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Productivity and quality changes in Greek public hospitals

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Abstract

The objective of this paper is to estimate productivity changes after the inclusion of quality variables for a panel of Greek public hospitals during the period 2002–2007. We measure hospital productivity and quality changes through a non-parametric estimation of the quality adjusted Malmquist productivity index by using the percentage of survival after admissions as a proxy of hospital care services quality. Even though the empirical results indicate on average deterioration both in productivity and quality there is considerable variation among the sample hospitals.

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Notes

  1. All previous studies on Greek health care efficiency (i.e., Athanassopoulos et al. 1999; Athanassopoulos and Gounaris 2001; Giokas 2001; Aletras et al. 2007; Karagiannis and Hatziprokopiou 2008; Karagiannis and Velentzas 2009) and productivity (i.e., Maniadakis and Thanassoulis 2004) measurement did not account for quality changes.

  2. DEA as any other method has advantages and disadvantages. For a detailed discussion of these see for example the first chapter in Fried et al. (2008).

  3. Despite the small sample size, our formulation satisfies Dyson et al. (2001) “rule of thumb”, which suggests that the number of DMUs should be greater than or equal to the double of the product between the number of inputs and the number of outputs. Otherwise, a great number of DMUs would artificially appear as efficient.

  4. Hospitals constitute the core of the Greek National Health System. They are governed by the Chairman of the Regional Health Administration Office and are managed by the Manager and the Board of Directors.

  5. We avoid including operational expenses as in input due to data inaccuracy. Since a large part of operational expenses consists of pharmaceuticals, there is the following peculiarity: the reported expenses as end-of-the year book values refer to that year outlays for pharmaceuticals even tough some of them have been used in previous years. This may be happen because either they were not paid in time or there was an agreement to be paid in parts. Since these details are not included in the data, it is impossible to figure out the actual annual pharmaceutical expenses from these end-of-the-year book values.

  6. Since this is the only variable used in ratio form it means that we do not impose any a priori CRS structure in the data and consequently in the implemented model. This concerns mentioned in Jacobs et al. (2006), p. 104 arises naturally when all variables are in ratio form, with a common denominator. For this reason we can use without problems a CRS formulation (9), as required by the proper definition of the conventional and the quality adjusted Malmquist productivity indices.

  7. As small hospitals are defined these with less than 100 beds, as medium these with 100–300 beds, and as large these with more than 300 beds.

  8. The corresponding VRS estimates, not reported here, are as expected no less than CRS estimates.

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Acknowledgments

Pythagoras II-Funding of research groups in the University of Macedonia, Priority Action 2.2.3.e, Measure 2.2, to be implemented within the framework of the Operational Programme “Education and Initial Vocational Training II (EPEAEK II)” and co-financed by the European Union [3rd Community Support Framework, 75% financed by the European Social Fund 25% National Resources].

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Correspondence to Roxani Karagiannis.

Appendix: Linear programming problems

Appendix: Linear programming problems

$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t + 1} ,y^{t + 1} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t + 1} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$
(10)
$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t + 1} (x^{t} ,y^{t} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t + 1} \ge 0,} } & { n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t + 1} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$
(11)
$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t} ,y^{t} ,\alpha^{t} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t} \ge 0, } } & {j = 1, \ldots ,J,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots K} \\ \end{array} $$
(12)

Similar for [D t+1 oc (x t+1y t+1α t+1)]−1 = max ϕ

$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t} (x^{t + 1} ,y^{t + 1} ,\alpha^{t + 1} )} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}}.} & {x_{n}^{t + 1} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t} \ge 0, } } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t + 1} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t} \ge 0,} } & {j = 1, \ldots ,J,} \\ {} & {z_{k} \ge 0,} & {k = 1, \ldots ,K} \\ \end{array} $$
(13)
$$ \begin{array}{*{20}c} {} & {\left[ {D_{oc}^{t + 1} \left( {x^{t} ,y^{t} ,\alpha^{t} } \right)} \right]^{ - 1} = \max \phi } & {} \\ {{\text{s}}.{\text{t}} .} & {x_{n}^{t} - \sum\limits_{k = 1}^{K} {z_{k} x_{k}^{t + 1} \ge 0,} } & {n = 1 ,\ldots ,N} \\ {} & { - \phi y_{m}^{t} + \sum\limits_{k = 1}^{K} {z_{k} y_{k}^{t + 1} \ge 0,} } & {m = 1, \ldots ,M,} \\ {} & { - \phi \alpha_{j}^{t} + \sum\limits_{k = 1}^{K} {z_{k} \alpha_{k}^{t + 1} \ge 0,} } & {j = 1,..,J,} \\ {} & {z_{k} \ge 0, } & {k = 1,. \ldots K} \\ \end{array} $$
(14)

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Karagiannis, R., Velentzas, K. Productivity and quality changes in Greek public hospitals. Oper Res Int J 12, 69–81 (2012). https://doi.org/10.1007/s12351-010-0080-4

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