Use of Prognostic

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Use of Prognostic Predictive Biomarkers in
Clinical Trial Design

• 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
• BRB-ArrayTools software
• Data archive
• Q/A message board
• Web based Sample Size Planning
• Clinical Trials
• Optimal 2-stage phase II designs
• Phase III designs using predictive biomarkers
• Phase II/III designs
• Development of gene expression based predictive
  classifiers

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Prognostic Predictive Biomarkers

• 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 would
• Save patients from unnecessary toxicity, and
  enhance their chance of receiving a drug that
  helps them
• Control medical costs
• Improve the success rate of clinical drug
  development

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• Predictive biomarkers
• Measured before treatment to identify who will or
  will not benefit from a particular treatment
• ER, HER2, KRAS
• Prognostic biomarkers
• Measured before treatment to indicate long-term
  outcome for patients untreated or receiving
  standard treatment
• Only have medical utility if therapeutically
  relevant
• Used to identify who does or does not require
  more intensive than standard treatment
• OncotypeDx

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Prognostic and Predictive Biomarkers in Oncology

• Single gene or protein measurement
• Scalar index or classifier that summarizes
  expression levels of multiple genes

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Prognostic Factors in Oncology

• Many prognostic factors are not used because they
  are not actionable
• Most prognostic factor studies are not conducted
  with an intended use
• They use a convenience sample of heterogeneous
  patients for whom tissue is available
• Retrospective studies of prognostic markers
  should be planned and analyzed with specific
  focus on intended use of the marker
• Design of prospective studies depends on context
  of use of the biomarker
• Treatment options and practice guidelines
• Other prognostic factors

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Clinical Utility

• Biomarker benefits patient by improving treatment
  decisions
• 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

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Prospective Evaluation of Prognostic Biomarker

• Identify low stage patients for whom standard of
  care is chemotherapy
• Find dataset of low stage patients who did not
  receive chemotherapy for whom archived tissue is
  available
• Develop prognostic classifier of risk without
  chemotherapy of low stage patients
• If the classifier identifies a group with a very
  low risk of recurrence in the absence of
  chemotherapy then
• Conduct RCT in which low stage patients who are
  low risk by biomarker classifier are randomized
  to - chemotherapy

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• If the predicted risk of recurrence is
  sufficiently low, then randomization may be
  omitted
• The test of the biomarker is a test of whether
  the risk is as low as predicted
• Absolute benefit of very low risk patients is by
  necessity very small
• This is the approach of TAILORx

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How Does This Approach Compare to the So Called
Gold Standard of Randomizing Patients to Receive
or Not Receive the Test?
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Prospective Marker Strategy Design

• Patients are randomized to either
• have marker measured and treatment determined
  based on marker result and clinical features
• dont have marker measured and receive standard
  of care treatment based on clinical features
  alone

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Randomize Patients to Test or No Test
Rx Determined by Test
Rx Determined By SOC
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Marker Strategy Design

• Inefficient
• Many patients get the same treatment regardless
  of which arm they are randomized to
• Uninformative
• Since patients in the standard of care arm do not
  have the marker measured, it is not possible to
  compare outcome for patients whose treatment is
  changed based on the marker result

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Apply Test to All Eligible Patients
Using phase II data, develop predictor of
response to new drug
Test Deterimined Rx Different From SOC
Test Determined Rx Same as SOC
Off Study
Use Test Determined Rx
Use SOC
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• MINDACT randomizes breast cancer patients whose
  Mammaprint based Rx differs from SOC
• Trial is sized to estimate risk of relapse of low
  risk Mammaprint patients randomized to no
  chemotherapy

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Predictive Biomarkers
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• Cancers of a primary site are in many cases a
  molecularly heterogeneous group of diseases which
  vary enormously in their responsiveness to
  treatment, particularly molecularly targeted
  treatment
• 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 tumors?

