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Motivated by an observational study of the effect of hospital ward versusintensive care unit admission on severe sepsis mortality, we develop methods toaddress two common problems in observational studies: (1) when there is a lackof covariate overlap between the treated and control groups, how to define aninterpretable study population wherein inference can be conducted withoutextrapolating with respect to important variables; and (2) how to userandomization inference to form confidence intervals for the average treatmenteffect with binary outcomes. Our solution to problem (1) incorporates existingsuggestions in the literature while yielding a study population that is easilyunderstood in terms of the covariates themselves, and can be solved using anefficient branch-and-bound algorithm. We address problem (2) by solving alinear integer program to utilize the worst case variance of the averagetreatment effect among values for unobserved potential outcomes that arecompatible with the null hypothesis. Our analysis finds no evidence for adifference between the sixty day mortality rates if all individuals wereadmitted to the ICU and if all patients were admitted to the hospital wardamong less severely ill patients and among patients with cryptic septic shock.We implement our methodology in R, providing scripts in the supplementarymaterial.

Discrete Optimization for Interpretable Study Populations and Randomization Inference in an Observational Study of Severe Sepsis Mortality