Data-adaptive exposure thresholds for the Horvitz-Thompson estimator of the Average Treatment Effect in experiments with network interference
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915137595637760 |
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| author | Thiyageswaran, Vydhourie McCormick, Tyler Brennan, Jennifer |
| author_facet | Thiyageswaran, Vydhourie McCormick, Tyler Brennan, Jennifer |
| contents | Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Values Assumption (SUTVA) in which a unit's treatment assignment affects the outcomes of its neighbors. This interference causes bias in naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness is to pair the Horvitz-Thompson estimator of the ATE with a known exposure mapping: a function that identifies which units in a given randomization are not subject to interference. For example, an exposure mapping can specify that any unit with at least $h$-fraction of its neighbors having the same treatment status does not experience interference. However, this threshold $h$ is difficult to elicit from domain experts, and a misspecified threshold can induce bias. In this work, we propose a data-adaptive method to select the "$h$"-fraction threshold that minimizes the mean squared error of the Hortvitz-Thompson estimator. Our method estimates the bias and variance of the Horvitz-Thompson estimator under different thresholds using a linear dose-response model of the potential outcomes. We present simulations illustrating that our method improves upon non-adaptive choices of the threshold. We further illustrate the performance of our estimator by running experiments on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method is robust to deviations from the linear potential outcomes model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-adaptive exposure thresholds for the Horvitz-Thompson estimator of the Average Treatment Effect in experiments with network interference Thiyageswaran, Vydhourie McCormick, Tyler Brennan, Jennifer Methodology Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Values Assumption (SUTVA) in which a unit's treatment assignment affects the outcomes of its neighbors. This interference causes bias in naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness is to pair the Horvitz-Thompson estimator of the ATE with a known exposure mapping: a function that identifies which units in a given randomization are not subject to interference. For example, an exposure mapping can specify that any unit with at least $h$-fraction of its neighbors having the same treatment status does not experience interference. However, this threshold $h$ is difficult to elicit from domain experts, and a misspecified threshold can induce bias. In this work, we propose a data-adaptive method to select the "$h$"-fraction threshold that minimizes the mean squared error of the Hortvitz-Thompson estimator. Our method estimates the bias and variance of the Horvitz-Thompson estimator under different thresholds using a linear dose-response model of the potential outcomes. We present simulations illustrating that our method improves upon non-adaptive choices of the threshold. We further illustrate the performance of our estimator by running experiments on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method is robust to deviations from the linear potential outcomes model. |
| title | Data-adaptive exposure thresholds for the Horvitz-Thompson estimator of the Average Treatment Effect in experiments with network interference |
| topic | Methodology |
| url | https://arxiv.org/abs/2405.15887 |