Stochastic Frontier Analysis of Hospital Mortality

Abstract

This study will employ stochastic frontier analysis (SFA) to estimate “best practice” frontiers for hospital risk-adjusted mortality and provide evidence of the extent to which variation in risk-adjusted mortality rates reflect “inefficiency” (deviation from best practice) versus random noise/omitted variables. Specifically, the study will provide evidence of the magnitude and scope of implied deviations from best practice, hospital characteristics that are associated with such deviations, and, for years with available data, the relationship between such deviations and process measures of hospital quality. It also will provide evidence of variation in hospital risk-adjusted mortality rankings over time and compare SFA-based rankings of hospital performance to other ranking approaches. A large literature uses SFA to estimate production and cost efficiency, including numerous studies of hospital cost efficiency. SFA also has been used to analyze cross-country differences in healthcare spending efficiency, and it has recently been used to analyze differences in infant mortality across countries and within the United Kingdom. Our approach will build on this research and pay particular attention to allowing for volume-driven heteroskedasticity in risk-adjusted mortality. Data from the 100 percent MedPar files are sued to calculate 30-day risk-adjusted mortality rates for three conditions, AMI, congestive heart failure, and pneumonia, for each acute care hospital, condition, and year during 2001-2006. The risk-adjusted mortality rates are calculated using logit analysis, conditioning on 30 co morbidities. Data on process measures of hospital quality are obtained for available years from Hospital Compare, and data on hospital characteristics are from the Medicare Provider of Service File and the American Hospital Association. The general approach is to model hospital risk-adjusted mortality for each of the three conditions as a function of (1) hospital characteristics that could influence mortality apart from deviations from best practice, (2) a heteroskedastic, symmetrically distributed random error term that reflects unobserved influences unrelated to best practice, and (3) a draw from a strictly nonnegative distribution that reflects possible deviation from best practice (including the half-normal, exponential, or truncated normal distributions). While much of the analysis will assume a continuous distribution for the random error, we will explore the feasibility of estimating models that explicitly consider count data. The results of the study should be of broad interest to researchers and policymakers concerned with hospital quality, outcomes versus process measures of quality, and sources of variation in risk-adjusted mortality across hospitals and over time.

Keywords: process measures of quality, risk-adjusted mortality, stochastic froniter analysis