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• Evaluating a predictive biomarker for treatment T
  involves an RCT of T versus a control C.
• Analysis of RCT determines whether the biomarker
  distinguishes the patients who benefit from T vs
  C from those who dont
• In this RCT, the biomarker should ideally be
• completely specified in advance
• focused on the single specific biomarker
• the trial sized with sufficient marker and
  marker patients for adequately powered separate
  analysis of T vs C differences in each stratum.
• Evaluating a predictive biomarker does not
  involve comparison of outcome of marker vs
  marker patient

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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 classifier
• Use the completely specified classifier in the
  primary analysis plan of a phase III trial of the
  new drug

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Guiding Principle

• The data used to develop the classifier should 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 not be exploratory

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Develop Predictor of Response to New Drug
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 Targeted/Enrichment Design

• Primarily for settings where the classifier is
  based on a single gene whose protein product is
  the target of the drug or the biology seems well
  understood
• eg trastuzumab
• With a strong biological basis for the
  classifier, it may be unacceptable to expose
  classifier negative patients to the new drug
• Analytical validation, biological rationale and
  phase II data provide basis for regulatory
  approval of the test
• Phase III study focused on test patients to
  provide data for approving the drug

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Principle

• If a drug is found safe and effective in a
  defined (test ) patient population, approval
  should not depend on finding the drug ineffective
  in some other (test -) population

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Evaluating the Efficiency of Enrichment Design

• Simon R and Maitnourim A. Evaluating the
  efficiency of targeted designs for randomized
  clinical trials. Clinical Cancer Research
  106759-63, 2004 Correction and supplement
  123229, 2006
• Maitnourim A and Simon R. On the efficiency of
  targeted clinical trials. Statistics in Medicine
  24329-339, 2005.
• reprints and interactive sample size calculations
  at http//linus.nci.nih.gov

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• 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

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TrastuzumabHerceptin

• 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

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Model for Two Treatments With Binary Response

• Molecularly targeted treatment T
• Control treatment C
• 1-? Proportion of patients that express target
• pc control response probability
• response probability for T patients who express
  target (R) is (pc ?1)
• Response probability for T patients who do not
  express target (R-) is (pc ?0)

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Randomized Ratio(normal approximation)

• RandRat nuntargeted/ntargeted
• ?1 rx effect in marker patients
• ?0 rx effect in marker - patients
• ? proportion of marker - patients
• If ?00, RandRat 1/ (1-?) 2
• If ?0 ?1/2, RandRat 1/(1- ?/2)2

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Randomized Rationuntargeted/ntargeted
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Screened Ratio

• Nuntargeted nuntargeted
• Ntargeted ntargeted/(1-?)
• ScreenRat Nuntargeted/Ntargeted(1- ?)RandRat

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Screened Ratio
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Decomposing Specificity of Treatment Effect from
Accuracy of Test

• RandRat nuntargeted/ntargeted

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Randomized Ratio sensitivityspecificity0.9
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Screened Ratio

• Nuntargeted nuntargeted

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Screened Ratio sensitivityspecificity0.9
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Web Based Software for Designing RCT of Drug and
Predictive Biomarker

• http//brb.nci.nih.gov

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• It can be very difficult to develop an effective
  and analytically validated predictive biomarker
  prior to launch of the phase III trial
• Even for anti-EGFR antibodies, a more effective
  biomarker turned out to be KRAS mutation, not
  EGFR expression
• For small molecule kinase inhibitors the task is
  more difficult
• In some settings it can be easier to use an
  analytically validated biomarker of poor outcome
  on the standard therapy

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• It can be very difficult to develop an effective
  and analytically validated predictive biomarker
  prior to launch of the phase III trial
• Even for anti-EGFR antibodies, a more effective
  biomarker turned out to be KRAS mutation, not
  EGFR expression
• For small molecule kinase inhibitors the task is
  more difficult
• In some settings it can be easier to use an
  analytically validated biomarker of poor outcome
  on the standard therapy

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• Score function S for distinguishing patients with
  favorable outcome on standard rx vs those with
  unfavorable outcome
• Developed on training set of pts receiving std rx
• GF(s)CDF of S in favorable pts
• GU(s)CDF of S in unfavorable pts
• Computed on test set of pts receiving std rx

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• GU(s)sensitivity of test for selecting pts with
  unfavorable outcome on std rx using threshold s
• 1-GF(s)specificity of test
• Plot of GU(s) vs GF(s) ROC curve

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• Latent classes
• LCF
• LCU
• PrLCF?
• PrSRespFLCFp1
• PrSRespFLCUp0
• PrERespFLCFp1
• PrSRespFLCUp0?

