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How efficient are New Zealand's District Health Boards at producing life expectancy gains for Māori and Europeans?

How efficient are New Zealand's District Health Boards at producing life expectancy gains for... resources in health in the expectation Objective: Use data envelopment analysis (DEA) to measure the efficiency of New Zealand’s Gthat these lead to increases in the District Health Boards (DHBs) at achieving gains in Māori and European life expectancy (LE). length and quality of life. Technological and organisational advances have meant Methods: Using life tables for 2006 and 2013, a two-output DEA model established the that population health status is now highly production possibility frontier for Māori and European LE gain. Confidence limits were determined by the efficacy and efficiency of generated from a 10,000 replicate Monte Carlo simulation. national health systems. Countries that invest Results: Results support the use of LE change as an indicator of DHB efficiency. DHB mean more in health, particularly through public income and education were related to initial LE but not to its rate of change. LE gains were sector funding, tend to achieve better health unrelated to either the initial level of life expectancy or to the proportion of Māori in the outcomes while macro socio-economic population. DHB efficiency ranged from 79% to 100%. Efficiency was significantly correlated factors have become relatively less important with DHB financial performance. 2,3 over time. It is self-evident that higher Conclusion: Changes in LE did not depend on the social characteristics of the DHB. The levels of health sector efficiency will produce statistically significant association between efficiency and financial performance supports its greater health gains. use as an indicator of managerial effectiveness. Data envelopment analysis (DEA) has been Implications for public health: Efficient health systems achieve better population health widely used to measure efficiency in the outcomes. DEA can be used to measure the relative efficiency of sub-national health health sector, but this and most other frontier authorities at achieving health gain and equity outcomes. production analyses have focused on the Key words: life expectancy, efficiency, data envelopment analysis, Maori, New Zealand performance of hospitals, health centres or specific services as decision-making units. There are just a few examples of DEA being stewardship role is retained at central level. in socio-economic factors such as age, applied to measure the efficiency of semi- In Spain, for example, health sector budgets income, education and ethnicity that autonomous sub-national health authorities are controlled by the 17 Comunidades are themselves closely related to health 5,6 at achieving population health outcomes. Autónomas; in Scotland, responsibility for outcomes. However, whilst acknowledging Hospital productivity may be measured health services rests with 14 Regional Health that these factors are important determinants in terms of patient throughput or health Boards; and in New Zealand (NZ) public sector of the baseline population health status, interventions, but the productivity of health health services are funded and provided they are not necessarily of great importance authorities should use broader measures (mainly) by 20 District Health Boards (DHBs). as determinants of the velocity of change in consistent with their mandate to increase population health status over time. The presence of multiple ‘decision-making overall population health and to reduce units’ makes it possible to compare their In this paper we first show that changes in life inequalities in health outcomes. In many performance but there has been some expectancy in NZ over the intercensal period countries publicly funded health systems are reluctance to make comparisons of from 2006 to 2013 were almost entirely decentralised or devolved to sub-national, outcomes between geographically defined unrelated to baseline socioeconomic and geographically defined health authorities, health authorities on the grounds that the demographic factors. Rather, we posit that although in most a governance and populations they serve differ considerably health change (specifically life expectancy 1. Planning Funding and Outcomes, Auckland and Waitemata District Health Boards, New Zealand 2. School of Population Health, University of Auckland, New Zealand 3. Centro de Investigaciones de Economía y Gestión en Salud, Universidad Politécnica de Valencia, Spain 4. Accounting and Finance, University of Auckland Business School, New Zealand Correspondence to: Dr Peter Sandiford, Waitemata District Health Board – Planning, Funding and Outcomes, Level 1 – 15 Shea Terrace, Takapuna, Auckland 0740, New Zealand; e-mail: peter.sandiford@waitematadhb.govt.nz Submitted: May 2016; Revision requested: July 2016; Accepted: August 2016 The authors have stated they have no conflict of interest. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. The copyright line for this article was changed on 5 April 2017, after original online publication. Aust NZ J Public Health. 2017; 41:125-9; doi: 10.1111/1753-6405.12618 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 125 © 2016 The Authors Sandiford, Vivas Consuelo and Rouse Article for the purpose of this analysis) has been unrelated to the size of a country (the Methods driven by changing patterns of exposure to correlation coefficient for the association The basic data used in this analysis were risk factors, whose strength and impact on between population size and life expectancy period lifetables produced by Statistics New health outcomes has been modified by health at birth in 2010 for 188 countries listed on Zealand for each ethnic group in each DHB sector intervention both at national and local the Gapminder website is 0.02), and here using data from the 2006 and 2013 censuses level. Further, we suggest that subnational we test the possibility at a smaller scale by in combination with mortality data from the variation in ethnic-specific changes in life measuring its correlation with the size of the periods 2005-07 and 2012-14. expectancy is partly determined by the DHB. LE gains have the additional advantage efficiency with which individual DHBs have that they are intuitively understood by both The life tables were produced using a used need-weighted population-based health sector managers and the general hierarchical Bayes model that copes with funding to produce better health outcomes. population. However, a more sophisticated sparse data by sharing information across We apply DEA as a widely used tool for the analysis would also take into account health- estimates, avoiding the need for manual measurement of DHB efficiency. related quality of life gains. smoothing. The methods yield explicit measures of uncertainty which are reflected It was assumed that each DHB received NZ healthcare system organisation in the 95% credibility limits provided equal inputs with which to increase LE. As with each table. A full description of the It is important to begin by explaining some noted above, the population-based funding methods is provided by Statistics NZ. We features that are specific to health in NZ. formula (PBFF) is designed to compensate derived the change in Māori and European NZ has a multi-ethnic population divided each DHB equitably for differences in costs to life