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A general characterization of optimal tie-breaker designs

Harrison H. Li, Art B. Owen

arXiv 25 Feb 2022 · Statistics — Methodology · publishedThe Annals of Statistics (2023) · 3 citations (OpenAlex)

arXiv:2202.12511 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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45
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Owen, A. B. and Varian, H (2020) Optimizing the tie-breaker regression discontinuity design self1.000145100%
2Metelkina, A. and Pronzato, L (2017) Information-regret compromise in covariate-adaptive treatment allocation0.87492100%
3Lehmann, E. L. and Romano, J. P (2005) Testing statistical hypotheses, volume 30.64441100%
4Kluger, D. and Owen, A. B (2021) Tie-breaker designs provide more efficient kernel estimates than regression discontinuity designs self0.64422100%
5Morrison, T. P. and Owen, A. B (2022) Optimality in multivariate tie-breaker designs self0.64422100%
6De Oliveira, O (2018) The implicit function theorem for maps that are only differentiable: An elementary proof0.40511100%
7R Core Team (2022) R: A Language and Environment for Statistical Computing0.40511100%
8Trochim, W. M. and Cappelleri, J. C (1992) Cutoff assignment strategies for enhancing randomized clinical trials0.40511100%
9Abdulkadiroglu, A., Angrist, J. D., Narita, Y., and Pathak, P. A (2017) Impact evaluation in matching markets with general tie-breaking0.40511100%
10Aiken, 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…0.40511100%

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