A New U-Statistic with Superior Design Sensitivity in Matched Observational Studies

• Activity Number: 268
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Paul R Rosenbaum*+
• Companies: University of Pennsylvania
• Keywords: Design sensitivity ; Observational study ; Randomization inference ; Sensitivity analysis ; U-statistic

Abstract

In an observational study of treatment effects, a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would alter the conclusions. The power of a sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude; in particular, if this specified magnitude is "no departure" then this is the power of a randomization test. A new family of u-statistics is proposed that includes Wilcoxon's signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study. In one situation with 250 pair differences that are Normal with expectation 1/2 and variance 1, the power of a sensitivity analysis that uses Wilcoxon's statistic is 0.08 while the power of another u-statistics is 0.66. The topic is examined by performing a sensitivity analysis in three observational studies, using an asymptotic measure called the design sensitivity, and by simulating power in finite samples. The three examples are drawn from epidemiology, clinical medicine and genetic toxicology.