expectancy for each DHB from these broadly into: indigenous Māori (16% in 2013); serve their respective populations. In a sense, lifetables. Asians (12%); Pacific, who identify ethnically the PBFF can be seen as a way of ensuring with one or other of the Pacific Islands (6%); ‘equality’ of purchasing power among DHBs. The first step in the analysis involved and the rest (66%), who are overwhelmingly The assumption that PBFF achieves equality testing the hypothesis that the change of European ethnicity and will be referred in inputs among the DHBs was tested post in life expectancy in each DHB between to here as European. The Māori and Pacific hoc by examining whether there was any 2006 and 2013 was unrelated to their populations experience higher levels of correlation between the calculated DHB baseline socioeconomic and demographic deprivation and have lower life expectancies. efficiency scores and several factors related characteristics, and to the change in these to healthcare costs that may or may not over this period. Accordingly, the correlation Equity in health in NZ is measured mainly have been adequately adjusted for by the between a wide variety of published in terms of the reduction or elimination of PBFF. These were: actual per capita DHB indicators from the 2006 census and the health inequalities between Māori and Pacific, funding; the size of the DHB population; the change in DHB life expectancy was calculated and European (sometimes grouped with proportion of Māori in the DHB population; and tested for statistical significance. Asians). Considerable effort has been devoted the proportion of the population aged 85 and to ensuring that ethnicity is measured The second step of the analysis used output- over; and DHB ‘rurality’ based on an indicator completely and accurately in the census and oriented data envelopment analysis under in recent review of the PBFF rural adjuster. in other national databases, including the the assumption of constant returns to scale 7 The efficiency scores of DHBs with tertiary mortality collection. Individuals can have to estimate the efficiency of each DHB at services were also compared with those of multiple ethnicities, however many analyses producing life expectancy gains in their DHBs without tertiary services to test that the (and the population-based funding formula) Māori and European populations. With this PBFF adjusts adequately for this factor. If the apply a prioritisation to produce a single tool we are effectively considering each DHB PBFF has failed to adequately compensate ethnicity code where Māori overrides all other as a production unit whose main outputs for higher costs, then one might expect to ethnicities, Pacific overrides all but Māori, and are gains in population life expectancy. We 8 see a negative correlation between actual per Asian is recorded in priority to European. restricted the analysis to Māori and European capita funding received and DHB efficiency. populations to avoid intractable complexity District Health Boards serve populations Conversely, if the PBFF overcompensates for in the analysis. The implications of this ranging (in 2013) from 33,000 to 552,000. cost differences then one might expect to restriction are addressed in the discussion. They receive funding on a capitation basis see a positive correlation between the actual with weightings and adjustments made to The intercensal change in life expectancy per capita funding and efficiency. Similarly, reflect variation in expected health-service at birth (LE) was chosen as the outcome any significant correlation between the other costs due to: difference in the age-sex of interest because it is a paramount goal variables and efficiency estimates would structure of the population in each ethnic of investment in healthcare, and as we suggest that the assumption of equal health group and deprivation decile; rurality; demonstrate, it is largely unrelated to purchasing power may have been violated. treatment of non-resident populations (e.g. socioeconomic factors. It can be plausibly DEA estimates of efficiency were calculated tourists); and unmet health needs in Māori assumed to be attributable in a large part 9,10 using Stata and Excel. DEA is a widely used and Pacific. The various cost-weights and to investments in health where these are non-parametric method for assessing the adjustors mean that some DHBs receive up taken in a broad sense to include measures efficiency of productive units and estimating to 24% above the population average while to modify risk factors and promote healthy 9 production possibility frontiers. Although others receive up to 12% less. lifestyles. The change in LE has the additional it does not rely on prior assumptions about advantage that as an output, it exhibits the nature of the productive process, noise constant returns to scale. This is evident in measurement is known to bias efficiency from the fact that population LE is generally 126 Australian and New Zealand Journal of Public Health 2017 vol . 41 no . 2 © 2016 The Authors Mortality NZ efficienc y at producing life expectancy gains estimates. Kao and Liu have shown that if where each DHB is represented as a point Table 2: Correlation of DHB socioeconomic indicators external estimates of measurement precision on the graph corresponding to its gain in with LE in 2006 and the change in LE, 2006 to 2013. are available then Monte Carlo simulation LE from 2006 to 2013 for Māori (vertical Proportion of the DHB Correlation Correlation methods can be used to produce unbiased axis) and Europeans (horizontal axis). The population / households with 2006 with change ‘stochastic’ efficiency estimates. A recent line enveloping the DHBs at the outer edge LE in LE (2006-13) review of methods to perform DEA in the represents the (non-stochastic) production No educational qualification -0.79*** 0.08 presence of measurement uncertainty possibility frontier for these two outputs. The University degree 0.68*** -0.15 recommended using Monte Carlo simulations four DHBs sitting on and defining the PPF 15 Age-standardised -0.34 0.30 where feasible. (Waikato, Counties Manukau, Hawkes Bay unemployment rate and Nelson Marlborough) have efficiencies In this case we used the 95% credibility Household income <$30,000 -0.70*** -0.06 of 100%. For the others, their efficiency can limits on the life table measures provided by Rental accommodation 0.26 0.26 be represented graphically as the ratio of Statistics New Zealand to simulate 10,000 Internet access 0.88*** -0.10 their distance from the origin to the distance replications of each DHB’s gain in Māori and No motor vehicle -0.15 -0.34 from the origin to the PPF (passing through European life expectancy (assuming a normal Age-standardised smoking rate -0.89*** 0.14 that point). So, in the case of Lakes DHB, the distribution of the error in life expectancy Rural residence -0.55* -0.06 efficiency is the length of line OA divided by estimates in each census year), thereby * p<0.05 ** p<0.01 *** p<0.001 the length of line OB as shown in Figure 1. producing 10,000 estimates of efficiency along with 95% percentile limits for each The efficiency of each DHB calculated in this The median efficiency in Table 3 was found DHB. Given their asymmetric distribution, way is shown in Table 3. Table 3 also shows to be positively correlated with the size of median efficiency values were reported. the median efficiency of each DHB derived the financial surplus in 2012/13 (r=0.46; Data on DHB financial deficits/supluses were from the Monte Carlo simulation, which p=0.0498), with Canterbury excluded because drawn from the 2012/13 Annual Report of the effectively creates 10,000 different PPFs and its surplus/deficit was not reported (given Controller and Auditor-General. calculates the DHBs’ efficiency for each of that insurance receipts from earthquake them. A 95 percentile confidence limit is Excel was used to calculate correlation damages made it incomparable). More provided for each Monte Carlo efficiency coefficients. Stata 13 was used to perform than half the DHBs were apparently able to estimate. It can be seen from Table 3 that a t-test (unequal variance) of the difference improve their LE comfortably within their the Monte Carlo efficiency estimates are in mean efficiency scores for DHBs with and PBFF allocations. Conversely, DHBs with consistently equal to, or smaller than, the without tertiary level hospitals. deficits had lower efficiency scores. Efficiency non-stochastic DEA estimates. This is because scores were not significantly correlated with deterministic DEA is known to overestimate the funding to population ratio (r=0.06; Results efficiency when there is measurement error p=0.81); the size of the DHB (r=0.05; p=0.85); or noise. Table 1 shows the Māori and European life the Māori proportion of its population table estimates of life expectancy for each DHB, and the change in these between Table 1: Life expectancy at birth for Māori and European in 2006 and 2013 by DHB (with 95% credibility limits). 2006 and 2013. Life expectancy has clearly Māori European District Health Board improved for both European and Māori in 2006* 2013* Change 2006 2013 Change all DHBs, but at a greater rate for the latter. Auckland 77.1 (76.0-78.1) 79.4 (78.3-80.5) 2.3 83.5 (83.2-83.7) 84.5 (84.3-84.7) 1.0 The change of life expectancy among Māori Bay of Plenty 72.5 (71.8-73.2) 74.9 (74.2-75.6) 2.4 82.0 (81.7-82.2) 83.1 (82.9-83.4) 1.1 Canterbury 76.5 (75.5-77.7) 78.7 (77.6-79.9) 2.2 81.0 (80.8-81.2) 81.9 (81.8-82.1) 0.9 from 2006 to 2013 was unrelated to the Capital and Coast 75.9 (74.8-77.1) 78.1 (77.0-79.3) 2.2 81.8 (81.5-82.1) 82.8 (82.5-83.0) 1.0 proportion of Māori in the DHB in 2006 Counties Manukau 72.5 (71.8-73.2) 74.7 (74.1-75.4) 2.3 82.5 (82.2-82.7) 83.7 (83.4-83.9) 1.2 (correlation coefficient r=-0.16; p=0.49). The Hawke’s Bay 71.2 (70.4-72.1) 73.9 (73.1-74.7) 2.7 80.8 (80.5-81.1) 81.9 (81.7-82.2) 1.2 change in Māori life expectancy was also not Hutt 73.8 (72.6-75.0) 76.2 (75.0-77.4) 2.4 80.9 (80.5-81.2) 81.9 (81.5-82.2) 1.0 significantly associated with the starting LE in Lakes 71.6 (70.8-72.5) 73.6 (72.8-74.4) 2.0 80.8 (80.4-81.2) 81.8 (81.5-82.2) 1.0 2006 (r=0.19; p=0.42), suggesting that change Midcentral 73.5 (72.5-74.5) 75.7 (74.8-76.7) 2.2 80.7 (80.4-80.9) 81.8 (81.5-82.1) 1.1 was not limited at the upper end of the range. Nelson Marlborough 77.7 (76.0-79.6) 80.3 (78.5-82.3) 2.6 81.0 (80.7-81.3) 82.2 (81.9-82.5) 1.2 This was also true for Europeans (r=0.31; Northland 71.2 (70.5-71.9) 73.5 (72.8-74.1) 2.3 81.6 (81.3-81.9) 82.6 (82.3-82.9) 1.0 p=0.19). South Canterbury 77.7 (74.9-81.0) 80.0 (77.2-83.6) 2.4 80.5 (80.1-80.9) 81.4 (81.0-81.8) 0.9 Table 2 presents the correlation with LE in Southern 76.1 (74.9-77.2) 78.4 (77.2-79.6) 2.3 80.4 (80.2-80.6) 81.3 (81.1-81.5) 0.9 2006 and the change by 2013 for a range Tairawhiti 70.3 (69.4-71.2) 72.6 (71.7-73.5) 2.3 80.7 (80.1-81.3) 81.8 (81.3-82.4) 1.1 of socioeconomic variables measured at Taranaki 73.5 (72.4-74.8) 75.9 (74.7-77.1) 2.4 80.6 (80.3-81.0) 81.7 (81.4-82.1) 1.1 DHB level. Although most of the indicators Waikato 72.3 (71.6-72.9) 74.4 (73.8-75.0) 2.1 81.0 (80.8-81.3) 82.3 (82.1-82.5) 1.2 were significantly associated with the Wairarapa 72.0 (70.3-73.8) 74.2 (72.5-76.0) 2.2 80.5 (80.0-81.0) 81.5 (81.0-81.9) 1.0 level of life expectancy in 2006, none of Waitemata 77.7 (76.7-78.6) 80.1 (79.1-81.1) 2.5 84.4 (84.2-84.6) 85.5 (85.3-85.7) 1.1 them was significantly associated with the West Coast 75.3 (72.8-78.0) 77.6 (75.2-80.6) 2.4 79.9 (79.4-80.4) 80.9 (80.4-81.4) 1.0 improvement in life expectancy over the Whanganui 71.0 (69.9-72.1) 73.4 (72.3-74.6) 2.5 80.5 (80.2-80.9) 81.6 (81.2-82.0) 1.0 subsequent seven years. Source: Statistics NZ * Statistics NZ uses the period 2005-7 and 2012-4 since mortality data was used from that range of dates. For simplicity we use the year of the census which A geometrical depiction of the classical DEA provided the population base for the life tables. efficiency analysis is provided in Figure 1 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 127 © 2016 The Authors Sandiford, Vivas Consuelo and Rouse Article (r=0.20; p=0.40); the proportion of its on service delivery of the 2011 earthquake. An obvious limitation of this study was its population aged 85 or over (r=-0.13; p=0.59); Capital and Coast also had a low efficiency omission of Asian and Pacific life expectancy nor the rurality of the population it serves score. It is notable that this DHB had four gains as outputs. Although DEA can readily (r=-0.06; p=0.81). Although the mean different Chief Executive Officers over cope with more than two outputs, the Monte efficiency of DHBs with a tertiary hospital was the intercensal period, each attempting Carlo simulation would have been far more lower than DHBs without one (86.2% versus unsuccessfully to tackle its chronic budget difficult to conduct and its discriminatory 90.6%) the difference was not statistically deficit, perhaps to the detriment of power would have been reduced. Also, the significant (p =0.23). population health outcomes. If the presence Asian life tables are not subdivided into South of a budget deficit is considered to be an Asians (predominantly of Indian, Sri Lankan, indicator of managerial effectiveness, then and Pakistani descent) and East Asians Discussion the significant correlation between efficiency (mainly ethnic Chinese and Korean), whose estimates and financial deficits/surpluses distribution differs across DHBs and whose This study has found reasonably high provides support for the validity of the LE gains may also have differed considerably. levels of efficiency in NZ DHBs. By means of efficiency estimates that we have calculated. Furthermore, Pacific and Asian populations comparison, Tigga and Mishra’s DEA study of Indeed, if the deficit were incorporated in some DHBs are very low. Incorporating inter-state health outcomes in India found 6 into the input measure (DHBs that run a health-related quality of life measures into a mean technical efficiency score of 84%. deficit effectively receive greater inputs than the outputs (perhaps as health expectancies) On the other hand, in a DEA comparison of the PBFF allocation), then the correlation would be valuable in any future such health system efficiency in OECD countries between efficiency and financial results analyses. all 28 countries studied were found to would have been even stronger (data not have efficiencies of 90% and over for life The approach used assumed that each DHB shown). expectancy at birth and at 65 years (but it did received equal levels of input based on the not examine change in life expectancy and The generally high level of efficiency for PBFF formula. Our tests of the validity of this NZ was not one of the included countries). all DHBs may reflect a relatively uniform assumption failed to identify any obvious standard of health sector management, but violation and