Adaptive clinical trials

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Adaptive clinical trials

• Jørn Wetterslev M.D., Ph.D.
• Copenhagen Trial Unit
• Centre for Clinical Intervention Research
• Rigshospitalet

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Presentation

• Group sequential design
• Adaptive clinical trial designs
• Flexible clinical trial designs

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Group Sequential Design

• Strategy for design, decision, analysis at
  interim analyses in a single trial
• Criteria for considering stop and continuation of
  a single trial
• Developed through several stages from Pocock,
  Haybittle-Peto, OBrien- Flemming

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Group Sequential Design

• Do the interim-analysis after randomisation of
  each group of patients
• Stop when the boundary is exceeded
• Continue if the boundary is not exceeded
• Adjust final estimates of intervention effect,
  confidence interval and P-value if the trial is
  stopped early !

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Adaptive design

• You want to get both the possibility to stop
  early and to continue late
• Adds rules for adjustment of trial design and
  analyses as the trial data accumulate
• Jennison, Turnbull, etc.

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Adaptive design

• Assumes thoroughly planned fixed design (sample
  size, doses, subpopulation)
• Assumes thoroughly planned group sequential
  design for early stopping
• Assumes thoroughly planned possibility for
  adaptation for later stopping, e.g., sample size
  expansion

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Several possibilities for adaptivity

• Change of sample size after interim analysis
• Change of target population
• Focusing on relevant doses

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Adaptation

• Adaptation is possible, with preservation of type
  I error
• Adaptation is simplest when a re-design point is
  prespecified, with rules for how data before and
  after this point will be combined

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Adapting sample size

• A two-stage example with re-estimation of sample
  size after 1. stage
• Implications for analysis and testing
• Implications for power and effectiveness of
  significance testing

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Adapting sample size

• Two-stage example Bauer KÖhnes method
• After fixed sample size N/2 for stage 1
  calculate P1
• After this calculate new sample size for stage 2
  based on intervention effect ?1 and variance s12
  from stage 1
• Do stage 2 and calculate P2 on stage 2 data alone

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Final combined P-value when sample size is
adapted

• Bauer KÖhnes test Biometrics 1994
• - Ln(P1P2) gt ½ ?24,1-a
• The overall type I error rate a is attained
  exactly by combining P-values with this test
  originally proposed by Fisher 1932

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Adapting inclusion (change of target population)

• An example with change of target population
• Implications for analysis
• Two-stage adaptive design Adjust P-value for
  multiple hypotheses testing (family-wise error
  adjustment)

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Change of target population

• Stage 1 adaptive design Adjust P-value by
  testing multiple hypotheses
• H1 no overall effect in full population
• H2 no effect in sub-population
• H1 H2
• P1,1 Stage 1 P-value from H1
• P1,2 Stage 1 P-value from H2
• P1,12 Stage 1 P-value from both H1 and H2

2
1
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Change of target population

• P1,1 0.20 and P1,2 0.02
• Leads to by a conservative Hochberg (Bonferroni)
  adjustment
• P1,12 min2min (P1,1,P1,2),max(P1,1, P1,2)
  0.04

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Change of target population

• Stage 2 restricted to sub-population only
• H1 no overall effect in full population
• H2 no effect in sub-population
• H1 Men H2
• 
  Older men
• P2,1 Stage 2 P-value from H1 not available
• P2,2 Stage 2 P-value from H2
• P2,12 Stage 2 P-value from both H1 and H2 P2,2

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Change of target population

• P2,1 undefined (or 1) as hypothesis effect in
  full population cannot be tested in subpopulation
  in stage 2
• P2,2 0.03 and P2,12 P2,2 0.03

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Change of target population

• P1,12 0.04
• P2,12 0.03
• Combining results from the two stages
• Final adjusted P maxP2 , P12 0.005

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Adapting doses

• In a trial starting out with multiple arms of
  different doses you may want to focus on only a
  few in stage 2 of the trial
• Essentially this implies re-using only a subgroup
  from stage 1 in the final analysis of both stages

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Dangers in adaptive design

• Expansion of sample size should be possible
  before the start of the trial
• Patient recruitment is logistically and
  economically feasible
• Or we will end up with a lot of trials stopped
  early for quasi futility

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Adaptive design is not necessarily flexible !

