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Steps on the Road to Predictive Medicine. Richard Simon, D.Sc. Chief, Biometric Research Branch National Cancer Institute http://brb.nci.nih.gov. BRB Website brb.nci.nih.gov. Powerpoint presentations Reprints & Presentations Reports BRB-ArrayTools software Web based Sample Size Planning

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Steps on the road to predictive medicine l.jpg

Steps on the Road to Predictive Medicine

Richard Simon, D.Sc.

Chief, Biometric Research Branch

National Cancer Institute

http://brb.nci.nih.gov


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BRB Websitebrb.nci.nih.gov

  • Powerpoint presentations

  • Reprints & Presentations Reports

  • BRB-ArrayTools software

  • Web based Sample Size Planning

    • Clinical Trials using predictive biomarkers

    • Development of gene expression based predictive classifiers


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  • Many cancer treatments benefit only a minority of patients to whom they are administered

    • Particularly true for molecularly targeted drugs

  • Being able to predict which patients are likely to benefit would

    • save patients from unnecessary toxicity, and enhance their chance of receiving a drug that helps them

    • Help control medical costs

    • Improve the success rate of clinical drug development


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Biomarkers to whom they are administered

  • Prognostic

    • Measured before treatment to indicate long-term outcome for patients untreated or receiving standard treatment

  • Predictive

    • Measured before treatment to select good patient candidates for a particular treatment


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Prognostic and Predictive Biomarkers in Oncology to whom they are administered

  • Single gene or protein measurement

    • HER2 protein staining 2+ or 3+

    • HER2 amplification

    • KRAS mutation

  • Index or classifier that summarizes contributions of multiple genes/proteins

    • Empirically determined based on genome-wide correlating gene expression to patient outcome after treatment


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Prospective Co-Development of Drugs and Companion Diagnostics

  • Develop a completely specified genomic classifier of the patients likely to benefit from a new drug

  • Establish analytical validity of the test

  • Design a pivotal RCT evaluating the new treatment with sample size, eligibility, and analysis plan prospectively based on use of the completely specified classifier/test.


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Guiding Principle Diagnostics

  • 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 can be exploratory

    • 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


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New Drug Developmental Strategy I Diagnostics

  • Restrict entry to the phase III trial based on the binary predictive classifier, i.e. targeted design


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Develop Predictor of Response to New Drug Diagnostics

Using phase II data, develop predictor of response to new drug

Patient Predicted Responsive

Patient Predicted Non-Responsive

Off Study

New Drug

Control


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Applicability of Design I Diagnostics

  • Primarily for settings where the classifier is based on a single gene whose protein product is the target of the drug

    • eg Herceptin

  • With substantial biological basis for the classifier, it may be unacceptable ethically to expose classifier negative patients to the new drug

  • Strong biological rationale or phase II data on unselected patients needed for approval of test


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Evaluating the Efficiency of Strategy (I) Diagnostics

  • Simon R and Maitnourim A. Evaluating the efficiency of targeted designs for randomized clinical trials. Clinical Cancer Research 10:6759-63, 2004; Correction and supplement 12:3229, 2006

  • Maitnourim A and Simon R. On the efficiency of targeted clinical trials. Statistics in Medicine 24:329-339, 2005



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Develop DiagnosticsPredictor of

Response to New Rx

Predicted Responsive

To New Rx

Predicted Non-responsive to New Rx

New RX

Control

New RX

Control

Developmental Strategy (II)


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Developmental Strategy (II) Diagnostics

  • Do not use the test 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

  • The purpose is not to demonstrate that repeating the classifier development process on independent data results in the same classifier


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Analysis Plan B Cancer Research 14:5984-93, 2008

  • 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.


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Sample size for Analysis Plan B for having developed a classifier

  • To have 90% power for detecting uniform 33% reduction in overall hazard at 3% two-sided level requires 297 events (instead of 263 for similar power at 5% level)

  • If 25% of patients are positive, then when there are 297 total events there will be approximately 75 events in positive patients

    • 75 events provides 75% power for detecting 50% reduction in hazard at 2% two-sided significance level

    • By delaying evaluation in test positive patients, 80% power is achieved with 84 events and 90% power with 109 events


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Analysis Plan C for having developed a classifier

  • Test for 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


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Sample Size Planning for Analysis Plan C for having developed a classifier

  • 88 events in classifier + patients needed to detect 50% reduction in hazard at 5% two-sided significance level with 90% power

  • If test is predictive but not prognostic, and if 25% of patients are positive, then 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


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Simulation Results for Analysis Plan C for having developed a classifier

  • 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


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Biomarker Adaptive Threshold Design for having developed a classifier

Wenyu Jiang, Boris Freidlin & Richard Simon

JNCI 99:1036-43, 2007


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Biomarker Adaptive Threshold Design for having developed a classifier

  • Randomized trial of T vs C

  • Have identified a univariate biomarker index B thought to be predictive of patients likely to benefit from T relative to C

  • Eligibility not restricted by biomarker

  • No threshold for biomarker determined

  • Biomarker value scaled to range (0,1)

  • Time-to-event data


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Procedure A for having developed a classifier

  • Compare T vs C for all patients

    • If results are significant at level .04 claim broad effectiveness of T

    • Otherwise proceed as follows


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Procedure A for having developed a classifier

  • Test T vs C restricted to patients with biomarker B > b

    • Let S(b) be log likelihood ratio statistic

  • Repeat for all values of b

  • Let S* = max{S(b)}

  • Compute null distribution of S* by permuting treatment labels

  • If the data value of S* is significant at 0.01 level, then claim effectiveness of T for a patient subset

