Randomization-Based Intervals for Binary Outcomes

• Activity Number: 495
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Watson*+ and Joseph Blitzstein
• Companies: Harvard University and Harvard University
• Keywords: Fisher randomization test ; potential outcomes ; nuisance parameters ; posterior predictive checks ; randomization based inference

Abstract

Intervals for average causal effects can be calculated by inverting Fisher randomization tests of sharp null hypotheses. Such intervals are appealing as they rely only on the randomization for inference and are distribution free. In the case of binary outcomes, it is not clear how to define a sharp null hypothesis. We show that a hypothesis that specifies an average causal effect for binary outcomes is not sharp because of the classic problem of nuisance parameters. We explore ways of dealing with the nuisance including Frequentist, Bayesian, and naive approaches corresponding to maximizing over, integrating out, and plugging in estimates of the nuisance parameters respectively. We demonstrate the approach with a simple example and examine the type one error properties. We present results for the simple and illustrative case of a completely randomized experiment and suggest extensions to different randomization schemes and estimands.