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ADAPTIVE BAYESIAN DESIGNS FOR DOSE RANGING DRUG

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ADAPTIVE BAYESIAN DESIGNS FOR DOSE RANGING DRUG Powered By Docstoc
					      WHY BAYES?
INNOVATIONS IN CLINICAL
TRIAL DESIGN & ANALYSIS
       Donald A. Berry
   dberry@mdanderson.org
Conclusion These data add to the growing evidence that
supports the regular use of aspirin and other NSAIDs … as
effective chemopreventive agents for breast cancer.




                                                            2
Results Ever use of aspirin or other NSAIDs … was
reported in 301 cases (20.9%) and 345 controls (24.3%)
(odds ratio 0.80, 95% CI 0.66-0.97).




                                                         3
  Bayesian analysis?
      Bayesian analysis of
 Naïve
 ―Results‖ is wrong
 Gives   Bayesians a bad
 name
 Anynaïve frequentist
 analysis is also wrong
                             4
What is Bayesian analysis?
 Bayes' theorem:
     '( q| X )  (q) * f( X | q )
  Assess prior  (subjective,
   include available evidence)
  Construct model f for data


                                       5
      Implication:
The Likelihood Principle
Where X is observed data,
the likelihood function
       LX(q) = f( X | q )
contains all the information
in an experiment relevant for
inferences about q
                                6
 Shortversion of LP:
 Take data at face value
 Data:
   Among cases:       301/1442
   Among controls:    345/1420
 But   ―Data‖ is deceptive
 These   are not the full data
                                  7
              The data
 Methods:
   ―Population-based  case-control
    study of breast cancer‖
   ―Study design published previously‖

 Aspirin/NSAIDs?  (2.25-hr ?naire)
 Includes superficial data:
   Among cases:        301/1442
   Among controls:     345/1420
 Other   studies (& fact published!!)
                                         8
    Silent multiplicities

 Are the most difficult problems in
 statistical inference
    render what we do irrelevant
 Can
 —and wrong!


                                   9
                                       
Which city is furthest north?
     Portland,   OR
     Portland,   ME
     Milan,   Italy
     Vladivostok,     Russia

                                10
    Beating a dead horse . . .
 Piattelli-Palmarini (inevitable illusions)
  asks: ―I have just tossed a coin 7 times.‖
  Which did I get?
    1: THHTHTT
    2: TTTTTTT
 Most people say 1. But ―the probabilities
  are totally even‖
 Most people are right; he’s totally wrong!
 Data: He presented us with 1 & 2!
                                          11
     THHTHTT or TTTTTTT?
   LR = Bayes factor of 1 over 2 =
           P(Wrote 1&2 | Got 1)
           P(Wrote 1&2 | Got 2)
 LR > 1  P(Got 1 | Wrote 1&2) > 1/2
 Eg: LR = (1/2)/(1/42) = 21 
  P(Got 1 | Wrote 1&2) = 21/22 = 95%
 [Probs ―totally even‖ if a coin was used
  to generate the alternative sequence]
                                        12
      Marker/dose interaction
  Marker negative Marker positive
  1.0                                          1.0
  0.9                                          0.9
  0.8                       Std (96)           0.8                             Hi (38)
  0.7                                          0.7
D                                            D
F 0.6               Low (93)                 F 0.6                           Std (41)
S 0.5                          Hi (95)       S 0.5
  0.4                                          0.4
                                                                     Low (36)
  0.3                                          0.3
  0.2                                          0.2
  0.1                                          0.1
  0.0                                          0.0
        0   1   2   3 4        5    6    7           0   1   2   3 4     5      6        7
                    Years                                        Years
                                                                                    13
Proportional hazards model
Variable      Comp       RelRisk     P
#PosNodes     10/1        2.7      <0.001
MenoStatus    pre/post    1.5       0.05
TumorSize     T2/T1       2.6      <0.001
Dose          ––          ––        NS
Marker        50/0        4.0      <0.001
MarkerxDose   ––          ––       <0.001
This analysis is wrong!
                                            14
  Data at face value?
 How   identified?
 Why am I showing you these
 results?
 What   am I not showing you?
 What   related studies show?

