arXiv 25 Feb 2022 · Statistics — Methodology · publishedThe Annals of Statistics (2023) · 3 citations (OpenAlex)
arXiv:2202.12511 · PDF · DOI · OpenAlex · Extracted main text
Tie-breaker designs trade off a statistical design objective with short-term gain from preferentially assigning a binary treatment to those with high values of a running variable $x$. The design objective is any continuous function of the expected information matrix in a two-line regression model, and short-term gain is expressed as the covariance between the running variable and the treatment indicator. We investigate how to specify design functions indicating treatment probabilities as a function of $x$ to optimize these competing objectives, under external constraints on the number of subjects receiving treatment. Our results include sharp existence and uniqueness guarantees, while accommodating the ethically appealing requirement that treatment probabilities are non-decreasing in $x$. Under such a constraint, there always exists an optimal design function that is constant below and above a single discontinuity. When the running variable distribution is not symmetric or the fraction of subjects receiving the treatment is not $1/2$, our optimal designs improve upon a $D$-optimality objective without sacrificing short-term gain, compared to the three level tie-breaker designs of Owen and Varian (2020) that fix treatment probabilities at $0$, $1/2$, and $1$. We illustrate our optimal designs with data from Head Start, an early childhood government intervention program.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Owen, A. B. and Varian, H (2020) Optimizing the tie-breaker regression discontinuity design self | 1.000 | 14 | 5 | 100% |
| 2 | Metelkina, A. and Pronzato, L (2017) Information-regret compromise in covariate-adaptive treatment allocation | 0.874 | 9 | 2 | 100% |
| 3 | Lehmann, E. L. and Romano, J. P (2005) Testing statistical hypotheses, volume 3 | 0.644 | 4 | 1 | 100% |
| 4 | Kluger, D. and Owen, A. B (2021) Tie-breaker designs provide more efficient kernel estimates than regression discontinuity designs self | 0.644 | 2 | 2 | 100% |
| 5 | Morrison, T. P. and Owen, A. B (2022) Optimality in multivariate tie-breaker designs self | 0.644 | 2 | 2 | 100% |
| 6 | De Oliveira, O (2018) The implicit function theorem for maps that are only differentiable: An elementary proof | 0.405 | 1 | 1 | 100% |
| 7 | R Core Team (2022) R: A Language and Environment for Statistical Computing | 0.405 | 1 | 1 | 100% |
| 8 | Trochim, W. M. and Cappelleri, J. C (1992) Cutoff assignment strategies for enhancing randomized clinical trials | 0.405 | 1 | 1 | 100% |
| 9 | Abdulkadiroglu, A., Angrist, J. D., Narita, Y., and Pathak, P. A (2017) Impact evaluation in matching markets with general tie-breaking | 0.405 | 1 | 1 | 100% |
| 10 | Aiken, L. S., West, S. G., Schwalm, D. E., Carroll, J. L., and Hsiun… (1998) Comparison of a randomized and two quasi-experimental designs in a single outcome evaluation: Efficacy of a university-level rem… | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 45 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Safe Policy Learning under Regression Discontinuity Designs with Multiple Cutoffs | 0.405 | 1 | 1 |
| 2 | Double machine learning and design in batch adaptive experiments | 0.405 | 1 | 1 |