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Updated: Jul 2, 2025

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Measuring Delay Discounting in Humans Using an Adjusting Amount Task
Published on: January 9, 2016
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Nonparametric analysis of delayed treatment effects using single-crossing constraints.
Nicholas C Henderson1, Kijoeng Nam2, Dai Feng3
1Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA.
Biometrical Journal. Biometrische Zeitschrift
|February 25, 2024
Summary
Novel immuno-oncology therapies can show delayed effects, causing survival curves to cross. This study introduces a flexible method to model these crossing survival curves and estimate treatment benefits, aiding clinical trial interpretation.
Area of Science:
- Biostatistics
- Clinical Trials
- Immunotherapy
Background:
- Clinical trials for novel immuno-oncology therapies often violate the proportional hazards assumption.
- Delayed treatment effects can lead to crossing survival curves in different treatment arms.
Purpose of the Study:
- To develop a flexible, nonparametric approach for estimating treatment arm-specific survival functions in the presence of crossing curves.
- To provide interpretable measures of treatment benefit, including crossing time and conditional survival probabilities.
Main Methods:
- A nonparametric statistical method is proposed to model survival functions that cross at most once.
- The approach estimates the time of survival curve crossing and associated conditional measures of treatment effect.
Main Results:
- The method successfully models scenarios with delayed treatment effects and crossing survival curves.
- It generates interpretable measures like crossing-conditional survival probabilities and restricted mean survival time.
Conclusions:
- This approach offers a valuable tool for analyzing immuno-oncology clinical trials with non-proportional hazards.
- It enhances the understanding of treatment benefits beyond traditional efficacy measures.
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