A latent variable approach to potential outcomes for emergency department admission decisions

Abstract

In emergency departments (EDs), care providers continuously weigh admissions against continued monitoring and treatment often without knowing their condition and health needs. To understand the decision process and its causal effect on outcomes, an observational study must contend with unobserved/missing information and a lack of exchangeability between admitted and discharged patients. Our goal was to provide a general framework to evaluate admission decisions from electronic healthcare records (EHRs). We describe admission decisions as a decision-making process in which the patient's health needs is a binary latent variable. We estimate latent health needs from EHR with only partial knowledge of the decision process (ie, initial evaluation, admission decision, length of stay). Estimated latent health needs are then used to understand the admission decision and the decision's causal impact on outcomes. For the latter, we assume potential outcomes are stochastically independent from the admission decision conditional on latent health needs. As a case study, we apply our approach to over 150 000 patient encounters with the ED from the University of Michigan Health System collected from August 2012 through July 2015. We estimate that while admitting a patient with higher latent needs reduces the 30-day risk of revisiting the ED or later being admitted through the ED by over 79%, admitting a patient with lower latent needs actually increases these 30-day risks by 3.0% and 7.6%, respectively.

Keywords: causal inference; emergency department admission decisions; latent variables; potential outcomes.

FIGURE 1

Bayesian network of admission decision model. Patient health needs H influences an initial observation Z. Care providers use this observation and other observations collected so far from treatment and testing until time T, when they make a final decision A on whether to admit or discharge. Dashed circle represents our latent variable, whereas rectangles represent observed variables

FIGURE 2

Structural model of treatment time T and admission decision A is constructed from, respectively, the first-passage time and exit location of Brownian motion B_t. To capture the dependence on patient characteristics X, latent health needs H, and initial observation Z, we assume Brownian motion starts at a point c(X, Z)b(X) and drifts at a speed of d(H)b(X) until reaching the boundary 0 (discharge) or b(X) (admit) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3

Results from parameter estimation: percent with higher latent health needs H = 1 (determined by α) and percent with higher initial observation (acuity 2) by latent health needs (determined by β) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 4

Estimated average treatment times and admission rates by sex, age, acuity, and latent health needs. Higher health needs is accompanied by shorter treatment times and better accuracy in the final decision compared to a lower health state [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 5

Risk of ED revisits and readmissions as a function of admission decisions and latent health needs H = 0 and H = 1 [Colour figure can be viewed at wileyonlinelibrary.com]