Data envelopment analysis in the presence of measurement error: case study from the National Database of Nursing Quality Indicators® (NDNQI®)

Data envelopment analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency [B. Hollingsworth, The measurement of efficiency and productivity of health care delivery. Health Economics 17(10) (2008), pp. 1107–1128], but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized [B.J. Gajewski, R. Lee, M. Bott, U. Piamjariyakul, and R.L. Taunton, On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process. Journal of Applied Statistics 36(9) (2009), pp. 933–944; J. Ruggiero, Data envelopment analysis with stochastic data. Journal of the Operational Research Society 55 (2004), pp. 1008–1012]. We propose to address measurement error systematically using a Bayesian method (Bayesian DEA). We will apply Bayesian DEA to data from the National Database of Nursing Quality Indicators to estimate nursing units’ efficiency. Several external reliability studies inform the posterior distribution of the measurement error on the DEA variables.We will discuss the case of generalizing the approach to situations where an external reliability study is not feasible.