• In adaptive designs all potential modifications
  are approved up front from regulatory authorities
• Sponsor must be blinded
• Responsibilities to implement changes falls to
  the data safety monitoring board (DSMB)

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Flexible design

• Unplanned changes without rules for when to
  change and how to change
• Implications for analysis
• The self designing trial ?
• (L. Fisher, Biometrics 1998)
• Loss of credibility, loss of efficiency, loss of
  blinding !?!
• Statistically odd / anomalous results (Burman
  Biometrics 2006)

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Adaptation / flexibility

• Unplanned adaptation is possible, as long as
  conditional type I error probability under the
  original design can be evaluated at the re-design
  point
• Flexible adaptive methods allow investigators to
  respond to un-anticipated developments
• Postponing some decisions at the design stage to
  be dealt with flexibly later - can create
  drawbacks with overenthusiastic use of flexible,
  adaptaive methods

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Advice

• Use group seqential design
• Start large and stop small if intervention effect
  is larger or variance is smaller than anticipated
• If adaptive design use rigid adaptation with
  everything planned from start of trial including
  statistical analyses and finance

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Thank you for your attention
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Background

• If 5 defects has been chosen as quality limit
  for the production of 1000 items
• and
• 50 items after passing of 100 items is defective
  there is no need to pass more items to reach the
  predefined quality limit !

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Stopping early for benefit

• Victor Montori et al. JAMA 2005
• 85 of trial stopped early for benefit did not
  correct p-values, C.I., and intervention effects
• Large overestimation of intervention effect when
  compared with large trials or meta-analyses

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Group Sequential Design

• Decide for the number of looks number of groups
  and the overall nominal ? ??i
• Decide the type of ?- spending to use
• Decide for ? which will eventually define the
  group size and calculate the fixed sample size
• Calculate the adjusted maximum sample size by
  multiplying fixed sample size with the adjusting
  factor from appropriate tables

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Group Sequential Interim-looks

• Test after each group i of acumulated data until
  a critical value of Z (or p) is reached or until
  maximum estimated sample size is reached
• Zi gt critical value Ci STOP
• Zi lt critical value Ci CONTINUE
• K-groups

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The Z - statistic

• Continuous variable X N(X, SD2)

X1 - X2
Z
(X1 - X2) ? I
SD
1
1
I Information

SD
?Var
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Zi statistic at the i-te interim-analysis

• Continuous variable X N(X, SD2)

X1i - X2i
Zi
(X1i - X2i) ? Ii
SDi
If k analyses then (Z1, .., Zk)
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Critically values ci of Z

• K interim looks (one-sided)
• c1 , c2 ,, ci ,., ck-1 , ck
• Z1 lt c1 , Z2 lt c2 ,, Z2 gtci
• Find cs recursively starting with c1
• then c2 ,. , ck-1 , ck

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Critically values ci of Zi

• Find cs recursively starting with c1 then c2 ,.
  , ci-1 , ci ,, ck
• With ci satisfying
• PrZ1ltc1 , Z2 lt c2 ,., Zk-1ltci-1, Zigt ci ai
• under H0 and a1 ak a

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Group Sequential Boundary
Zk
Reject H0
C1
C2
C3
C4
Z?
-1.96 (plt0.025)
IF2
IF1
IF3
IF4
100
(N IS)
(Number of patients randomised)
IFk Ik / IMax
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Group Sequential Boundaries
Zk
Reject H0
Z2
Z?
-1.96 (plt0.025)
Accept H0
IF2
IF1
IF3
IF4
100
(Number of patients randomised)
IFk Ik / IMax
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References

• Gordon Lan David DeMets 1983
• Jennison Turnbull, GSD
• Phrma
• Burmann Is flexible desigs sound?
• Susan Todd, Statistics in Medicine 2006