Employing post-DEA cross-evaluation and cluster analysis in a sample of Greek NHS hospitals

To increase Data Envelopment Analysis (DEA) discrimination of efficient Decision Making Units (DMUs), by complementing "self-evaluated" efficiencies with "peer-evaluated" cross-efficiencies and, based on these results, to classify the DMUs using cluster analysis. Healthcare, which is deprived of such studies, was chosen as the study area. The sample consisted of 27 small- to medium-sized (70-500 beds) NHS general hospitals distributed throughout Greece, in areas where they are the sole NHS representatives. DEA was performed on 2005 data collected from the Ministry of Health and the General Secretariat of the National Statistical Service. Three inputs -hospital beds, physicians and other health professionals- and three outputs -case-mix adjusted hospitalized cases, surgeries and outpatient visits- were included in input-oriented, constant-returns-to-scale (CRS) and variable-returns-to-scale (VRS) models. In a second stage (post-DEA), aggressive and benevolent cross-efficiency formulations and clustering were employed, to validate (or not) the initial DEA scores. The "maverick index" was used to sort the peer-appraised hospitals. All analyses were performed using custom-made software. Ten benchmark hospitals were identified by DEA, but using the aggressive and benevolent formulations showed that two and four of them respectively were at the lower end of the maverick index list. On the other hand, only one 100% efficient (self-appraised) hospital was at the higher end of the list, using either formulation. Cluster analysis produced a hierarchical "tree" structure which dichotomized the hospitals in accordance to the cross-evaluation results, and provided insight on the two-dimensional path to improving efficiency. This is, to our awareness, the first study in the healthcare domain to employ both of these post-DEA techniques (cross efficiency and clustering) at the hospital (i.e. micro) level. The potential benefit for decision-makers is the capability to examine high and low "all-round" performers and maverick hospitals more closely, and identify and address problems typically overlooked by first-stage DEA.