hence the observed differences The 95% confidence limits for DHB efficiency it could also be because policy directions and in efficiency scores are unlikely to be due to all overlapped at some point, but that does service guidelines provided by the Ministry differences in DHB funding. not exclude the possibility there are in of Health allow little scope for any particular fact significant differences between them. In output-oriented DEA with two or more DHB to shine over the rest, or because Canterbury DHB had the lowest efficiency. outputs the slope of the production improvements in health outcomes are largely Canterbury’s efficiency was probably affected possibility frontier defines opportunity costs determined by national historical trends (such by the health impact and disruptive effects and how these vary as life expectancy gains as the decline in smoking and the obesity approach the maxima. In the flat and vertical epidemic), that affect all DHBs similarly, even segments there are no opportunity costs. Table 3: Efficiency of District Health Boards at if their starting levels of LE are quite different. A non-zero and non-infinite slope within achieving life expectancy gains for their Māori and European populations. Efficiency (%) Figure 1: Gain in Maori and European life expectancy by DHB 2006 to 2013. Non- Stochastic DEA District Health Board stochastic (95% confidence DEA limits) Auckland 86 86 (77–96) Bay of Plenty 96 94 (86–100) Canterbury 82 79 (71–93) Capital and Coast 83 83 (74–94) Counties Manukau 100 98 (90–100) Hawke’s Bay 100 100 (90–100) Hutt 90 87 (76–100) Lakes 86 84 (74–95) Midcentral 93 92 (83–100) Nelson Marlborough 100 100 (90–100) Northland 86 86 (77–94) South Canterbury 89 85 (67–100) Southern 87 83 (74–99) Tairawhiti 93 92 (79–100) Taranaki 92 91 (82–100) Waikato 100 98 (90–100) Wairarapa 83 83 (70–100) Waitemata 93 92 (84–100) West Coast 89 88 (70–100) Whanganui 91 89 (78–100) 128 Australian and New Zealand Journal of Public Health 2017 vol . 41 no . 2 © 2016 The Authors Mortality NZ efficienc y at producing life expectancy gains this frontier implies opportunity costs such can achieve different levels of LE gain for References that gains for one ethnic group can only Māori and Europeans. Those achieving 1. Barthold D, Nandi A, Mendoza Rodríguez JM, Heymann be attained at the expense of gains for the higher Māori LE gains could be considered J. Analyzing whether countries are equally efficient at improving longevity for men and women. Am J Public other ethnic group. One might challenge to be pursuing higher degrees of equity. For Health. 2014;104(11):2163-9. this feature of DEA on the grounds that it example, although Hawkes Bay and Nelson 2. Preston SH. The changing relationship beween mortality and level of economic development. Popul should always be possible to increase Māori Marlborough DHBs were both 100% efficient, Stud. 1975;29(2):231-48. life expectancy without sacrificing European the former achieved a LE gain for Māori of 3. Riley JC. The timing and pace of health transitions life expectancy (and vice versa). There are 2.68 compared with 2.60 for the latter. The around the world. Popul Dev Rev. 2005;31(4):741-64. 4. Hollingsworth B. The measurement of efficiency many health interventions which increase opportunity cost of the 0.08-year greater and productivity of health care delivery. Health Econ. both Māori and European life expectancy gain in Māori life expectancy was a 0.02-year 2008;17(10):1107-28. 5. Rouse P, Swales R. Pricing public health care services (e.g. water chlorination). However, many lower gain in European LE (1.17 versus 1.19). using DEA: Methodology versus politics. Ann Oper Res. interventions have disproportionate life However, Māori make up 24.1% of Hawkes 2006;145(1):265-80. 6. Tigga NS, Mishra US. On measuring technical efficiency expectancy gains for one or other ethnicity: Bay’s population but only 8.9% of Nelson of the health system in india an application of data for example, rheumatic fever programmes; Marlborough’s. Thus the higher LE gain in envelopment analysis. J Health Manag. 2015;17(3): melanoma treatment; housing insulation Hawkes Bay will have a much higher impact 285-98. 7. Blakely T, Atkinson JN, Fawcett J. Ethnic counts on subsidies; bowel screening; smoking on the actual number of years of life gained mortality and census data (mostly) agree for 2001-2004: cessation; hepatitis treatment, aortic in Hawkes Bay than a similar gain for Māori New Zealand Census-Mortality Study update. N Z Med J. 2008;121(1281):58-62. aneurysm screening, etc. The actions of health would have had in Nelson Marlborough. 8. Ministry of Health. Ethnicity Data Protocols for the Health service planners in having to make choices Hence for any given DHB’s mix of Māori and and Disability Sector. Wellington (NZ): Government of New Zealand; 2004. between these interventions demonstrates European population, there is probably only 9. Penno E, Gauld R. How are New Zealand’s District Health the very real opportunity costs to one one point on the PPF that maximises total Boards funded and does it matter if we can’t tell?’. N Z ethnicity of making greater life expectancy expected years of life gained. Med J. 2013;126:e1376. 10. Ministry of Health. Population-based Funding Formula gains for another. To our knowledge this is the first study to Review: 2015 Technical Report. Wellington (NZ): Government of New Zealand; 2016. By assessing efficiency in terms of Māori formally quantify the efficiency of NZ’s DHBs 11. Statistics New Zealand. New Zealand Period Life Tables: and European LE gains it was hoped that in achieving life expectancy gains. It has also Methodology for 2012-14 [Internet]. Wellington (NZ): Government of New Zealand; 2015. [cited 2015 Oct 9]. it would be possible to judge the extent to demonstrated the feasibility of Monte Carlo Available from: http://www.stats.govt.nz/browse_for_ which DHBs are pursuing greater equity based stochastic DEA. Future analyses could stats/health/life_expectancy/period-life-tables.aspx as well as overall population health gain, extend this work to incorporate health- 12. Gapminder. Data in Gapminder World – Excel Data [Internet]. Stockholm (SWE): Gapminder; 2016 [cited since both are fundamental health sector related quality of life measures and other 2016 Mar 8]. Available from: http://www.gapminder. goals. DHBs operating at 100% efficiency ethnic groups. org/data/ 13. Moore D, Blick G, Whelen C. Review of the Rural and Tertiary Adjusters. Wellington (NZ): Sapere Research Group; 2015. 14. Kao C, Liu S-T. Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks. Eur J Oper Res. 2009;196(1):312-22. 15. Dyson RG, Shale EA. Data envelopment analysis, operational research and uncertainty. J Oper Res Soc. 2010;61(1):25-34. 16. Controller and Auditor-General – Tumuaki o te Mana Arotake. Annual Report 2012/13. Wellington (NZ): Zealand Office of the Auditor-General; 2013. 17. Kao C, Liu ST. Measuring performance improvement of Taiwanese commercial banks under uncertainty. Eur J Oper Res. 2014;235(3):755-64. 18. Medeiros J, Schwierz C. Efficiency Estimates of Health Care Systems. Brussels (BEL): European Commission; 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 129 © 2016 The Authors http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Australian and New Zealand Journal of Public Health Wiley

How efficient are New Zealand's District Health Boards at producing life expectancy gains for Māori and Europeans?

