Neil Christy | Searcharxiv

arXiv2024

Counting Defiers: A Design-Based Model of an Experiment Can Reveal Evidence Beyond the Average Effect

Using only a binary intervention and outcome and the design of the randomization within an experiment, we construct a design-based likelihood of the joint distribution of potential outcomes in the sample -- the numbers of always takers, compliers, defiers, and never takers. We develop a visualization to show that samples with defiers can sometimes generate the data in more ways than samples without, yielding a higher likelihood. This likelihood can vary within the Frechet bounds, even though the traditional likelihood does not. Evidence is weak, but it exists, as we illustrate with health applications and our dbmle package.

econ.EM↗

arXiv2024

Starting Small: Prioritizing Safety over Efficacy in Randomized Experiments Using the Exact Finite Sample Likelihood

We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over efficacy. We propose a finite sample Bayesian decision rule and a finite sample maximum likelihood decision rule. We show that in finite samples from 2 to 50, it is possible for these rules to achieve better performance according to established maximin and maximum regret criteria than a rule based on the Boole-Frechet-Hoeffding bounds. We also propose a finite sample maximum likelihood criterion. We apply our rules and criterion to an actual clinical trial that yielded a promising estimate of efficacy, and our results point to safety as a reason for why results were mixed in subsequent trials.

econ.EM↗