text: 424,164,1514786754812780560,366380609,Evan Rosenman,"New paper with @LMiratrix just hit arXiv: <LINK> ""Designing Experiments Toward Shrinkage Estimation"" considers how to design an RCT when the goal is to merge its causal estimates with those from an observational study to yield greater accuracy. (1/4) We operate in a stratified setting, and propose using an Empirical Bayes shrinker to combine the estimates, such that we have strong guarantees of risk reduction. We proceed using \kappa_2, a shrinker proposed in <LINK>. (2/4) We show the exact risk of \kappa_2 can be computed via a numerical integral discussed in Bao and Kan (2013). The RCT design is optimized over the value of this integral. We propose three heuristics -- Neyman, naive, and robust allocations -- for designing under uncertainty. (3/4) Lastly, we show in a simulation study that the resultant designs outperform, whether or not there is unmeasured confounding in the observational study. We hope these results can help researchers to better leverage obs. data while retaining risk reduction guarantees. (4/4) Addendum: I am deeply disappointed that I did not start this thread with: ""A paper for Pesach!""",https://arxiv.org/abs/2204.06687,"We consider how increasingly available observational data can be used to improve the design of randomized controlled trials (RCTs). We seek to design a prospective RCT, with the intent of using an Empirical Bayes estimator to shrink the causal estimates from our trial toward causal estimates obtained from an observational study. We ask: how might we design the experiment to better complement the observational study in this setting? We propose using an estimator that shrinks each component of the RCT causal estimator toward its observational counterpart by a factor proportional to its variance. First, we show that the risk of this estimator can be computed efficiently via numerical integration. We then propose algorithms for determining the best allocation of units to strata (the best ""design""). We consider three options: Neyman allocation; a ""naive"" design assuming no unmeasured confounding in the observational study; and a ""defensive"" design accounting for the imperfect parameter estimates we would obtain from the observational study with unmeasured confounding. We also incorporate results from sensitivity analysis to establish guardrails on the designs, so that our experiment could be reasonably analyzed with and without shrinkage. We demonstrate the superiority of these experimental designs with a simulation study involving causal inference on a rare, binary outcome. ",Designing Experiments Toward Shrinkage Estimation,5,"['New paper with @LMiratrix just hit arXiv:  <LINK>\n""Designing Experiments Toward Shrinkage Estimation"" considers how to design an RCT when the goal is to merge its causal estimates with those from an observational study to yield greater accuracy. (1/4)', 'We operate in a stratified setting, and propose using an Empirical Bayes shrinker to combine the estimates, such that we have strong guarantees of risk reduction. We proceed using \\kappa_2, a shrinker proposed in https://t.co/Gle8NlpGto. (2/4)', 'We show the exact risk of \\kappa_2 can be computed via a numerical integral discussed in Bao and Kan (2013). The RCT design is optimized over the value of this integral. We propose three heuristics -- Neyman, naive, and robust allocations -- for designing under uncertainty. (3/4)', 'Lastly, we show in a simulation study that the resultant designs outperform, whether or not there is unmeasured confounding in the observational study. We hope these results can help researchers to better leverage obs. data while retaining risk reduction guarantees. (4/4)', 'Addendum: I am deeply disappointed that I did not start this thread with: ""A paper for Pesach!""']",22,04,1127