • The purpose of the study is to evaluate the new treatment overall and for the pre-defined subsets; not to modify or refine the classifier
- 44. • R Simon. Using genomics in clinical trial design, Clinical Cancer Research 14:5984-93, 2008 • R Simon. Designs and adaptive analysis plans for pivotal clinical trials of therapeutics and companion diagnostics, Expert Opinion in Medical Diagnostics 2:721-29, 2008
- 45. Analysis Plan B (Fall-back Plan) • Compare the new drug to the control overall for all patients ignoring the classifier. – If poverall≤ 0.03 claim effectiveness for the eligible population as a whole • Otherwise perform a single subset analysis evaluating the new drug in the classifier + patients – If psubset≤ 0.02 claim effectiveness for the classifier + patients.
- 46. Analysis Plan C (Interaction Plan) • Test for difference (interaction) between treatment effect in test positive patients and treatment effect in test negative patients • If interaction is significant at level int then compare treatments separately for test positive patients and test negative patients • Otherwise, compare treatments overall
- 47. Sample Size Planning for Analysis Plan C • 88 events in test + patients needed to detect 50% reduction in hazard at 5% two- sided significance level with 90% power • If 25% of patients are positive, when there are 88 events in positive patients there will be about 264 events in negative patients – 264 events provides 90% power for detecting 33% reduction in hazard at 5% two-sided significance level
- 48. Simulation Results for Analysis Plan C • Using int=0.10, the interaction test has power 93.7% when there is a 50% reduction in hazard in test positive patients and no treatment effect in test negative patients • A significant interaction and significant treatment effect in test positive patients is obtained in 88% of cases under the above conditions • If the treatment reduces hazard by 33% uniformly, the interaction test is negative and the overall test is significant in 87% of cases
- 49. • It can be difficult to identify a single completely defined classifier candidate prior to initiation of the phase III trial evaluating the new treatment
- 50. Generalization of Biomarker Adaptive Threshold Design (Global Test Approach) • Have identified K candidate predictive binary classifiers B1 , …, BK thought to be predictive of patients likely to benefit from T relative to C • Eligibility not restricted by candidate biomarkers
- 51. End of Trial Analysis • Compare T to C for all patients at significance level overall (e.g. 0.03) – If overall H0 is rejected, then claim effectiveness of T for eligible patients – Otherwise
- 52. • Test T vs C restricted to patients positive for Bk for k=1,…,K – Let Sk be log likelihood ratio statistic for treatment effect in patients positive for Bk (k=1,…,K) • Let S* = max{Sk)} , k* = argmax{Sk)} • Compute null distribution of S* by permuting treatment labels • If the unpermutted data value of S* is significant at level 0.05- overall ,claim effectiveness of T for patients positive for Bk*
- 53. Cross-Validated Adaptive Signature Design (Clinical Cancer Research, Jan 2010) W Jiang, B Freidlin, R Simon
- 54. Cross-Validated Adaptive Signature Design End of Trial Analysis • Compare T to C for all patients at significance level overall (e.g. 0.03) – If overall H0 is rejected, then claim effectiveness of T for eligible patients – Otherwise
- 55. Otherwise • Partition the full data set into K parts P1 ,…,PK • Form a training set by omitting one of the K parts, e.g. part k. – Trk={1,…,n}-Pk • The omitted part Pk is the test set • Using the training set, develop a predictive binary classifier B-k of the subset of patients who benefit preferentially from the new treatment compared to control • Classify the patients i in the test set as sensitive B-k(xi)=1 or insensitive B-k(xi)=0 – Let Sk={j in Pk : B-k(xi)=1}
- 56. • Repeat this procedure K times, leaving out a different part each time • After this is completed, all patients in the full dataset are classified as sensitive or insensitive – Scv=∪ Sk
- 57. • For patients classified as sensitive, compare outcomes for patients who received new treatment T to those who received control treatment C. – Outcomes for patients in Scv ∩ T vs outcomes for patients in Scv ∩ C • Compute a test statistic Dsens – e.g. the difference in response proportions or log-rank statistic for survival • Generate the null distribution of Dsens by permuting the treatment labels and repeating the entire K-fold cross-validation procedure • Perform test at significance level 0.05 - overall
- 58. • If H0 is rejected, claim superiority of new treatment T for future patients with expression vector x for which B(x)=1 where B is the classifier of sensitive patients developed using the full dataset • The estimate of treatment effect for future sensitive patients is Dsens computed from the cross-validated sensitive subset Scv • The stability of the sensitive subset {x:B(x)=1} can be evaluated based on applying the classifier development algorithm to non-parametric bootstrap samples of the full dataset {1,...,n}
- 59. 70% Response to T in Sensitive Patients 25% Response to T Otherwise 25% Response to C 20% Patients Sensitive, n=400 ASD CV-ASD Overall 0.05 Test 0.486 0.503 Overall 0.04 Test 0.452 0.471 Sensitive Subset 0.01 Test 0.207 0.588 Overall Power 0.525 0.731
- 60. Prediction Based Analysis of Clinical Trials • Using cross-validation we can evaluate any classification algorithm for identifying the patients sensitive to the new treatment relative to the control using any set of covariates. • The algorithm and covariates should be pre-specified. • The algorithm A, when applied to a dataset D should provide a function B(x;A,D) that maps a covariate vector x to {0,1}, where 1 means that treatment T is prefered to treatment C for the patient. • The algorithm can be simple or complex, frequentist or Bayesian based. – Prediction effectiveness depends on the algorithm and the dataset – Complex algorithms may over-fit the data and provide poor results • Including Bayesian models with many parameters and non-informative priors • Prediction effectiveness for the given clinical trial dataset can be evaluated by cross-validation
- 61. Conclusions • A more personalized oncology is rapidly developing based (so far) on information in the tumor genome • Genomics has spawned new and interesting areas of biostatistics including methods for p>n prediction problems, systems biology and the design of predictive clinical trials • There are important opportunities and great needs for young biostatisticians with rigorous training in biostatistics and high motivation for trans-disciplinary research in biology and biomedicine
- 62. Acknowledgements • Kevin Dobbin • Boris Freidlin • Wenyu Jiang • Aboubakar Maitournam • Michael Radmacher • Jyothi Subramarian • Yingdong Zhao
- 63. BRB-ArrayTools • Architect – R Simon • Developer – Emmes Corporation • Contains wide range of analysis tools that I have selected • Designed for use by biomedical scientists • Imports data from all gene expression and copy-number platforms – Automated import of data from NCBI Gene Express Omnibus • Highly computationally efficient • Extensive annotations for identified genes • Integrated analysis of expression data, copy number data, pathway data and data other biological data
- 64. 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 forrest – Tree of binary classifiers for k- classes • Survival risk-group – Supervised pc’s – With clinical covariates – Cross-validated K-M curves • Predict quantitative trait – LARS, LASSO • Feature selection options – Univariate t/F statistic – Hierarchical random variance model – Restricted by fold effect – Univariate classification power – Recursive feature elimination – Top-scoring pairs • Validation methods – Split-sample – LOOCV – Repeated k-fold CV – .632+ bootstrap • Permutational statistical significance
- 65. BRB-ArrayTools June 2009 • 10,000+ Registered users • 68 Countries • 1000+ Citations

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