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Increasing power for observational studies of aberrant response: An adaptive approach
Author(s) -
Heng Siyu,
Kang Hyunseung,
Small Dylan S.,
Fogarty Colin B.
Publication year - 2021
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12424
Subject(s) - observational study , outcome (game theory) , rank (graph theory) , econometrics , test (biology) , statistics , computer science , mathematics , medicine , biology , mathematical economics , paleontology , combinatorics
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 ≤ − 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.