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Wiley
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© 2017 Public Health Association of Australia
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1326-0200
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10.1111/1753-6405.12618
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Abstract

resources in health in the expectation Objective: Use data envelopment analysis (DEA) to measure the efficiency of New Zealand’s Gthat these lead to increases in the District Health Boards (DHBs) at achieving gains in Māori and European life expectancy (LE). length and quality of life. Technological and organisational advances have meant Methods: Using life tables for 2006 and 2013, a two-output DEA model established the that population health status is now highly production possibility frontier for Māori and European LE gain. Confidence limits were determined by the efficacy and efficiency of generated from a 10,000 replicate Monte Carlo simulation. national health systems. Countries that invest Results: Results support the use of LE change as an indicator of DHB efficiency. DHB mean more in health, particularly through public income and education were related to initial LE but not to its rate of change. LE gains were sector funding, tend to achieve better health unrelated to either the initial level of life expectancy or to the proportion of Māori in the outcomes while macro socio-economic population. DHB efficiency ranged from 79% to 100%. Efficiency was significantly correlated factors have become relatively less important with DHB financial performance. 2,3 over time. It is self-evident that higher Conclusion: Changes in LE did not depend on the social characteristics of the DHB. The levels of health sector efficiency will produce statistically significant association between efficiency and financial performance supports its greater health gains. use as an indicator of managerial effectiveness. Data envelopment analysis (DEA) has been Implications for public health: Efficient health systems achieve better population health widely used to measure efficiency in the outcomes. DEA can be used to measure the relative efficiency of sub-national health health sector, but this and most other frontier authorities at achieving health gain and equity outcomes. production analyses have focused on the Key words: life expectancy, efficiency, data envelopment analysis, Maori, New Zealand performance of hospitals, health centres or specific services as decision-making units. There are just a few examples of DEA being stewardship role is retained at central level. in socio-economic factors such as age, applied to measure the efficiency of semi- In Spain, for example, health sector budgets income, education and ethnicity that autonomous sub-national health authorities are controlled by the 17 Comunidades are themselves closely related to health 5,6 at achieving population health outcomes. Autónomas; in Scotland, responsibility for outcomes. However, whilst acknowledging Hospital productivity may be measured health services rests with 14 Regional Health that these factors are important determinants in terms of patient throughput or health Boards; and in New Zealand (NZ) public sector of the baseline population health status, interventions, but the productivity of health health services are funded and provided they are not necessarily of great importance authorities should use broader measures (mainly) by 20 District Health Boards (DHBs). as determinants of the velocity of change in consistent with their mandate to increase population health status over time. The presence of multiple ‘decision-making overall population health and to reduce units’ makes it possible to compare their In this paper we first show that changes in life inequalities in health outcomes. In many performance but there has been some expectancy in NZ over the intercensal period countries publicly funded health systems are reluctance to make comparisons of from 2006 to 2013 were almost entirely decentralised or devolved to sub-national, outcomes between geographically defined unrelated to baseline socioeconomic and geographically defined health authorities, health authorities on the grounds that the demographic factors. Rather, we posit that although in most a governance and populations they serve differ considerably health change (specifically life expectancy 1. Planning Funding and Outcomes, Auckland and Waitemata District Health Boards, New Zealand 2. School of Population Health, University of Auckland, New Zealand 3. Centro de Investigaciones de Economía y Gestión en Salud, Universidad Politécnica de Valencia, Spain 4. Accounting and Finance, University of Auckland Business School, New Zealand Correspondence to: Dr Peter Sandiford, Waitemata District Health Board – Planning, Funding and Outcomes, Level 1 – 15 Shea Terrace, Takapuna, Auckland 0740, New Zealand; e-mail: peter.sandiford@waitematadhb.govt.nz Submitted: May 2016; Revision requested: July 2016; Accepted: August 2016 The authors have stated they have no conflict of interest. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. The copyright line for this article was changed on 5 April 2017, after original online publication. Aust NZ J Public Health. 2017; 41:125-9; doi: 10.1111/1753-6405.12618 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 125 © 2016 The Authors Sandiford, Vivas Consuelo and Rouse Article for the purpose of this analysis) has been unrelated to the size of a country (the Methods driven by changing patterns of exposure to correlation coefficient for the association The basic data used in this analysis were risk factors, whose strength and impact on between population size and life expectancy period lifetables produced by Statistics New health outcomes has been modified by health at birth in 2010 for 188 countries listed on Zealand for each ethnic group in each DHB sector intervention both at national and local the Gapminder website is 0.02), and here using data from the 2006 and 2013 censuses level. Further, we suggest that subnational we test the possibility at a smaller scale by in combination with mortality data from the variation in ethnic-specific changes in life measuring its correlation with the size of the periods 2005-07 and 2012-14. expectancy is partly determined by the DHB. LE gains have the additional advantage efficiency with which individual DHBs have that they are intuitively understood by both The life tables were produced using a used need-weighted population-based health sector managers and the general hierarchical Bayes model that copes with funding to produce better health outcomes. population. However, a more sophisticated sparse data by sharing information across We apply DEA as a widely used tool for the analysis