Title: Sensitivity Analysis for matched pair analysis of binary data: From worst case to average case analysis,
Abstract: In matched observational studies where treatment assignment is not
randomized, sensitivity analysis helps investigators determine how sensitive
their estimated treatment effect is to some unmeasured con- founder. The
standard approach calibrates the sensitivity analysis according to the worst
case bias in a pair. This approach will result in a conservative sensitivity
analysis if the worst case bias does not hold in every pair. In this paper, we
show that for binary data, the standard approach can be calibrated in terms of
the average bias in a pair rather than worst case bias. When the worst case
bias and average bias differ, the average bias interpretation results in a less
conservative sensitivity analysis and more power. In many studies, the average
case calibration may also carry a more natural interpretation than the worst
case calibration and may also allow researchers to incorporate additional data
to establish an empirical basis with which to calibrate a sensitivity analysis.
We illustrate this with a study of the effects of cellphone use on the
incidence of automobile accidents. Finally, we extend the average case
calibration to the sensitivity analysis of confidence intervals for
attributable effects.