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• The maximum treatment effect is ?. It can be
  achieved if one selects a threshold t small
  enough that the specificity of the test for
  excluding cases with favorable outcome on the
  standard treatment is 1. If the specificity is 1,
  then the size of the treatment effect does not
  depend on the sensitivity of the test
• Proportion randomized (1-?)GU(t)?GF(t)

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• Simon and Maitnourim showed that the ratio of
  number of patients needed to randomize for a
  targeted design compared to a standard design
  that does not use the biomarker is approximately
  equal to the square of the ratio of the treatment
  effects for the two designs
• For the standard design the treatment effect is
  (1-?)?

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• If the threshold is selected for specificity 1,
  then the randomization ratio equals (1-?)2
• Hence if half of the patients have favorable
  outcome with standard treatment, i.e. ?0.5, then
  the targeted design requires only one quarter the
  number of randomized patients as the standard
  design.

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Stratification Design
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Stratification Design

• Use the test to structure a prospective specified
  primary 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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Not Interaction Design

• Requiring a significant interaction at 5 level
  to justify evaluating treatment effects in
  subsets
• was useful in the context of post-hoc subset
  analysis when drugs were non-specific cytotoxins,
  the subsets were not biology based and the prior
  probability of qualitative interactions was low
• is not useful for focused co-development of
  molecularly targeted drugs when the subset
  analysis is part of the primary analysis plan and
  the study-wise type I error is controlled
• is an example of how progress could be
  unnecessarily stymied by making co-development
  impracticably expensive

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• R Simon. Using genomics in clinical trial design,
  Clinical Cancer Research 145984-93, 2008
• R Simon. Designs and adaptive analysis plans for
  pivotal clinical trials of therapeutics and
  companion diagnostics, Expert Opinion in Medical
  Diagnostics 2721-29, 2008

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Analysis Plan A

• Compare the new drug to the control for
  classifier positive patients
• If pgt0.05 make no claim of effectiveness
• If p? 0.05 claim effectiveness for the
  classifier positive patients and
• Compare new drug to control for classifier
  negative patients using 0.05 threshold of
  significance

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Sample size for Analysis Plan A

• 88 events in classifier patients needed to
  detect 50 reduction in hazard at 5 two-sided
  significance level with 90 power
• 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
• Sequential futility monitoring may have enabled
  early cessation of accrual of classifier negative
  patients
• Not much earlier with time-to-event endpoint

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• Study-wise false positivity rate is limited to 5
  with analysis plan A
• It is not necessary or appropriate to require
  that the treatment vs control difference be
  significant overall before doing the analysis
  within subsets

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Analysis Plan B(Limited confidence in test)

• 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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• This analysis strategy is designed to not
  penalize sponsors for having developed a
  classifier
• It provides sponsors with an incentive to develop
  genomic classifiers

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Sample size for Analysis Plan B

• 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

• Test for difference (interaction) between
  treatment effect in test positive patients and
  treatment effect in test negative patients at an
  elevated level ?int (e.g. .10)
• 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

• 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

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Simulation Results for Analysis Plan C

• Using ?int0.10, 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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Does the RCT Need to Be Significant Overall for
the T vs C Treatment Comparison?

• No
• It is incorrect to require that the overall T vs
  C comparison be significant to claim that T is
  better than C for test patients but not for
  test patients
• That requirement has been traditionally used to
  protect against data dredging. It is
  inappropriate for focused trials of a treatment
  with a companion test.

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Development of Genomic Classifiers

• During phase II development or
• Adaptively during phase III trial
• Using archived specimens from previous phase III
  trial

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Biomarker Adaptive Threshold Design

• Wenyu Jiang, Boris Freidlin Richard Simon
• JNCI 991036-43, 2007

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Biomarker Adaptive Threshold Design

• Randomized trial of T vs C
• Have identified a biomarker score 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

• 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

• Test T vs C restricted to patients with biomarker
  B gt b
• Let S(b) be log likelihood ratio statistic
• Repeat for all values of b
• Let S maxS(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 bootstrap interval estimates of
  the threshold b

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Estimation of Threshold
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Estimated Power of Broad Eligibility Design
(n386 events) vs Adaptive Design A (n412
events) 80 power for 30 hazard reduction
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Procedure B

• S(b)log likelihood ratio statistic for treatment
  effect in subset of patients with B?b
• SmaxS(0)R, maxS(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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Sample Size Planning (A)

• 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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Sample Size Planning (B)

