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

TL;DR

This paper introduces methods for defining interpretable study populations and applying randomization inference in observational studies, specifically addressing covariate overlap issues and confidence interval construction for binary outcomes.

Contribution

It develops a discrete optimization approach using branch-and-bound and linear integer programming to improve inference and interpretability in observational studies.

Findings

No significant mortality difference between ICU and ward admissions for less severe cases.

Method provides clear, covariate-based study populations without extrapolation.

Implementation available in R with supplementary scripts.

Abstract

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 utilize 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 sixty 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.