arXiv 21 Feb 2022 · Statistics — Methodology · publishedElectronic Journal of Statistics (2024) · 1 citations (OpenAlex)
arXiv:2202.10030 · PDF · DOI · OpenAlex · Extracted main text
In a tie-breaker design (TBD), subjects with high values of a running variable are given some (usually desirable) treatment, subjects with low values are not, and subjects in the middle are randomized. TBDs are intermediate between regression discontinuity designs (RDDs) and randomized controlled trials (RCTs). TBDs allow a tradeoff between the resource allocation efficiency of an RDD and the statistical efficiency of an RCT. We study a model where the expected response is one multivariate regression for treated subjects and another for control subjects. We propose a prospective D-optimality, analogous to Bayesian optimal design, to understand design tradeoffs without reference to a specific data set. For given covariates, we show how to use convex optimization to choose treatment probabilities that optimize this criterion. We can incorporate a variety of constraints motivated by economic and ethical considerations. In our model, D-optimality for the treatment effect coincides with D-optimality for the whole regression, and, without constraints, an RCT is globally optimal. We show that a monotonicity constraint favoring more deserving subjects induces sparsity in the number of distinct treatment probabilities. We apply the convex optimization solution to a semi-synthetic example involving triage data from the MIMIC-IV-ED database.
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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 | A. B. Owen and H. Varian (2020) Optimizing the tie-breaker regression discontinuity design self | 1.000 | 5 | 3 | 100% |
| 2 | H. Li and A. B. Owen (2023) A general characterization of optimality in tie-breaker designs | 0.843 | 3 | 3 | 100% |
| 3 | R. D. Cook and L. Thibodeau (1980) Marginally restricted d-optimal designs | 0.737 | 3 | 2 | 100% |
| 4 | C. J. Nachtsheim (1989) On the design of experiments in the presence of fixed covariates | 0.737 | 3 | 2 | 100% |
| 5 | A. Atkinson, A. Donev, and R. Tobias (2007) Optimum experimental designs, with SAS, volume 34 of Oxford Statistical Science Series | 0.693 | 5 | 1 | 100% |
| 6 | D. Cook and V. Fedorov (1995) Constrained optimization of experimental design | 0.644 | 2 | 2 | 100% |
| 7 | A. Goldberger (1972) Selection bias in evaluating treatment effects: Some formal illustrations | 0.644 | 2 | 2 | 100% |
| 8 | D. M. Kluger and A. B. Owen (2023) Kernel regression analysis of tie-breaker designs self | 0.644 | 2 | 2 | 100% |
| 9 | J. Yang, A. Mandal, and D. Majumdar (2016) Optimal designs for $2^k$ factorial experiments with binary response | 0.511 | 2 | 1 | 100% |
| 10 | S. Boyd and L. Vandenberghe (2004) Convex Optimization | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 44 scored citations.