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Tuesday, May 10, 2022 [Link to join] (ID: 996 2837 2037, Password: 386638)
- Speaker 1: Tim Morrison (Stanford University)
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Title: Optimality in multivariate tie-breaker designs
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Abstract: Tie-breaker designs (TBDs), in which subjects with extreme values are assigned treatment deterministically and those in the middle are randomized, are intermediate between regression discontinuity designs (RDDs) and randomized controlled trials (RCTs). TBDs thus provide a convenient mechanism by which to trade off between the treatment benefit of an RDD and the statistical efficiency gains of an RCT. We study a model where the expected response is one multivariate regression for treated subjects and another one for control subjects. For a given set of subject data we show how to use convex optimization to choose treatment probabilities that optimize a prospective D-optimality condition (expected information gain). We can incorporate economically motivated linear constraints on those treatment probabilities as well as monotonicity constraints that have a strong ethical motivation. Our condition can be used in two scenarios: known covariates with random treatments, and random covariates with random treatments.
- Speaker 2: Harrison Li (Stanford University)
- Title: A general characterization of optimal tie-breaker designs
- Abstract: Tie-breaker designs trade off between statistical efficiency and a preference for assigning a binary treatment to individuals with high values of a quantitative running variable x. Motivating examples include university scholarship programs and promotions for e-commerce companies. We explicitly characterize tie-breaker designs that optimize a D-optimality efficiency criterion under a two-line regression model, subject to equality constraints on the expected proportion of treated individuals and the covariance between x and the binary treatment indicator. Our results extend to any running variable distribution F with finite variance and any efficiency criterion depending continuously on the expected information matrix in the regression. If we additionally require treatment probabilities to be non-decreasing in x, an optimal design requires just two probability levels when the running variable distribution F is continuous. By contrast, the original tie-breaker design in Owen and Varian (2020) has three probability levels fixed at 0, 0.5, and 1. We find large efficiency gains for our optimal designs compared to using those three levels when fewer than half of the subjects are to be treated, or F is not symmetric. We illustrate these gains with a data example based on Head Start, a U.S. government early-childhood intervention program.
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