would also take into account health- estimates, avoiding the need for manual measurement of DHB efficiency. related quality of life gains. smoothing. The methods yield explicit measures of uncertainty which are reflected It was assumed that each DHB received NZ healthcare system organisation in the 95% credibility limits provided equal inputs with which to increase LE. As with each table. A full description of the It is important to begin by explaining some noted above, the population-based funding methods is provided by Statistics NZ. We features that are specific to health in NZ. formula (PBFF) is designed to compensate derived the change in Māori and European NZ has a multi-ethnic population divided each DHB equitably for differences in costs to life expectancy for each DHB from these broadly into: indigenous Māori (16% in 2013); serve their respective populations. In a sense, lifetables. Asians (12%); Pacific, who identify ethnically the PBFF can be seen as a way of ensuring with one or other of the Pacific Islands (6%); ‘equality’ of purchasing power among DHBs. The first step in the analysis involved and the rest (66%), who are overwhelmingly The assumption that PBFF achieves equality testing the hypothesis that the change of European ethnicity and will be referred in inputs among the DHBs was tested post in life expectancy in each DHB between to here as European. The Māori and Pacific hoc by examining whether there was any 2006 and 2013 was unrelated to their populations experience higher levels of correlation between the calculated DHB baseline socioeconomic and demographic deprivation and have lower life expectancies. efficiency scores and several factors related characteristics, and to the change in these to healthcare costs that may or may not over this period. Accordingly, the correlation Equity in health in NZ is measured mainly have been adequately adjusted for by the between a wide variety of published in terms of the reduction or elimination of PBFF. These were: actual per capita DHB indicators from the 2006 census and the health inequalities between Māori and Pacific, funding; the size of the DHB population; the change in DHB life expectancy was calculated and European (sometimes grouped with proportion of Māori in the DHB population; and tested for statistical significance. Asians). Considerable effort has been devoted the proportion of the population aged 85 and to ensuring that ethnicity is measured The second step of the analysis used output- over; and DHB ‘rurality’ based on an indicator completely and accurately in the census and oriented data envelopment analysis under in recent review of the PBFF rural adjuster. in other national databases, including the the assumption of constant returns to scale 7 The efficiency scores of DHBs with tertiary mortality collection. Individuals can have to estimate the efficiency of each DHB at services were also compared with those of multiple ethnicities, however many analyses producing life expectancy gains in their DHBs without tertiary services to test that the (and the population-based funding formula) Māori and European populations. With this PBFF adjusts adequately for this factor. If the apply a prioritisation to produce a single tool we are effectively considering each DHB PBFF has failed to adequately compensate ethnicity code where Māori overrides all other as a production unit whose main outputs for higher costs, then one might expect to ethnicities, Pacific overrides all but Māori, and are gains in population life expectancy. We 8 see a negative correlation between actual per Asian is recorded in priority to European. restricted the analysis to Māori and European capita funding received and DHB efficiency. populations to avoid intractable complexity District Health Boards serve populations Conversely, if the PBFF overcompensates for in the analysis. The implications of this ranging (in 2013) from 33,000 to 552,000. cost differences then one might expect to restriction are addressed in the discussion. They receive funding on a capitation basis see a positive correlation between the actual with weightings and adjustments made to The intercensal change in life expectancy per capita funding and efficiency. Similarly, reflect variation in expected health-service at birth (LE) was chosen as the outcome any significant correlation between the other costs due to: difference in the age-sex of interest because it is a paramount goal variables and efficiency estimates would structure of the population in each ethnic of investment in healthcare, and as we suggest that the assumption of equal health group and deprivation decile; rurality; demonstrate, it is largely unrelated to purchasing power may have been violated. treatment of non-resident populations (e.g. socioeconomic factors. It can be plausibly DEA estimates of efficiency were calculated tourists); and unmet health needs in Māori assumed to be attributable in a large part 9,10 using Stata and Excel. DEA is a widely used and Pacific. The various cost-weights and to investments in health where these are non-parametric method for assessing the adjustors mean that some DHBs receive up taken in a broad sense to include measures efficiency of productive units and estimating to 24% above the population average while to modify risk factors and promote healthy 9 production possibility frontiers. Although others receive up to 12% less. lifestyles. The change in LE has the additional it does not rely on prior assumptions about advantage that as an output, it exhibits the nature of the productive process, noise constant returns to scale. This is evident in measurement is known to bias efficiency from the fact that population LE is generally 126 Australian and New Zealand Journal of Public Health 2017 vol . 41 no . 2 © 2016 The Authors Mortality NZ efficienc y at producing life expectancy gains estimates. Kao and Liu have shown that if where each DHB is represented as a point Table 2: Correlation of DHB socioeconomic indicators external estimates of measurement precision on the graph corresponding to its gain in with LE in 2006 and the change in LE, 2006 to 2013. are available then Monte Carlo simulation LE from 2006 to 2013 for Māori (vertical Proportion of the DHB Correlation Correlation methods can be used to produce unbiased axis) and Europeans (horizontal axis). The population / households with 2006 with change ‘stochastic’ efficiency estimates. A recent line enveloping the DHBs at the outer edge LE in LE (2006-13) review of methods to perform DEA in the represents the (non-stochastic) production No educational qualification -0.79*** 0.08 presence of measurement uncertainty possibility frontier for these two outputs. The University degree 0.68*** -0.15 recommended using Monte Carlo simulations four DHBs sitting on and defining