Importance of Statistical Evidence in Estimating Valid DEA Scores.

Data Envelopment Analysis (DEA) allows healthcare scholars to measure productivity in a holistic manner. It combines a production unit's multiple outputs and multiple inputs into a single measure of its overall performance relative to other units in the sample being analyzed. It accomplishes this task by aggregating a unit's weighted outputs and dividing the output sum by the unit's aggregated weighted inputs, choosing output and input weights that maximize its output/input ratio when the same weights are applied to other units in the sample. Conventional DEA assumes that inputs and outputs are used in different proportions by the units in the sample. So, for the sample as a whole, inputs have been substituted for each other and outputs have been transformed into each other. Variables are assigned different weights based on their marginal rates of substitution and marginal rates of transformation. If in truth inputs have not been substituted nor outputs transformed, then there will be no marginal rates and therefore no valid basis for differential weights. This paper explains how to statistically test for the presence of substitutions among inputs and transformations among outputs. Then, it applies these tests to the input and output data from three healthcare DEA articles, in order to identify the effects on DEA scores when input substitutions and output transformations are absent in the sample data. It finds that DEA scores are badly biased when substitution and transformation are absent and conventional DEA models are used.

Measuring hospital efficiency with Data Envelopment Analysis: nonsubstitutable vs. substitutable inputs and outputs.

There is a conflict between Data Envelopment Analysis (DEA) theory's requirement that inputs (outputs) be substitutable, and the ubiquitous use of nonsubstitutable inputs and outputs in DEA applications to hospitals. This paper develops efficiency indicators valid for nonsubstitutable variables. Then, using a sample of 87 community hospitals, it compares the new measures' efficiency estimates with those of conventional DEA measures. DEA substantially overestimated the hospitals' efficiency on the average, and reported many inefficient hospitals to be efficient. Further, it greatly overestimated the efficiency of some hospitals but only slightly overestimated the efficiency of others, thus making any comparisons among hospitals questionable. These results suggest that conventional DEA models should not be used to estimate the efficiency of hospitals unless there is empirical evidence that the inputs (outputs) are substitutable. If inputs (outputs) are not substitutes, efficiency indicators valid for nonsubstitutability should be employed, or, before applying DEA, the nonsubstitutable variables should be combined using an appropriate weighting scheme or statistical methodology.

Improving the efficiency of distributive and clinical services in hospital pharmacy.

Three problems impede the assessment of hospital pharmacy efficiency. First, although multiple efficiency indicators are utilized to measure a large variety of activities, it has not been possible to validly measure overall efficiency. Second, there have been no widely-used clinical activity indicators, so key outputs often have not been accounted for. Third, there has been no effective methodology for identifying when declines in efficiency are normal random variations and when they represent true decreases in performance. This paper presents a procedure that simultaneously addresses these three problems. It analyzes data from a group of U.S. hospital pharmacies that collect an inclusive set of clinical and distributional indicators. It employs Data Envelopment Analysis to develop comprehensive efficiency measures from the numerous outputs and inputs. It applies statistical Panel Data Analysis to estimate confidence intervals within which each pharmacy's true efficiency resides, and to develop control charts for signaling when a pharmacy's efficiency has declined by more than can be attributed to random variation. This integrated efficiency evaluation system is transferable to other hospital pharmacy systems, thereby offering decision makers a better way of measuring, controlling and improving hospital pharmacy efficiency.