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					Oscar Della Pasqua & Gijs Santen
Clinical Pharmacology Modelling & Simulation, GlaxoSmithKline, UK
Division of Pharmacology, Leiden University, The Netherlands
Time course of HAMD in Depression
Linear mixed-effects model
 HAMD response

  Yij = baselinei*baseffectj + tmteffectz,j + η1i + η2i*j + εij

   Fixed Effects
       Interaction baseline*time
       Interaction treatment effect*time

    Two Random Effects
       multivariate distribution with mean 0 and unknown variance-
        covariance matrix

    Residual Error
 See Santen et al, Clin Pharmacol Ther, Sept 2009.
Model fitting
Diagnostics – Goodness-of-fit
   Diagnostics – NPDE




One random effect (same MLE as MMRM)   New model with two random effects
Typical clinical trial design

 2 active treatment arms, one placebo arm
 150 patients per arm
 Trial duration of 6-8 weeks
 Observations every 1-2 weeks
 Endpoint: HAMD
 Statistical analysis: LOCF / MMRM
Interim analysis: current situation
   ~50% of trials fail. Early detection of failing trials is
    worthwhile!


   Important factors for an interim analysis include recruitment
    rate, treatment duration, timing of IA

   Even though recruitment rate is not known at the start of the
    study, criteria for and timing of interim analysis is defined
    a priori.

   Inaccurate expectation about the informative value and
    risk of making a wrong decision.
Major issues for an interim analysis (IA):
   recruitment rate, study duration and timing of IA
Timing & enrolment: impact of recruitment
rate
Patients in study




                    450                                            450

                                               ‘Completers line’


                    150                                            150
                                                                                                 ‘Completers line’

                      0                                              0
                          0     56                   180                 0   56                  180

                      Time (days from start of enrolment)           Time (days from start of enrolment)




                          The slower recruitment the higher the impact of an interim analysis
 Timing & enrolment: impact of treatment
 duration
                                             ‘Completers line for a
                                             shorter treatment duration
Patients in study




                    450                                                   450


                                               ‘Completers line’ for
                    150                        a longer treatment         150

                      0                                                     0
                          0     56                  180                         0   56               180
                     Time (days from start of enrolment)                   Time (days from start of enrolment)




                              Shorter treatment duration  earlier interim analysis, more impact
Interim analysis

   Which parameter should be used to infer decisions?

   What about the timing of the interim analysis?
    - When is enough information available?

   How to best compare different decision criteria?
    Incoming data on enrolment     Simulate dataset from historical trials with:
                                   1. negative treatment arm ( HAMD=0)
1                                  2. positive treatment arm ( HAMD=2)




                 Interim analysis is performed on
2                the simulated datasets using the
                       actual enrolment data



                  Best performing decision criteria
3
                      and timing are selected




               Decision is made whether analysis is
4
                 performed now or is postponed.
Posterior Predictive Power
  1   Data obtained until                  WinBUGS
      time t is analysed
                                           MCMC
      using the longitudinal
      model



  2
      BOOTSTRAP                    Posterior distributions




  3    1000 new trials are simulated with the
       projected number of patients from
       these posterior distributions.
       Conditional power is computed


                 Posterior Predictive Power: ..%
Interim analysis: Decisions

          Goalpost for                           Goalpost for
          stopping for                           stopping for
          futility                               efficacy
Density




                         Surface
                         required to
                         trigger
                         decision

                           Posterior predictive power (%)

Decision criteria to be determined:
•Futility goalpost (e.g. 50%)
•Efficacy goalpost (e.g. 90%)
•Degree of evidence required to trigger a decision (e.g. 85%)
Choice of decision criteria
 Main goal is to maximise difference between ‘power’ and ‘type I error’

 Type I error may never be higher than 5%, type II error should remain
   below 20%

 This is done separately for futility and efficacy testing

 STOP efficacious treatment arms for efficacy, but not at the cost of
  inflating the false positive rate

 STOP non-efficacious treatment arms for futility without inflating the false
  negative rate
Interim Analysis - An example
 3 treatment arms
 150 patients / arm
 Paroxetine CR 12.5 mg, 25 mg and placebo
 Study design includes clinical assessments at weeks
    1,2,3,4,6 and 8

   An interim analysis is initially proposed with at least 25%
    completers, around day 70 from the start of enrolment.
     – Assess impact of recruitment rate on timing and
     – Determine optimal decision criteria for the IA.
                         Selection of timing & criteria

                                                               Goalpost for                           Goalpost for
                                                               stopping for                           stopping for
                                  90%                          futility                               efficacy
(power – type I error)




                                                     Density
                                         95%                                  Surface
                                                                              required to
                                                                              trigger
                                                                              decision

                                                                                Posterior predictive power (%)
                          Decision boundary (%PPP)
                         Determining timing & criteria
                                                                              Recruitment rate
                                     Parameters:
                                     Futility goalpost at 45%




                                               Cumulative patient enrolment
                                     Efficacy goalpost at 60%
                                     Degree of evidence at 85% (both)
(power – type I error)




                                     Use of the proposed implementation for the
                                     interim analysis of data from the actual trial did
                                     result in the correct decision!
                                                                                     Day




           Additional conditions:
           - Inefficacious treatment arm should be stopped for efficacy in <5% (Type I error)
           - Treatment arm  = 2 points HAMD should be stopped for futility in <20% (Type II error)
Conclusions
 Decisions about futility and efficacy during and IA are affected by
   enrolment rate.

 Historical clinical data can be used in a Bayesian framework to optimise
   an interim analysis.

 In contrast to adaptive design protocols, the proposed method
   optimises the criteria and the timing at which decisions should be made
   about futility and efficacy.

 The uncertainty of parameters estimates obtained at the interim
   analysis is factored in a Bayesian framework.

 Work in progress to show the application of the methodology in other
   therapeutic indications.
The success of R&D to address unmet medical
needs does not depend only on finding new targets,
it depends on better decision making.

				
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