Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 111, Issue 514, Pages 447-458Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2015.1112802
Keywords
Average treatment effect; Causal inference; Causal risk difference; Common support; Full matching; Integer programming
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Motivated by an observational study of the effect of hospital ward versus intensive care unit admission on severe sepsis mortality, we develop methods to address two common problems in observational studies: (1) when there is a lack of covariate overlap between the treated and control groups, how to define an interpretable study population wherein inference can be conducted without extrapolating with respect to important variables; and (2) how to use randomization inference to form confidence intervals for the average treatment effect with binary outcomes. Our solution to problem (1) incorporates existing suggestions in the literature while yielding a study population that is easily understood in terms of the covariates themselves, and can be solved using an efficient branch-and-bound algorithm. We address problem (2) by solving a linear integer program to use the worst-case variance of the average treatment effect among values for unobserved potential outcomes that are compatible with the null hypothesis. Our analysis finds no evidence for a difference between the 60-day mortality rates if all individuals were admitted to the ICU and if all patients were admitted to the hospital ward among less severely ill patients and among, patients with cryptic septic shock. We implement our methodology in R, providing scripts in the supplementary material.
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