• 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
  80.6753
• 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 ? With
Proportional Hazards
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Events (D) Needed for Overall Test to Detect
Hazard Ratio ? Limited to Fraction ?
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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 80.6753
• Formula B.2 gives D230 events to have 53 power
  for overall test and thus approximate 80 power
  for B
• Overall test needs D472 events for 80 power for
  detecting the diluted treatment effect

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Multiple Biomarker Design

• Have identified K candidate binary classifiers B1
  , , BK thought to be predictive of patients
  likely to benefit from T relative to C
• Eligibility not restricted by candidate
  classifiers
• For notation let B0 denote the classifier with
  all patients positive

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• Test T vs C restricted to patients positive for
  Bk for k0,1,,K
• Let S(Bk) be log likelihood ratio statistic for
  treatment effect in patients positive for Bk
  (k1,,K)
• Let S maxS(Bk) , k argmaxS(Bk)
• For a global test of significance
• Compute null distribution of S by permuting
  treatment labels
• If the data value of S is significant at 0.05
  level, then claim effectiveness of T for patients
  positive for Bk

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• Test T vs C restricted to patients positive for
  Bk for k0,1,,K
• Let S(Bk) be log likelihood ratio statistic for
  treatment effect in patients positive for Bk
  (k1,,K)
• Let S maxS(Bk) , k argmaxS(Bk)
• The new treatment is superior to control for the
  population defined by k
• Repeating the analysis for bootstrap samples of
  cases provides
• an estimate of the stability of k (the
  indication)
• an interval estimate S (the size of treatment
  effect for the size of treatment effect in the
  target population)

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Adaptive Signature Design

• Boris Freidlin and Richard Simon
• Clinical Cancer Research 117872-8, 2005

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Adaptive Signature DesignEnd of Trial Analysis

• Compare E to C for all patients at significance
  level 0.04
• If overall H0 is rejected, then claim
  effectiveness of E 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 T based on
  classifier
• Perform test at significance level 0.01
• 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 (j1,,M)
• Select genes with interaction significant at
  level ?

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Classification of Stage 2 Patients

• For ith 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 ith 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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Treatment effect restricted to subset.10 of
patients sensitive, 10 sensitivity genes, 10,000
genes, 400 patients.
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Empirical PowerRR for Control Patients 25
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Cross-Validated Adaptive Signature Design(to be
submitted for publication)

• 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
  sensitive (classifier ) or insensitive
  (classifier -)
• 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

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• Compare T to C for sensitive patients by
  computing a test statistic S e.g. the difference
  in response proportions or log-rank statistic
  (for survival)
• Generate the null distribution of S by permuting
  the treatment labels and repeating the entire
  K-fold cross-validation procedure
• Perform test at significance level 0.05 -
  ?overall
• If H0 is rejected, claim effectiveness of T for
  subset defined by classifier
• The sensitive subset is determined by developing
  a classifier using the full dataset

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70 Response to T in Sensitive Patients25
Response to T Otherwise25 Response to C20
Patients Sensitive
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Does It Matter If the Randomization in the RCT
Was Not Stratified By the Test?

• No
• Stratification improves balance of stratification
  factors in overall comparisons
• Stratification does not improve comparability of
  treatment (T) and control (C) groups within test
  positive patients or within test negative
  patients.
• In a fully prospective trial, stratification of
  the randomization by the test is only useful for
  ensuring that all patients have adequate test
  performed

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Information about a predictive biomarker may
develop following completion of the pivotal
trials

• It may be infeasible to conduct a new
  prospective trial for a previously approved drug
• KRAS for anti-EGFR antibodies in colorectal
  cancer
• HER2 for doxorubicin in breast cancer

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• In some cases the benefits of a prospective trial
  can be closely achieved by the carefully planned
  use of archived tissue from a previously
  conducted randomized clinical trial

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Use of Archived Specimens in Evaluation of
Prognostic and Predictive BiomarkersRichard M.
Simon, Soonmyung Paik and Daniel F. Hayes

• Claims of medical utility for prognostic and
  predictive biomarkers based on analysis of
  archived tissues can be considered to have either
  a high or low level of evidence depending on
  several key factors.
• Studies using archived tissues, when conducted
  under ideal conditions and independently
  confirmed can provide the highest level of
  evidence.
• Traditional analyses of prognostic or predictive
  factors, using non analytically validated assays
  on a convenience sample of tissues and conducted
  in an exploratory and unfocused manner provide a
  very low level of evidence for clinical utility.

