Satellite Symposium

1
Bayesian posterior predictive probability - what
do interim analyses mean for decision making?
Oscar Della Pasqua Gijs Santen Clinical
Pharmacology Modelling Simulation,
GlaxoSmithKline, UK Division of Pharmacology,
Leiden University, The Netherlands
2
Time course of HAMD in Depression
3
Linear mixed-effects model

• HAMD response
• Yij baselineibaseffectj tmteffectz,j ?1i
  ?2ij eij
• ? Fixed Effects
• Interaction baselinetime
• Interaction treatment effecttime
• ? Two Random Effects
• multivariate distribution with mean 0 and unknown
  variance-covariance matrix
• ? Residual Error

See Santen et al, Clin Pharmacol Ther, Sept 2009.
4
Model fitting
5
Diagnostics Goodness-of-fit
6
Diagnostics NPDE
One random effect (same MLE as MMRM)
New model with two random effects
7
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

8
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.

9
Major issues for an interim analysis (IA)
recruitment rate, study duration and timing of IA
10
Timing enrolment impact of recruitment rate
450
450
Patients in study
Completers line
150
150
Completers line
0
0
0
0
56
180
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
11
Timing enrolment impact of treatment duration
450
Patients in study
150
0
0
56
180
Time (days from start of enrolment)
Shorter treatment duration ? earlier interim
analysis, more impact
12
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?

13
Simulate dataset from historical trials with1.
negative treatment arm (? HAMD0)2. positive
treatment arm (? HAMD2)
Incoming data on enrolment
14
Posterior Predictive Power
Data obtained until time t is analysed using the
longitudinal model
WinBUGS MCMC
Posterior distributions
1000 new trials are simulated with the projected
number of patients from these posterior
distributions. Conditional power is computed
Posterior Predictive Power ..
15
Interim analysis Decisions
Density
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)

16
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

17
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.

18
Selection of timing criteria
90
95
(power type I error)
19
Determining timing criteria
Parameters Futility goalpost at 45 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!

• Additional conditions
• Inefficacious treatment arm should be stopped
  for efficacy in lt5 (Type I error)
• Treatment arm ? 2 points HAMD should be
  stopped for futility in lt20 (Type II error)

20
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.

21

• The success of RD to address unmet medical
  needs does not depend only on finding new
  targets, it depends on better decision making.