                                 15
              Solutions?
 Short answer: I don’t know!
 A solution:
   Superviseexperiment yourself
   Become an expert on substance
 Partial   solution:
   Supervise supervisors
   Learn as much substance as you can
 Danger: You risk projecting
 yourself as uniquely scientific
                                     16
      A consequence

 Statisticians   come to believe
 NOTHING!!




                                    17
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        18
Bayes in pharma
  and FDA …




                  19
http://www.cfsan.fda.gov/~frf/bayesdl.html
http://www.prous.com/bayesian2004/
      BAYES AND
PREDICTIVE PROBABILITY

          component of
   Critical
   experimental design


   In   monitoring trials

                             23
Example calculation
  Data:   13 A's and 4 B's

  Likelihood    p13 (1–p)4



                               24
    Posterior density of p
for uniform prior: Beta(14,5)

                         13   4
                        p (1–p)




     0   .1   .2   .3   .4   .5   .6   .7   .8       .9   1
                                                 p            25
      Laplace’s rule of
        succession
P(A wins next pair | data)
 = EP(A wins next pair | data, p)
 = E(p | data)
 = mean of Beta(14, 5)
 = 14/19
                                26
Updating w/next observation
                                                    Beta(15, 5)

                  Beta(14, 6)



           prob 5/19                                     prob 14/19




  0   .1     .2   .3   .4   .5   .6   .7   .8       .9    1
                                                p
                                                                      27
     Suppose 17 more
       observations
P(A wins x of 17 | data)
= EP(A wins x | data, p)
=E   [( )
      17
      x    p x(1–p)17–x   | data, p]
                                      28
    Best fitting binomial vs.
    predictive probabilities
Binomial, p=14/19




0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17


Predictive, p ~ beta(14,5)



0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17

                                                                                29
Comparison of predictive
    with posterior
                       13   4
.15                   p (1–p)



.10




.05




.00
       1    3
  0 0 .1 2 .2 4 .35   6.47   8 9 10 11 .7 13 .8 15 .9 17 1
                                       12     14    16
                             .5 .6
                                                p            30
 Example: Baxter’s DCLHb &
   predictive probabilities
          Cross-Linked Hemoglobin
 Diaspirin
 Blood substitute; emergency trauma
 Randomized controlled trial (1996+)
   Treatment:  DCLHb
   Control: saline
   N = 850 (= 2x425)
   Endpoint: death

                                   31
 Waiver of informed consent
 Data Monitoring Committee
 First DMC meeting:
             DCLHb      Saline
  Dead       21 (43%)    8 (20%)
  Alive      28         33
  Total      49         41
 P-value?   No formal interim analysis
                                      32
  Predictive probability of
future results (after n = 850)
  Probability of significant
   survival benefit for DCLHb
   after 850 patients: 0.00045
  DMC   paused trial: Covariates?
  No   imbalance
  DMC   stopped trial
                                     33
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        34
       BAYES AS A
    FREQUENTIST TOOL
 Design  a Bayesian trial
 Check operating characteristics
 Adjust design to get  = 0.05
  frequentist design
 That’s fine!
 We have 50+ such trials at MDACC

                                 35
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        36
    ADAPTIVE DESIGN
 Look at accumulating data …
  without blushing
 Update probabilities
 Find predictive probabilities
 Modify future course of trial
 Give details in protocol
 Simulate to find operating
  characteristics
                                  37
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        38
        Giles, et al JCO (2003)
 Troxacitabine(T) in acute myeloid
 leukemia (AML) when combined with
 cytarabine (A) or idarubicin (I)
 Adaptive   randomization to:
               IA vs TA vs TI
 Max   n = 75
 End   point: CR (time to CR < 50 days)
                                       39
          Randomization
 Adaptive