the PPF 15 Age-standardised -0.34 0.30 where feasible. (Waikato, Counties Manukau, Hawkes Bay unemployment rate and Nelson Marlborough) have efficiencies In this case we used the 95% credibility Household income <$30,000 -0.70*** -0.06 of 100%. For the others, their efficiency can limits on the life table measures provided by Rental accommodation 0.26 0.26 be represented graphically as the ratio of Statistics New Zealand to simulate 10,000 Internet access 0.88*** -0.10 their distance from the origin to the distance replications of each DHB’s gain in Māori and No motor vehicle -0.15 -0.34 from the origin to the PPF (passing through European life expectancy (assuming a normal Age-standardised smoking rate -0.89*** 0.14 that point). So, in the case of Lakes DHB, the distribution of the error in life expectancy Rural residence -0.55* -0.06 efficiency is the length of line OA divided by estimates in each census year), thereby * p<0.05 ** p<0.01 *** p<0.001 the length of line OB as shown in Figure 1. producing 10,000 estimates of efficiency along with 95% percentile limits for each The efficiency of each DHB calculated in this The median efficiency in Table 3 was found DHB. Given their asymmetric distribution, way is shown in Table 3. Table 3 also shows to be positively correlated with the size of median efficiency values were reported. the median efficiency of each DHB derived the financial surplus in 2012/13 (r=0.46; Data on DHB financial deficits/supluses were from the Monte Carlo simulation, which p=0.0498), with Canterbury excluded because drawn from the 2012/13 Annual Report of the effectively creates 10,000 different PPFs and its surplus/deficit was not reported (given Controller and Auditor-General. calculates the DHBs’ efficiency for each of that insurance receipts from earthquake them. A 95 percentile confidence limit is Excel was used to calculate correlation damages made it incomparable). More provided for each Monte Carlo efficiency coefficients. Stata 13 was used to perform than half the DHBs were apparently able to estimate. It can be seen from Table 3 that a t-test (unequal variance) of the difference improve their LE comfortably within their the Monte Carlo efficiency estimates are in mean efficiency scores for DHBs with and PBFF allocations. Conversely, DHBs with consistently equal to, or smaller than, the without tertiary level hospitals. deficits had lower efficiency scores. Efficiency non-stochastic DEA estimates. This is because scores were not significantly correlated with deterministic DEA is known to overestimate the funding to population ratio (r=0.06; Results efficiency when there is measurement error p=0.81); the size of the DHB (r=0.05; p=0.85); or noise. Table 1 shows the Māori and European life the Māori proportion of its population table estimates of life expectancy for each DHB, and the change in these between Table 1: Life expectancy at birth for Māori and European in 2006 and 2013 by DHB (with 95% credibility limits). 2006 and 2013. Life expectancy has clearly Māori European District Health Board improved for both European and Māori in 2006* 2013* Change 2006 2013 Change all DHBs, but at a greater rate for the latter. Auckland 77.1 (76.0-78.1) 79.4 (78.3-80.5) 2.3 83.5 (83.2-83.7) 84.5 (84.3-84.7) 1.0 The change of life expectancy among Māori Bay of Plenty 72.5 (71.8-73.2) 74.9 (74.2-75.6) 2.4 82.0 (81.7-82.2) 83.1 (82.9-83.4) 1.1 Canterbury 76.5 (75.5-77.7) 78.7 (77.6-79.9) 2.2 81.0 (80.8-81.2) 81.9 (81.8-82.1) 0.9 from 2006 to 2013 was unrelated to the Capital and Coast 75.9 (74.8-77.1) 78.1 (77.0-79.3) 2.2 81.8 (81.5-82.1) 82.8 (82.5-83.0) 1.0 proportion of Māori in the DHB in 2006 Counties Manukau 72.5 (71.8-73.2) 74.7 (74.1-75.4) 2.3 82.5 (82.2-82.7) 83.7 (83.4-83.9) 1.2 (correlation coefficient r=-0.16; p=0.49). The Hawke’s Bay 71.2 (70.4-72.1) 73.9 (73.1-74.7) 2.7 80.8 (80.5-81.1) 81.9 (81.7-82.2) 1.2 change in Māori life expectancy was also not Hutt 73.8 (72.6-75.0) 76.2 (75.0-77.4) 2.4 80.9 (80.5-81.2) 81.9 (81.5-82.2) 1.0 significantly associated with the starting LE in Lakes 71.6 (70.8-72.5) 73.6 (72.8-74.4) 2.0 80.8 (80.4-81.2) 81.8 (81.5-82.2) 1.0 2006 (r=0.19; p=0.42), suggesting that change Midcentral 73.5 (72.5-74.5) 75.7 (74.8-76.7) 2.2 80.7 (80.4-80.9) 81.8 (81.5-82.1) 1.1 was not limited at the upper end of the range. Nelson Marlborough 77.7 (76.0-79.6) 80.3 (78.5-82.3) 2.6 81.0 (80.7-81.3) 82.2 (81.9-82.5) 1.2 This was also true for Europeans (r=0.31; Northland 71.2 (70.5-71.9) 73.5 (72.8-74.1) 2.3 81.6 (81.3-81.9) 82.6 (82.3-82.9) 1.0 p=0.19). South Canterbury 77.7 (74.9-81.0) 80.0 (77.2-83.6) 2.4 80.5 (80.1-80.9) 81.4 (81.0-81.8) 0.9 Table 2 presents the correlation with LE in Southern 76.1 (74.9-77.2) 78.4 (77.2-79.6) 2.3 80.4 (80.2-80.6) 81.3 (81.1-81.5) 0.9 2006 and the change by 2013 for a range Tairawhiti 70.3 (69.4-71.2) 72.6 (71.7-73.5) 2.3 80.7 (80.1-81.3) 81.8 (81.3-82.4) 1.1 of socioeconomic variables measured at Taranaki 73.5 (72.4-74.8) 75.9 (74.7-77.1) 2.4 80.6 (80.3-81.0) 81.7 (81.4-82.1) 1.1 DHB level. Although most of the indicators Waikato 72.3 (71.6-72.9) 74.4 (73.8-75.0) 2.1 81.0 (80.8-81.3) 82.3 (82.1-82.5) 1.2 were significantly associated with the Wairarapa 72.0 (70.3-73.8) 74.2 (72.5-76.0) 2.2 80.5 (80.0-81.0) 81.5 (81.0-81.9) 1.0 level of life expectancy in 2006, none of Waitemata 77.7 (76.7-78.6) 80.1 (79.1-81.1) 2.5 84.4 (84.2-84.6) 85.5 (85.3-85.7) 1.1 them was significantly associated with the West Coast 75.3 (72.8-78.0) 77.6 (75.2-80.6) 2.4 79.9 (79.4-80.4) 80.9 (80.4-81.4) 1.0 improvement in life expectancy over the Whanganui 71.0 (69.9-72.1) 73.4 (72.3-74.6) 2.5 80.5 (80.2-80.9) 81.6 (81.2-82.0) 1.0 subsequent seven years. Source: Statistics NZ * Statistics NZ uses the period 2005-7 and 2012-4 since mortality data was used from that range of dates. For simplicity we use the year of the census which A geometrical depiction of the classical DEA provided the population base for the life tables. efficiency analysis is provided in Figure 1 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 127 © 2016 The Authors Sandiford, Vivas Consuelo and Rouse Article (r=0.20; p=0.40); the proportion of its on service delivery of the 2011 earthquake. An obvious limitation of this study was its population aged 85 or over (r=-0.13; p=0.59); Capital and Coast also had a low efficiency omission of Asian and Pacific life expectancy nor the rurality of the population it serves score. It is notable that this DHB had four gains as outputs. Although DEA can readily (r=-0.06; p=0.81). Although the mean different Chief Executive Officers over cope with more than two outputs, the Monte efficiency of DHBs with a tertiary hospital was the intercensal period, each attempting Carlo simulation would have been far more lower than DHBs without one (86.2% versus unsuccessfully to tackle its