The Conditional Power in Survival Time Analysis
Andreas Kühnapfel
Institute for Medical Informatics, Statistics and Epidemiology
University of Leipzig
20 March 2014
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Clinical Trial: Generally
2 treatments
randomised trial
survival as endpoint
superiority trial
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Clinical Trial: Mathematics
number of patients n
signi�cance level α (= 0.05)
e�ect (clinically relevant) hazard ratio θ
power 1− β (= 0.8)
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Clinical Trial: Analyses
interim analyses
observed data
observed e�ect smaller than expected e�ect
conditional power
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Clinical Trial: Kaplan-Meier Curves
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Conditional Power
Probability of achieving a signi�cant result
at the end of study,
given the data from interim analysis.
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Problem: Occurance of Cure
Kaplan-Meier curves
survival fractions
standard models do not �t
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Problem: Survival Functions
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
Kaplan−Meier
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Problem: Survival Functions
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
Kaplan−Meier
Exponential
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Solution: Allowing for Cure
non-mixture models consider survival fractions
proportional hazard assumption
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Solution: Survival Functions
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
Kaplan−Meier
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Solution: Survival Functions
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
Kaplan−Meier
Non−Mixture−Exponential
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Solution: Survival Functions
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Time
Survival
Kaplan−Meier
Non−Mixture−Exponential
Exponential
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Calculations
based on non-mixture models
exponential, Weibull type and Gamma type survival
derivation of conditional power functions
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Example: Non-Hodgkin Lymphoma
Is there any di�erence in view of the treatment e�ect
between standard dosage (CHOEP)
and some moderate increase in dosage (highCHOEP)?
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Example: Interim Analysis
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Non−Mixture Model with Exponential Survival
Time
Survival
CHOEP
highCHOEP
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Example: Conditional Power Function
40 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
0.0
0.2
0.4
0.6
0.8
1.0
Non−Mixture Model with Exponential Survival
log(Hazard Ratio) = log(Hazard highCHOEP / Hazard CHOEP)
Conditio
nal P
ow
er
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Overview
1 Clinical Trial
2 Conditional Power
3 Problem
4 Solution
5 Calculations
6 Example
7 Prospect and Alternatives
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Prospect and Alternatives
non-inferiority trials
Cox model
Bayesian approach
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