 Assign1/3 to IA (standard)
 throughout (unless only 2 arms)
 Adaptive to TA and TI based on
 current results
 Final   results   
                                   40
Patient   Prob IA   Prob TA   Prob TI   Arm   CR<50
   1       0.33      0.33      0.33     TI     not
   2       0.33      0.34      0.32     IA     CR
   3       0.33      0.35      0.32     TI     not
   4       0.33      0.37      0.30     IA     not
   5       0.33      0.38      0.28     IA     not
   6       0.33      0.39      0.28     IA     CR
   7       0.33      0.39      0.27     IA     not
   8       0.33      0.44      0.23     TI     not
   9       0.33      0.47      0.20     TI     not
  10       0.33      0.43      0.24     TA     CR
  11       0.33      0.50      0.17     TA     not
  12       0.33      0.50      0.17     TA     not
  13       0.33      0.47      0.20     TA     not
  14       0.33      0.57      0.10     TI     not
  15       0.33      0.57      0.10     TA     CR
  16       0.33      0.56      0.11     IA     not
  17       0.33      0.56      0.11     TA     CR
                                                      41
   Patient    Prob IA   Prob TA   Prob TI   Arm   CR<50
     18        0.33      0.55      0.11     TA     not
     19        0.33      0.54      0.13     TA     not
     20        0.33      0.53      0.14     IA     CR
     21        0.33      0.49      0.18     IA     CR
     22        0.33      0.46      0.21     IA     CR
                                            IA
Drop 23        0.33      0.58      0.09            CR
     24        0.33      0.59      0.07     IA     CR
 TI 25         0.87      0.13        0      IA     not
     26        0.87      0.13        0      TA     not
     27        0.96      0.04        0      TA     not
     28        0.96      0.04        0      IA     CR
     29        0.96      0.04        0      IA     not
     30        0.96      0.04        0      IA     CR
     31        0.96      0.04        0      IA     not
     32        0.96      0.04        0      TA     not
     33        0.96      0.04        0      IA     not
     34        0.96      0.04        0      IA     CR
                                                          42
             Compare n = 75
Summary of results

CR rates:
  IA: 10/18 = 56%
  TA: 3/11 = 27%
  TI:   0/5 = 0%
Criticisms . . .
                     43
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        44
       Example: Adaptive
     allocation of therapies
 Design for phase II: Many drugs
 Advanced breast cancer (MDA);
  endpoint is tumor response
 Goals:
    Treat effectively
    Learn quickly
                                    45
          Comparison:
        Standard designs
 One drug (or dose) at a time;
  no drug/dose comparisons
 Typical comparison by null
  hypothesis:
  response rate = 20%
 Progress is slow!

                                  46
        Standard designs
 One   stage, 14 patients:
  If 0 responses then stop
  If ≥ 1 response then phase III

 Two stages, first stage 20
 patients:
  If≤ 4 or ≥ 9 responses then stop
  Else second set of 20 patients
                                      47
    An adaptive allocation
 When   assigning next patient, find
  r = P(rate ≥ 20%|data) for each drug
  [Or, r = P(drug is best|data)]
 Assign drugs in proportion to r
 Add drugs as become available
 Drop drugs that have small r
 Drugs with large r  phase III

                                     48
Suppose 10 drugs, 200 patients
  9 drugs have mix of response rates
  20% & 40%, 1 (―nugget‖) has 60%
 Standard 2-stage design finds nugget
  with probability < 70% (After 110
  patients on average)
 Adaptive design finds nugget with
  probability > 99% (After about 50
  patients on average)
 Adaptive also better at finding 40%

                                         49
Suppose 100 drugs, 2000 patients
 99 drugs have mix of response rates
  20% & 40%, 1 (―nugget‖) has 60%
 Standard 2-stage design finds nugget
  with probability < 70% (After 1100
  patients on average)
 Adaptive design finds nugget with
  probability > 99% (After about 500
  patients on average)
 Adaptive also better at finding 40%

                                         50
        Consequences
 Recall   goals:
  (1) Treat effectively
  (2) Learn quickly
 Attractive   to patients, in and out
  of the trial
 Better drugs identified faster;
  move through faster
                                         51
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        52
Example: Seamless phase II/III

