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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