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Sharp bounds on the relative treatment effect for ordinal outcomes
Jiannan Lu1, Yunshu Zhang2, Peng Ding3
1Analysis and Experimentation, Microsoft Corporation, Redmond, Washington.
Biometrics
|November 20, 2019
Summary
The relative treatment effect offers a clear interpretation for ordinal outcomes, unlike the average treatment effect. This study derives sharp bounds for this effect, allowing for arbitrary dependence between potential outcomes.
Area of Science:
- Statistics
- Biostatistics
- Econometrics
Background:
- Average treatment effect (ATE) is challenging to interpret for ordinal outcomes.
- Ordinal outcomes are common in various fields, including medicine and social sciences.
- Existing methods often assume independence of potential outcomes, limiting applicability.
Purpose of the Study:
- To propose the relative treatment effect (RTE) as a robust measure for ordinal outcomes.
- To derive sharp bounds for the RTE that are identifiable from observed data.
- To relax the assumption of independent potential outcomes.
Main Methods:
- Derivation of sharp bounds for the relative treatment effect using marginal distributions of potential outcomes.
- Development of statistical methods to estimate these bounds.
- Consideration of arbitrary dependence structures between potential outcomes.
Main Results:
- The relative treatment effect is shown to be a well-defined and interpretable measure for ordinal outcomes.
- Sharp bounds for the RTE are derived and proven to be identifiable.
- The proposed method accommodates dependence between potential outcomes, unlike previous approaches.
Conclusions:
- The relative treatment effect provides a valuable alternative to ATE for ordinal data.
- The derived bounds offer a practical tool for causal inference with ordinal outcomes.
- This work advances statistical methods for handling complex dependencies in treatment effect estimation.
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