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Use of Archived Specimens in Evaluation of
Prognostic and Predictive BiomarkersRichard M.
Simon, Soonmyung Paik and Daniel F. Hayes

• For Level I Evidence
• (i) archived tissue adequate for a successful
  assay must be available on a sufficiently large
  number of patients from a phase III trial that
  the appropriate analyses have adequate
  statistical power and that the patients included
  in the evaluation are clearly representative of
  the patients in the trial.
• (ii) The test should be analytically and
  pre-analytically validated for use with archived
  tissue.
• (iii) The analysis plan for the biomarker
  evaluation should be completely specified in
  writing prior to the performance of the biomarker
  assays on archived tissue and should be focused
  on evaluation of a single completely defined
  classifier.
• iv) the results from archived specimens should be
  validated using specimens from a similar, but
  separate, study.

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Revised Levels of Evidence for Tumor Marker
Studies
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New Paradigms for Clinical Trials in Predictive
Medicine

• Developments in biotechnology have forced
  statisticians to focus on prediction problems
• This has led to important new methodological
  developments for pgtgtn problems in which number of
  genes is much greater than the number of cases
• Statistics has over-focused on inference. Many of
  the methods and much of the conventional wisdom
  of biostatistics are based on inference problems

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Some statisticians believe that accurate
prediction is not possible for pgtgtn

• Accurate prediction is often possible, but
  standard statistical methods for model building
  and evaluation are not effective

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• pgtn prediction problems are not multiple
  comparison problems
• Feature selection should be optimized for
  accurate prediction, not for controlling the
  false discovery rate
• Goodness of fit to training data should not be
  used to guide model building nor to evaluate
  model performance

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• Odds ratios, hazard ratios and statistical
  significance of regression coefficients are not
  proper measures of predictive accuracy

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• Validation of a predictive model means that the
  model predicts accurately for independent data

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Prediction Based Clinical Trials

• Using cross-validation we can evaluate new
  methods for analysis of clinical trials in terms
  of their intended use which is informing
  therapeutic decision making

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• fj(x) probability of response for patient with
  covariate vector x who receives treatment j

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Single Hypothesis Testing Based Decision Making
in an RCT

• Test H0 ExfT(x) ExfC(x)
• or fT(x) fC(x) for all x
• If you reject H0 then treat future patients with
  T, otherwise treat future patients with C

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Other Approaches
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Predicting the Effect of Analysis Methods on
Patient Outcome

• At the conclusion of the trial randomly partition
  the patients into 10 equally sized sets P1 , ,
  P10
• Let D-i denote the full dataset minus data for
  patients in Pi
• Using 10-fold complete cross-validation, omit
  patients in Pi
• Analyze trial using only data in D-i with both
  the standard analysis and the alternative
  analysis

126

• For each patient j in Pi record the
  cross-validated treatment recommendations based
  on D-i

127

• Let ST denote the set of cases for which the
  standard analysis recommends C and the
  alternative analysis recommends T
• Let SC denote the set of cases for which the
  standard analysis recommends T and the
  alternative analysis recommends C

128

• For patients in ST compare outcomes for patients
  who received T versus those who received C
• For patients in SC compare outcomes for patients
  who received T versus those who received C

129

• Hence, alternative methods for analyzing RCTs
  can be evaluated in an unbiased manner with
  regard to their value to patients using the
  actual RCT data

130
Conclusions

• New biotechnology and knowledge of tumor biology
  provide important opportunities to improve
  therapeutic decision making
• Treatment of broad populations with regimens that
  do not benefit most patients is increasingly no
  longer necessary nor economically sustainable
• The established molecular heterogeneity of human
  diseases requires the use new approaches to the
  development and evaluation of therapeutics

131
Conclusions

• Some of the conventional wisdom about statistical
  analysis of clinical trials is not applicable to
  trials dealing with co-development of drugs and
  diagnostic
• e.g. subset analysis if the overall results are
  not significant or if an interaction test is not
  significant or if the randomization was not
  stratified by the subsetting variable

132
Conclusions

• 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?
• The information doesnt have to be perfect to be
  much better than what we currently have

133
Conclusions

• Co-development of drugs and companion diagnostics
  increases the complexity of drug development
• It does not make drug development simpler,
  cheaper and quicker
• But it may make development more successful and
  it has great potential value for patients and for
  the economics of health care