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Abstract
DEA, a non-parametric methodology to assess efficiency of production units, is quite sensitive to missing data. In this paper, we propose a new approach called Average Ratio Method to replace missing input or output values. This method has several advantages such as being computational efficient, being consistent with the various DEA models and producing better results when compared to other methods. The proposed methodology is used to evaluate the efficiency of 41 clinics in Kansas with sparse data, and to identify the level of utilization of resources for providing better services.
Keywords
Data envelopment analysis, missing data, health care, efficiency measurement
1. Introduction
Data Envelopment Analysis (DEA) is widely recognized as an effective tool for measuring the relative efficiency of Decision Making Units (DMUs) using a set of multiple inputs and multiple outputs [1]. This is indicated by the vast number of DEA applications in various fields, since its development by Charnes et al. [2]. The accuracy and the certainty of the results depend on the quality and quantity of the data used, since DEA is sensitive to missing data. However it is common to find cases with sparse data, limiting the robustness of the DEA analysis. In this paper, we propose a new methodology called Average Ratio Method based on the concept of correlation, to replace the missing values of the inputs and outputs.
The classic assumption of DEA is availability of numerical data for each input and output, with the data assumed to be positive for all DMUs [3]. This particular assumption limits the applicability of the DEA methodology to well designed studies with ample data. In order to allow DEA analysis in cases of missing data, the minimal data requirements where defined. These requirements state that at least one DMU should have a complete set of inputs and outputs and each DMU should have at least one input and at least one output [4]. The difficulty involved in replacing missing data values emanates from the fact that DEA is based on a single set of data (unlike statistical analysis for example) [5]. The accuracy of a DEA analysis directly depends on the quality and quantity of the data, since the results are more sensitive to data errors, missing values, and...