  • Compute point and interval estimates of the threshold b


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Procedure B for having developed a classifier

  • S(b)=log likelihood ratio statistic for treatment effect in subset of patients with Bb

  • S*=max{S(0)+R, max{S(b)}}

  • Compute null distribution of T by permuting treatment labels

  • If the data value of T is significant at 0.05 level, then reject null hypothesis that T is ineffective

  • Compute point and interval estimates of the threshold b


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Estimation of Threshold for having developed a classifier


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Prostate Cancer Data for having developed a classifier


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Prostate Cancer Data for having developed a classifier


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Sample Size Planning (A) for having developed a classifier

  • Standard broad eligibility trial is sized for 80% power to detect reduction in hazard D at significance level 5%

  • Biomarker adaptive threshold design is sized for 80% power to detect same reduction in hazard D at significance level 4% for overall analysis


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Estimated Power of Broad Eligibility Design (n=386 events) vs Adaptive Design A (n=412 events) 80% power for 30% hazard reduction


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Sample Size Planning (B) vs Adaptive Design A (n=412 events)

  • Estimate power of procedure B relative to standard broad eligibility trial based on Table 1 for the row corresponding to the expected proportion of sensitive patients ( ) and the target hazard ratio for sensitive patients

    • e.g. =25% and =.4 gives RE=.429/.641=.67

  • When B has power 80%, overall test has power 80*.67=53%

  • Use formula B.2 to determine the approximate number of events needed for overall test to have power 53% for detecting =.4 limited to =25% of patients


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Events needed to Detect Hazard Ratio vs Adaptive Design A (n=412 events)  With Proportional Hazards



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Example Sample Size Planning for Procedure B

  • Design a trial to detect =0.4 (60% reduction) limited to =25% of patients

    • Relative efficiency from Table 1 .429/.641=.67

  • When procedure B has power 80%, standard test has power 80%*.67=53%

  • Formula B.2 gives D’=230 events to have 53% power for overall test and thus approximate 80% power for B

  • Overall test needs D=472 events for 80% power for detecting the diluted treatment effect


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Adaptive Signature Design

Boris Freidlin and Richard Simon

Clinical Cancer Research 11:7872-8, 2005


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Adaptive Signature Design End of Trial Analysis

  • Compare T to C for all patients at significance level overall

    • If overall H0 is rejected, then claim effectiveness of T for eligible patients

    • Otherwise


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  • 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 T compared to control C

    • Compare T to C for patients accrued in second stage who are predicted responsive to E based on classifier

      • Perform test at significance level 0.05 - overall

      • If H0 is rejected, claim effectiveness of T for subset defined by classifier



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Classifier Development

  • Using data from stage 1 patients, fit all single gene logistic models (j=1,…,M)

  • Select genes with interaction significant at level 


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Classification of Stage 2 Patients

  • For i’th stage 2 patient, selected gene j votes to classify patient as preferentially sensitive to T if


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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


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Simulation Parameters

  • Gene expression levels of sensitivity genes MVN

    • mean m, variance v1 and correlation r in sensitive patients

    • mean 0, variance v2 and correlation r in non-sensitive patients

  • Gene expression levels of other genes MVN with mean 0, variance v0 and correlation r in all patients


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  • Treatment-expression interaction parameters ( *) same for all sensitivity genes

  • * value scaled (depending on K) so that log odds ratio of treatment effect is 5 for hypothetical patient with sensitivity gene expression levels at their expected values

    • i.e. m *K=5

  • Intercept  scaled for control response rate of 25%


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Treatment effect restricted to subset. 10% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients.


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Treatment effect restricted to subset. 25% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients.


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Overall treatment effect, no subset effect. 10% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients.


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Stronger treatment effect for sensitive subset. 10% of patients sensitive, 10 sensitivity genes, 10,000 genes, 400 patients.


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Empirical Power RR for Control Patients 25%


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Cross-Validated Adaptive Signature Design

Wenyu Jiang, Boris Freidlin, Richard Simon


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Cross-Validated Adaptive Signature DesignEnd of Trial Analysis

  • Compare T to C for all patients at significance level overall

    • If overall H0 is rejected, then claim effectiveness of T for eligible patients

    • Otherwise


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  • Otherwise:

    • Partition the full data set into K parts

    • Form a training set by omitting one of the K parts. The omitted part is the test set

      • Using the training set, develop a predictive classifier of the subset of patients who benefit preferentially from the new treatment T compared to control C using the methods developed for the ASD

      • Classify the patients in the test set as either sensitive or not sensitive to T relative to C

    • 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

    • Compare T to C for sensitive patients by computing a test statistic S e.g. the difference in response proportions

    • Generate the null distribution of S by permuting the treatment labels and repeating the entire K-fold cross-validation proceedure

    • Perform test at significance level 0.05 - overall

    • If H0 is rejected, claim effectiveness of E for subset defined by classifier

      • The sensitive subset is determined by developing a classifier using the full dataset


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80% Response to T in Sensitive Patients 25% Response to T or C Otherwise10% Patients Sensitive


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70% Response to T in Sensitive Patients 25% Response to T or C Otherwise20% Patients Sensitive


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70% Response to T in Sensitive Patients 25% Response to T or C Otherwise30% Patients Sensitive


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35% Response to T 25% Response to CNo Subset Effect


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25% Response to T 25% Response to CNo Subset Effect