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Sharp bounds on the relative treatment effect for ordinal outcomes
Author(s) -
Lu Jiannan,
Zhang Yunshu,
Ding Peng
Publication year - 2020
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13148
Subject(s) - ordinal data , econometrics , ordinal scale , treatment effect , statistics , mathematics , measure (data warehouse) , ordinal regression , marginal distribution , computer science , medicine , random variable , data mining , traditional medicine
For ordinal outcomes, the average treatment effect is often ill‐defined and hard to interpret. Echoing Agresti and Kateri, we argue that the relative treatment effect can be a useful measure, especially for ordinal outcomes, which is defined as γ = pr { Y i ( 1 ) > Y i ( 0 ) } − pr { Y i ( 1 ) < Y i ( 0 ) } , with Y i ( 1 ) and Y i ( 0 ) being the potential outcomes of unit i under treatment and control, respectively. Given the marginal distributions of the potential outcomes, we derive the sharp bounds on γ , which are identifiable parameters based on the observed data. Agresti and Kateri focused on modeling strategies under the assumption of independent potential outcomes, but we allow for arbitrary dependence.