Efficiency, heterogeneity and cost function analysis: empirical evidence from pathology services in the National Health Service in England

Abstract

Pathology services are increasingly recognized as key to effective healthcare delivery – underpinning diagnosis, long-term disease management and research. To the extent that pathology services affect a patient’s treatment pathway, significant healthcare costs are influenced directly by the performance of these services. Given pressures on the UK Department of Health to make efficiency savings and that little is known about the efficiency of pathology laboratories, this area offers unlocked potential for efficiency gains. We adopt a time varying inefficiency model, with laboratory-specific time paths for inefficiency, to identify potential savings in pathology services based on a panel of 57 English laboratories over a 5 year period. We apply a range of approaches to account for observable and unobservable heterogeneity between laboratories. We find potential efficiency savings of 13% in pathology services in this sample, which implies the potential for an annual saving of £390m in pathology across the NHS. Our study also provides valuable insights into the impact of a range of factors influencing laboratory costs.

Keywords:

• stochastic frontier analysis
• costs
• total factor productivity
• pathology

Jel Classification:

• C23
• C81
• D24
• I11

Acknowledgements

The authors thank Dr Phill Wheat for providing some useful code and Professor Claire Hulme for some useful comments on several drafts of this article. We thank the two anonymous referees. We dedicate this work to the memory of the late Professor Rick Jones.

Notes

¹ NHS Institute for Innovation and Improvement: Pathology lean practice case studies, http://www.institute.nhs.uk/quality_and_value/lean_thinking/leean_case_studies.html

² If pathology is classed as diagnostic medicine, then there exists some SF work in this area (Dismuke and Sena, 1999). However, this study concerns patient-based, in-hospital activity such as computerized axial tomography (CAT) scans, whereas our study involves pathology laboratories – which are independent of their host hospitals and do not have direct patient contact – conducting blood and tissue tests. We therefore view pathology services as distinct from this kind of diagnostic medicine.

³ Some key performance indicators are being introduced, but have not yet been employed (Liebmann, 2011).

⁴ We use operating costs rather than total costs (including capital charges), meaning the production process is not strictly entirely modelled. Capital costs are budgeted centrally at trust (hospital) level, rather than laboratory level, meaning assigning specific capital charges to laboratories can only be estimated. We note that this has been found in pathology elsewhere, for example New Zealand (France and Francis, 2005). Moreover, this is not particular to pathology (Drummond et al., 2005, p. 64).

⁵ Clinical Pathology Accreditation: http://www.cpa-uk.co.uk/

⁶ Hausman tests (1978) consistently favoured RE over FE estimation; we are also interested in examining time-invariant variables, which we are unable to do in a FE framework.

⁷ Because of an unbalanced panel, a Baltagi and Li (1990) adaptation of the Breusch and Pagan (1980) test has been used and confirms the use of panel methods.

⁸ Within this framework, the temporal pattern of inefficiency can be tested statistically, which is a key advantage over alternative approaches, such as Cornwell et al. (1990).

⁹ Foundation status of a NHS trust (a trust is a hospital or small group of hospitals) means that it operates under an independent, not-for-profit regime, allowing it financial autonomy which it does not have without having foundation status (Marini et al., 2008). Trusts apply for foundation status, which is granted by the regulator, monitor, if the trust has satisfied the regulator of its financial competence. Foundation status has not been awarded to all NHS trusts.

¹⁰ Variables are mean scaled to allow direct interpretation of the first order terms.

¹¹ Types of laboratory include rural, urban and metropolitan; rural is the reference case for modelling.

¹² Lai and Huang (2010, p. 3), lament that ‘there are only limited systematic treatments of tests or model selection criteria in the existing SF literatures.’

¹³ H₀: additional translog terms (squared and cross terms) are jointly equal to zero.

¹⁴ H₀: observable or unobservable heterogeneity variables are jointly equal to zero.

¹⁵ H₀: log likelihood model (a) is equal to log likelihood model (b).

¹⁶ H₀: model (a) is equal to model (b).

¹⁷ 2 (functional forms) × 3 (heterogeneity variable specifications) × 5 (types of efficiency model).

¹⁸ In our sample, 27 laboratories are observed twice, 7 are observed 3 times, 2 are observed 4 times and 21 are observed in every year – 5 times.

¹⁹ Mutter et al. (2013) demonstrate using healthcare data that endogeneity can bias efficiency scores.

²⁰ As this variable is constructed using a variable that is also in the models, we check the correlation of the two variables for collinearity concerns. The correlation between the two variables is −0.34. We therefore do not see this as an issue. In any case, we note that collinearity is less an issue in panel data models than in cross sectional or time series alternatives (Baltagi, 2008).

²¹ We are aware that the Vuong test has no degrees of freedom restriction, meaning that it imposes no penalty for additional parameters estimated and so is likely to, in this case, favour the Cuesta model which has more parameters than the TRE model. Therefore, as a robustness check, we have also tested the P&L (which has fewer parameters than the TRE) against the TRE, and the test favours the P&L. Because our LR test preferred the Cuesta to the P&L, and the Vuong preferred the P&L to the TRE, we prefer the Cuesta to the TRE.

²² In addition, we have tested the presence of inefficiency using the LR test procedure outlined in Coelli et al. (2005, p. 258), which also confirms our result, but we do not report the test results here.

²³ Which is preferred of the three candidate BC92 models, see Table 5.

²⁴ Because our model is estimated in logarithms, we have applied an exponential retransformation to recover our estimate of the effect on costs. To illustrate, for the Cuesta s(iii) model, exp(0.16) = 1.17, meaning that the beta on TYPE: Metropolitan from this model implies that costs are 17% higher than for TYPE: Rural laboratories.

²⁵ According to anecdotal evidence from pathologists, these features are more prevalent in London and the South and thus are likely driving this variation in costs.

²⁶ We note that the AC curve appears to be flattening towards the extreme of the sample (Fig. 5). However, given that MC remains lower than AC at this point, this must be being driven by factors other than size which are associated with higher costs when size increases. However, further research with different data would be needed to draw any conclusion on the point at which size economies are exhausted.

Additional information

Funding

This work was funded under an Innovation in Quantitative Methods scholarship provided by the University of Leeds.