GÜNTER HEIMANN Model-Based Tests for TQT Trials Introduction Summary of Methods Type I Error Summary and Conclusions version 0.2 1 Model-Based Tests for Thorough QTc Trials CSRC Thinktank Meeting Washington D.C., February 2, 2012 GÜNTER HEIMANN Modeling & Simulation Statistics Novartis AG, Basel
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GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 1
Model-Based Tests for ThoroughQTc TrialsCSRC Thinktank MeetingWashington D.C., February 2, 2012
I adjusts for diurnal variation pt and PK concentrationsI any correlation structure within subject k allowedI additional fixed effects (such as a stratum effect for study
or cohort) can be addedI non-linear models also possible
Hypotheses: ϑCmax ≥ 10 versus ϑCmax < 10
I or corresponding adjustment for non-linear models
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 5
Test Statistic and Test
Test statistic: ϑCmax
There are two approaches to obtain critical values for√n(ϑCmax − ϑCmax): the delta-method
I requires knowledge of joint distribution of√
n(ϑ− ϑ) and√n(Cmax − Cmax)
I can only be applied in certain linear models
the bootstrap
I is based on resampling of entire subjects (PK and QTc)I can be applied in linear and non-linear modelsI and is hence recommended
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 6
Type I Error for Small Sample Sizes
1
All methods are slightly liberal for small sample sizes
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 7
Type I Error for Moderate Sample Sizes
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0.7 0.75 0.8
pro
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Linear model, residual variance = 40, n = 100 per group, 1,000 simulations
popular rule
delta method
bootstrap
alpha = 0.05
H0
Delta method and bootstrap control type I error for moderate sample sizes (n>40)
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 8
Type I Error is Controlled Asymptotically
1
Asymptotic power curves can be calculated explicitly! Delta method and bootstrap control the type I error asymptotically
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 9
Type I Error Control is not Warranted
0
0.02
0.04
0.06
0.08
0.1
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0.14
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0.24
0.26
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0.7 0.75 0.8
pro
ba
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ity t
o r
eje
ct
slope
Linear model, residual variance = 40, n = 300 per group, 10,000 simulations
popular rule
delta method
alpha = 0.05
H0
The simulated and the
asymptotic power curves
coincide for both methods!
The delta method controls
the type I error asymptotically!
The popular rule does not!
GÜNTER HEIMANN
Model-Based Tests forTQT Trials
Introduction
Summary of Methods
Type I Error
Summary andConclusions
version 0.2 10
Summary and Conclusions
I Statistical tests which control the type I error are availablefor linear and non-linear models.
I Simulations across wide range of scenarios (linear andnon-linear) demonstrate type I error control.
I Theoretical proofs available for linear models, confirmedby simulations.
I Asymptotic power curves are available for sample sizecalculations.
I Method can be adjusted to accomodate strata (studies &cohorts).
I However, these methods rely on additional assumptionsI the pre-specified model (linear, Emax, ...)I no histeresis
I Further research ongoing to overcome these issues