Increasing Power for Observational Studies of Aberrant Response: An Adaptive Approach

In many observational studies, the interest is in the effect of treatment on bad, aberrant outcomes rather than the average outcome. For such settings, the traditional approach is to define a dichotomous outcome indicating aberration from a continuous score and use the Mantel-Haenszel test with matched data. For example, studies of determinants of poor child growth use the World Health Organization's definition of child stunting being height-for-age z-score $\leq -2$. The traditional approach may lose power because it discards potentially useful information about the severity of aberration. We develop an adaptive approach that makes use of this information and asymptotically dominates the traditional approach. We develop our approach in two parts. First, we develop an aberrant rank approach in matched observational studies and prove a novel design sensitivity formula enabling its asymptotic comparison with the Mantel-Haenszel test under various settings. Second, we develop a new, general adaptive approach, the two-stage programming method, and use it to adaptively combine the aberrant rank test and the Mantel-Haenszel test. We apply our approach to a study of the effect of teenage pregnancy on stunting.