 Drug   vs placebo, randomized
 Local  control (or biomarker, etc):
  early endpoint related to survival?
 May   depend on treatment


                                    53
   *Inoue et al (2002 Biometrics)
Conventional drug development
                          Survival
        Local            advantage Market
       control           No survival
                         advantage     Not
       No local
        control Stop
   Phase II               Phase III

    6 mos   9-12 mos       > 2 yrs

     Seamless phase II/III
     < 2 yrs (usually)                       54
        Seamless phases
 Phase II: Two centers; 10 pts/mo.
  drug vs placebo. If predictive
  probabilities look good, expand to
 Phase III: Many centers; 40+ pts/mo.
  (Initial centers accrue during set-up)
 Max sample size: 900

[Single trial: survival data from both
 phases combined in final analysis]
                                           55
            Early stopping
 Use predictive probs of stat. signif.
 Frequent analyses (total of 18)
  using predictive probabilities:
   To switch to Phase III
   To stop accrual
     For futility
     For efficacy

   To   submit NDA
                                      56
      Comparisons

Conventional Phase III designs:
Conv4 & Conv18, max N = 900
(same power as adaptive design)




                                  57
Expected N under H0
1000
                            884
                   855
 800


 600

           431
 400


 200


       0
           Bayes   Conv4   Conv18

                                    58
Expected N under H1
1000
                   887      888

 800

           649
 600


 400


 200


       0
           Bayes   Conv4   Conv18
                                    59
               Benefits
 Durationof drug development is
 greatly shortened under adaptive
 design:
   Fewer  patients in trial
   No hiatus for setting up phase III
   Use all patients to assess phase III
    endpoint and relationship between
    local control and survival
                                           60
     Possibility of large N
N   seldom near 900
 When   it is, it’s necessary!
 Thispossibility gives Bayesian
 design its edge
 [Other reason for edge is
 modeling local control/survival]

                                    61
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        62
                                    *




*Berry, et al. Case Studies in Bayesian Statistics 2001
     Example: Stroke and
    adaptive dose-response
 Adaptive   doses in Phase II setting:
  learn efficiently and rapidly about
  dose-response relationship
 Pfizer trial of a neutrofil inhibitory
  factor; results recently announced
 Endpoint: stroke scale at week 13
 Early endpoints: weekly stroke scale
                                      64
Standard Parallel Group Design
Equal sample sizes at each of k
 doses.




                Doses             65
True dose-response curve
       (unknown)
 Response




            Doses          66
Observe responses (with error)
      at chosen doses
   Response




              Doses          67
Dose at which 95% max effect
   Response




                      True ED95




              Doses               68
Uncertainty about ED95
Response




                  True ED95




           Dose
                         ?    69
Uncertainty about ED95
Response




           Dose
                         ?   70
        Solution:
Increase number of doses
  Response




                     ED95




                            71
             Doses
But, enormous sample size, and . . .
wasted dose assignments—always!
      Response




                            ED95




                                   72

                    Doses
  Our adaptive approach
 Observe  data continuously
 Select next dose to maximize
  information about ED95, given
  available evidence
 Stop dose-ranging trial when
  know ED95 & response at ED95
  ―sufficiently well‖


                                  73
    Our approach (cont’d)
Info accrues         Longitudinal Model
                Copenhagen Stroke Database
gradually       50

                40
about each      30
patient;        20

prediction      10


using            0

                -10
longitudinal    -20

model           -30
                     -40 -30 -20 -10 0 10 20 30 40 50
                       Difference from baseline in SSS week 3

                                                            74
  Our approach (cont’d)

 Modeldose-response
 (borrow strength from
 neighboring doses)
 Many   doses (logistical issues)


                                 75
Possible decisions each day:
 Stop trial and drug’s development
 Stop and set up confirmatory trial
 Continue dose-finding (what dose?)

