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The European Journal of Health Economics

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01-12-2013 | Original Paper

Quantifying short run cost-effectiveness during a gradual implementation process

Authors: Gijs van de Wetering, Willem H. Woertman, Andre L. Verbeek, Mireille J. Broeders, Eddy M. M. Adang

Published in: The European Journal of Health Economics | Issue 6/2013

Abstract

This paper examines the short run inefficiencies that arise during gradual implementation of a new cost-effective technology in healthcare. These inefficiencies arise when health gains associated with the new technology cannot be obtained immediately because the new technology does not yet supply all patients, and when there is overcapacity for the old technology in the short run because the supply of care is divided among two mutually exclusive technologies. Such efficiency losses are not taken into account in standard textbook cost-effectiveness analysis in which a steady state is presented where costs and effects are assumed to be unchanging over time. A model is constructed to quantify such short run inefficiencies as well as to inform the decision maker about the optimal implementation pattern for the new technology. The model operates by integrating the incremental net benefit equations for both the period of co-existence of mutually exclusive technologies and the period after complete substitution of the old technology. It takes into account the rate of implementation of the new technology, depreciation of capital of the old technology as well as the demand curves for both technologies. The model is applied to the real world case of converting from screen film to digital mammography in the Netherlands.

Of course, since l represents a proportion, it holds that l(t) = 1 for t ≥ λ.

The quantity n is a proportion, so that n(t) = 0 for t > λ.

To see this,\( \begin{aligned} \overline{\text{INB}}_{\text{SR}} = & \frac{{{\text{INB}}_{\text{LR}} }}{\mu } \cdot \left(\mathop \int\limits_{0}^{\lambda } \frac{t}{\lambda }{\text{d}}t + \mathop \int\limits_{\lambda }^{\mu } 1{\text{d}}t\right) - \frac{{\alpha \cdot C_{\text{o}} }}{\mu } \cdot \left(\mathop \int\limits_{0}^{\lambda } \frac{t}{\lambda } - \frac{t}{\mu }{\text{d}}t + \mathop \int\limits_{\lambda }^{\mu } 1 - \frac{t}{\mu }{\text{d}}t\right) \\ = & \frac{{{\text{INB}}_{\text{LR}} }}{\mu } \cdot \left( {\left[ {\frac{{t^{2} }}{2\lambda }} \right]_{0}^{\lambda } + \left[ t \right]_{\lambda }^{\mu } } \right) - \frac{{\alpha \cdot C_{\text{o}} }}{\mu } \cdot \left( {\left[ {\frac{{t^{2} }}{2\lambda } - \frac{{t^{2} }}{2\mu }} \right]_{0}^{\lambda } + \left[ {t - \frac{{t^{2} }}{2\mu }} \right]_{\lambda }^{\mu } } \right) \\ = & \frac{{{\text{INB}}_{\text{LR}} }}{\mu } \cdot \left( {\frac{\lambda }{2} + \left( {\mu - \lambda } \right)} \right) - \frac{{\alpha \cdot C_{\text{o}} }}{\mu } \cdot \left( {\frac{\mu }{2} - \frac{\lambda }{2}} \right) \\ = & \left( {1 - \frac{\lambda }{2\mu }} \right){\text{INB}}_{\text{LR}} - \alpha \cdot C_{\text{o}} \cdot \left( { \frac{1}{2} - \frac{\lambda }{2\mu }} \right) \\ \end{aligned} \).

Of course, in the rather unlikely case where \( \alpha \cdot C_{\text{o}} = {\text{INB}}_{\text{LR}} \), the short run INB function is constant in λ, and it does not matter how the implementation rate is chosen.

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Title: Quantifying short run cost-effectiveness during a gradual implementation process
Authors: Gijs van de Wetering
Willem H. Woertman
Andre L. Verbeek
Mireille J. Broeders
Eddy M. M. Adang
Publication date: 01-12-2013
Publisher: Springer Berlin Heidelberg
Published in: The European Journal of Health Economics / Issue 6/2013
Print ISSN: 1618-7598
Electronic ISSN: 1618-7601
DOI: https://doi.org/10.1007/s10198-012-0435-2

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Quantifying short run cost-effectiveness during a gradual implementation process

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