chronic budget difficult to conduct and its discriminatory 90.6%) the difference was not statistically deficit, perhaps to the detriment of power would have been reduced. Also, the significant (p =0.23). population health outcomes. If the presence Asian life tables are not subdivided into South of a budget deficit is considered to be an Asians (predominantly of Indian, Sri Lankan, indicator of managerial effectiveness, then and Pakistani descent) and East Asians Discussion the significant correlation between efficiency (mainly ethnic Chinese and Korean), whose estimates and financial deficits/surpluses distribution differs across DHBs and whose This study has found reasonably high provides support for the validity of the LE gains may also have differed considerably. levels of efficiency in NZ DHBs. By means of efficiency estimates that we have calculated. Furthermore, Pacific and Asian populations comparison, Tigga and Mishra’s DEA study of Indeed, if the deficit were incorporated in some DHBs are very low. Incorporating inter-state health outcomes in India found 6 into the input measure (DHBs that run a health-related quality of life measures into a mean technical efficiency score of 84%. deficit effectively receive greater inputs than the outputs (perhaps as health expectancies) On the other hand, in a DEA comparison of the PBFF allocation), then the correlation would be valuable in any future such health system efficiency in OECD countries between efficiency and financial results analyses. all 28 countries studied were found to would have been even stronger (data not have efficiencies of 90% and over for life The approach used assumed that each DHB shown). expectancy at birth and at 65 years (but it did received equal levels of input based on the not examine change in life expectancy and The generally high level of efficiency for PBFF formula. Our tests of the validity of this NZ was not one of the included countries). all DHBs may reflect a relatively uniform assumption failed to identify any obvious standard of health sector management, but violation and hence the observed differences The 95% confidence limits for DHB efficiency it could also be because policy directions and in efficiency scores are unlikely to be due to all overlapped at some point, but that does service guidelines provided by the Ministry differences in DHB funding. not exclude the possibility there are in of Health allow little scope for any particular fact significant differences between them. In output-oriented DEA with two or more DHB to shine over the rest, or because Canterbury DHB had the lowest efficiency. outputs the slope of the production improvements in health outcomes are largely Canterbury’s efficiency was probably affected possibility frontier defines opportunity costs determined by national historical trends (such by the health impact and disruptive effects and how these vary as life expectancy gains as the decline in smoking and the obesity approach the maxima. In the flat and vertical epidemic), that affect all DHBs similarly, even segments there are no opportunity costs. Table 3: Efficiency of District Health Boards at if their starting levels of LE are quite different. A non-zero and non-infinite slope within achieving life expectancy gains for their Māori and European populations. Efficiency (%) Figure 1: Gain in Maori and European life expectancy by DHB 2006 to 2013. Non- Stochastic DEA District Health Board stochastic (95% confidence DEA limits) Auckland 86 86 (77–96) Bay of Plenty 96 94 (86–100) Canterbury 82 79 (71–93) Capital and Coast 83 83 (74–94) Counties Manukau 100 98 (90–100) Hawke’s Bay 100 100 (90–100) Hutt 90 87 (76–100) Lakes 86 84 (74–95) Midcentral 93 92 (83–100) Nelson Marlborough 100 100 (90–100) Northland 86 86 (77–94) South Canterbury 89 85 (67–100) Southern 87 83 (74–99) Tairawhiti 93 92 (79–100) Taranaki 92 91 (82–100) Waikato 100 98 (90–100) Wairarapa 83 83 (70–100) Waitemata 93 92 (84–100) West Coast 89 88 (70–100) Whanganui 91 89 (78–100) 128 Australian and New Zealand Journal of Public Health 2017 vol . 41 no . 2 © 2016 The Authors Mortality NZ efficienc y at producing life expectancy gains this frontier implies opportunity costs such can achieve different levels of LE gain for References that gains for one ethnic group can only Māori and Europeans. Those achieving 1. 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The measurement of efficiency many health interventions which increase opportunity cost of the 0.08-year greater and productivity of health care delivery. Health Econ. both Māori and European life expectancy gain in Māori life expectancy was a 0.02-year 2008;17(10):1107-28. 5. Rouse P, Swales R. Pricing public health care services (e.g. water chlorination). However, many lower gain in European LE (1.17 versus 1.19). using DEA: Methodology versus politics. Ann Oper Res. interventions have disproportionate life However, Māori make up 24.1% of Hawkes 2006;145(1):265-80. 6. Tigga NS, Mishra US. On measuring technical efficiency expectancy gains for one or other ethnicity: Bay’s population but only 8.9% of Nelson of the health system in india an application of data for example, rheumatic fever programmes; Marlborough’s. Thus the higher LE gain in envelopment analysis. J Health Manag. 2015;17(3): melanoma treatment; housing insulation Hawkes Bay will have a much higher impact 285-98. 7. Blakely T, Atkinson JN, Fawcett J. Ethnic counts on subsidies; bowel screening; smoking on the actual number of years of life gained mortality and census data (mostly) agree for 2001-2004: cessation; hepatitis treatment, aortic in Hawkes Bay than a similar gain for Māori New Zealand Census-Mortality Study update. N Z Med J. 2008;121(1281):58-62. aneurysm screening, etc. The actions of health would have had in Nelson Marlborough. 8. Ministry of Health. Ethnicity Data Protocols for the Health service planners in having to make choices Hence for any given DHB’s mix of Māori and and Disability Sector. Wellington (NZ): Government of New Zealand; 2004. between these interventions demonstrates European population, there is probably only 9. Penno E, Gauld R. How are New Zealand’s District Health the very real opportunity costs to one one point on the PPF that maximises total Boards funded and does it matter if we can’t tell?’. 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Wellington (NZ): Zealand Office of the Auditor-General; 2013. 17. Kao C, Liu ST. Measuring performance improvement of Taiwanese commercial banks under uncertainty. Eur J Oper Res. 2014;235(3):755-64. 18. Medeiros J, Schwierz C. Efficiency Estimates of Health Care Systems. Brussels (BEL): European Commission; 2017 vol . 41 no . 2 Australian and New Zealand Journal of Public Health 129 © 2016 The Authors

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