Size of confirmatory trial based on
 info from dose-ranging phase
Choices by decision analysis (Human
 safeguard: DSMB)
                                   76
      Dose-response trial
 Learn efficiently and rapidly about
  dose-response; if + go to Phase III
 Assign dose to maximize info
  about dose-response parameters
  given current info
 Use predictive probabilities, based
  on early endpoints
 Doses in continuum, or preset grid
                                        77
Dose-response trial (cont’d)
 Learn   about SD on-line
     dose-ranging when know
 Halt
 dose sufficiently well
 Seamless   switch from dose-
 ranging to confirmatory trial—
 2 trials in 1!

                                  78
          Advantages over
          standard design
 Fewer  patients (generally);
  faster & more effective learning
 Better at finding ED95
 Tends to treat patients in trial
  more effectively
 Drops duds early —actual trial!

                                 79
      Dose-assignment
         simulation
 Assumes  particular dose-
  response curve
 Assumes SD = 12

 Shows weekly results, several
 patients at a time (green circles)

                                  80
                        Prior
       30
       25
       20
E(f)

       15
       10
       5
       0




            0.0   0.5           1.0   1.5
                                            81
                         DOSE
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              82
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              83
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              84
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              85
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              86
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              87
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              88
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              89
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              90
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              91
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              92
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              93
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              94
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              95
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              96
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




         0.0       0.5                        1.0       1.5
                                                              97
                                DOSE
               green=obs, blue=imputed, black=true mn
                              DATA
    30
    25
    20
    15
Y

    10
    5
    0




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                                                              98
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                                                              99
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                                                              100
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                                                              101
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                                                              104
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                                                              105
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                                                              106
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                                                              115
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                                                              116
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                                                              117
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                                                              122
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                                                              123
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                                                              124
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                                                              125
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                                                              126
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                                                              127
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                                                              128
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                                                              129
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                                                              130
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                                                 Estimated
                                                   ED95
    0




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                                                        Confirmatory
                   Ao e s n
                   sD e il
                   s s km
                   i d y-
                   ge
                   ns
                    e b oa
                        nt
                       Wu o
                         ei
  1.5    1.5
         1.0
0.5
  0.DOSE 1.0
         0.5
         0.0




               0    0
                    1   0
                        2   0
                            3
                                134
                        E
                        E
                        K
                        W
                Estimated f unctions
    20
    15




                                              d:/data/build13/run11/
    10
F

    5
    0




         0.0   0.5               1.0   1.5
                                             135
                         Z
                                Doses assigned across all simulations
             0.14




                                                                                                                      20
             0.12




                                                                                                                      15
             0.10
             0.08
Proportion




                                                                                                                      10
             0.06
             0.04




                                                                                                                      5
             0.02
             0.0




                                                                                                                      0
                    0   0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1   1.1   1.2   1.3   1.4   1.5
                                                                                                                136
                                                  ASSIGNED DOSES
                              Black: median; Red: upper & lower quartiles; Green: Nominal
                Estimated f unctions (no dose effect)
    20
    15




                                                           d:/data/build13/run12/
    10
F

    5
    0




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                                                          137
                         Z
                                Doses assigned across all simulations




                                                                                                                      20
             0.25
             0.20




                                                                                                                      15
             0.15
Proportion




                                                                                                                      10
             0.10




                                                                                                                      5
             0.05
             0.0




                                                                                                                      0
                    0   0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1   1.1   1.2   1.3   1.4   1.5
                                                                                                                138
                                                  ASSIGNED DOSES
                              Black: median; Red: upper & lower quartiles; Green: Nominal
  Consequences of Using
Bayesian Adaptive Approach
 Fundamental     change in the
  way we do medical research
 More rapid progress
 We’ll get the dose right!
 Better treatment of patients
 . . . at less cost
                                  139
              Reactions
 FDA:  Positive. ―Makes coming to
 work worthwhile.‖ ―In five years
 all trials may be seamless.‖
 Pfizer   management: Enthusiastic
 Other    companies: Cautious

