The matched-pairs design enables
researchers to efficiently infer causal effects from randomized
experiments. In this paper, we exploit the key feature of the
matched-pairs design and develop a sensitivity analysis for missing
outcomes due to truncation-by-death, in which the outcomes of
interest (e.g., quality of life measures) are not even well defined
for some units (e.g., deceased patients). Our key idea is that if
two nearly identical observations are paired prior to the
randomization of the treatment, the missingness of one unit's
outcome is informative about the potential missingness of the other
unit's outcome under an alternative treatment condition. We
consider the average treatment effect among always-observed pairs
(ATOP) whose units exhibit no missing outcome regardless of their
treatment status. The naive estimator based on available pairs is
unbiased for the ATOP if two units of the same pair are identical in
terms of their missingness patterns. The proposed sensitivity
analysis characterizes how the bounds of the ATOP widen as the
degree of the within-pair similarity decreases. We further extend
the methodology to the matched-pairs design in observational
studies. Our simulation studies show that informative bounds can be
obtained under some scenarios when the proportion of missing data is
not too large. The proposed methodology is also applied to the
randomized evaluation of the Mexican universal health insurance
program. |