                                  140
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        141
 Example: Extraim analysis
 Endpoint: CR (detect 0.42 vs 0.32)
 80% power: N = 800
 Two extraim analyses, one at 800
 Another after up to 300 added pts
 Maximum n = 1400 (only rarely)
 Accrual: 70/month
 Delay in assessing response
                                       142
 After 800 patients, have response
  info on 450
 Find predictive probability of stat
  significance when full info on 800
 Also when full info on 1400
 Continue if . . .
 Stop if . . .
 If continue, n via predictive power
 Repeat at second extraim analysis
                                        143
Table 1: p0=0.42
   p1     P(succ)   meanSS    sdSS    P(800)   P(1400)   P(succ1)   P(succ2)
  0.37 0.0001        844.6    122.0   0.8707   0.0194    0.0001     0.0001
  0.42 0.0243       1011.2    247.6   0.5324   0.2360    0.0084     0.0059
  0.47 0.4467       1188.5    254.5   0.2568   0.5484    0.1052     0.0914
  0.52 0.9389       1049.9    248.7   0.4435   0.2693    0.4217     0.2590
  0.57 0.9989        874.2    149.1   0.7849   0.0268    0.7841     0.1729

Table 2: p0=0.32
   p1     P(succ)   meanSS    sdSS    P(800)   P(1400)   P(succ1)   P(succ2)
  0.27 0.0001        836.5    111.1   0.8937   0.0152    0.0005     0.0000
  0.32 0.0284       1013.1    246.3   0.5238   0.2338    0.0094     0.0083
  0.37 0.4757       1186.6    252.0   0.2513   0.5339    0.1083     0.1044
  0.42 0.9545       1045.5    245.9   0.4485   0.2449    0.4316     0.2505
  0.47 0.9989        922.7    181.0   0.6632   0.0258    0.6632     0.2111
                    vs 0.80
Table 3: p0=0.22
   p1     P(succ)   meanSS    sdSS    P(800)   P(1400)   P(succ1)   P(succ2)
  0.17 0.0000        827.7     95.3   0.9163   0.0086    0.0000     0.0000
  0.22 0.0288       1013.3    246.6   0.5242   0.2340    0.0090     0.0062
  0.27 0.5484       1199.0    246.3   0.2313   0.5392    0.1089     0.1063
  0.32 0.9749       1074.4    234.8   0.3702   0.2030    0.3577     0.2065
  0.37 0.9995       1024.7    205.4   0.4121   0.0508    0.3977     0.1685
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        145
 Decision-analytic approach
 For each trial design …
 List possible results
   Calculate their predictive probabilities
   Evaluate their utilities

 Average    utilities by probabilities to
  give utility of trial with that design
 Compare utilities of various designs
 Choose design with high utility
                                           146
   Choosing sample size*
 Special case of above
 One utility: Effective overall
  treatment of patients, both those
   after the trial
   in the trial

 Example,dichotomous endpoint:
 Maximize expected number of
 successes over all patients
                                      147
  *Cheng et al (2003 Biometrika)
     Compare Joffe/Weeks
      JNCI Dec 18, 2002
―Many respondents viewed the main
societal purpose of clinical trials as
benefiting the participants rather than as
creating generalizable knowledge to
advance future therapy. This view, which
was more prevalent among specialists
such as pediatric oncologists that
enrolled greater proportions of patients
in trials, conflicts with established
principles of research ethics.‖
                                         148
         Maximize effective
         treatment overall
 What    is ―overall‖?
    patients who will be treated
 All
 with therapies assessed in trial
 Call   it N, ―patient horizon‖
 Enough     to know mean of N
 Enough to know magnitude of N:
 100? 1000? 1,000,000?
                                    149
   Goal: maximize expected number of successes in N
   Either one- or two-armed trial
   Suppose n = 1000 is right for N = 1,000,000
   Then for other N’s use n =




                                                   150
Optimal allocations
in a two-armed trial




                       151
Knowledge about success rate r
                                 152
              OUTLINE
 Silentmultiplicities
 Bayes and predictive probabilities
 Bayes as a frequentist tool
 Adaptive designs:
   Adaptive randomization
   Investigating many phase      II drugs
   Seamless Phase II/III trial
   Adaptive dose-response
   Extraim analysis
 Trial   design as decision analysis        153

				
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