The directional hybrid measure of efficiency in data envelopment analysis

The efficiency measurement is a subject of great interest. The majority of studies on DEA models have been carried out using radial or non-radial approaches regarding the application of DEA for the efficiency measurement. This paper, based on the directional distance function, proposes a new generalized hybrid measure of efficiency under generalized returns to scale with the existence of both radial and non-radial inputs and outputs. It extends the hybrid measure of efficiency from Tone (2004) to a more general case. The proposed model is not only flexible enough for the decision-maker to adjust the radial and non-radial inputs and outputs to attain the efficiency score but also avoids the computational and interpretive difficulties, thereby giving rise to an important clarification and understanding of the generalized DEA model. Furthermore, several frequently-used DEA models (such as the CCR, BCC, ERM and SBM models) which depend on the radial or non-radial approaches are derived while their results were compared to the ones obtained from this hybrid model. The empirical examples emphasize the consequence of the proposed measure

Availability and affordability of blood pressure-lowering medicines and the effect on blood pressure control in high-income, middle-income, and low-income countries: an analysis of the PURE study data

Background: Hypertension is considered the most important risk factor for cardiovascular diseases, but its control is poor worldwide. We aimed to assess the availability and affordability of blood pressure-lowering medicines, and the association with use of these medicines and blood pressure control in countries at varying levels of economic development. Methods: We analysed the availability, costs, and affordability of blood pressure-lowering medicines with data recorded from 626 communities in 20 countries participating in the Prospective Urban Rural Epidemiological (PURE) study. Medicines were considered available if they were present in the local pharmacy when surveyed, and affordable if their combined cost was less than 20% of the households' capacity to pay. We related information about availability and affordability to use of these medicines and blood pressure control with multilevel mixed-effects logistic regression models, and compared results for high-income, upper-middle-income, lower-middle-income, and low-income countries. Data for India are presented separately because it has a large generic pharmaceutical industry and a higher availability of medicines than other countries at the same economic level. Findings: The availability of two or more classes of blood pressure-lowering drugs was lower in low-income and middle-income countries (except for India) than in high-income countries. The proportion of communities with four drug classes available was 94% in high-income countries (108 of 115 communities), 76% in India (68 of 90), 71% in upper-middle-income countries (90 of 126), 47% in lower-middle-income countries (107 of 227), and 13% in low-income countries (nine of 68). The proportion of households unable to afford two blood pressure-lowering medicines was 31% in low-income countries (1069 of 3479 households), 9% in middle-income countries (5602 of 65 471), and less than 1% in high-income countries (44 of 10 880). Participants with known hypertension in communities that had all four drug classes available were more likely to use at least one blood pressure-lowering medicine (adjusted odds ratio [OR] 2·23, 95% CI 1·59–3·12); p<0·0001), combination therapy (1·53, 1·13–2·07; p=0·054), and have their blood pressure controlled (2·06, 1·69–2·50; p<0·0001) than were those in communities where blood pressure-lowering medicines were not available. Participants with known hypertension from households able to afford four blood pressure-lowering drug classes were more likely to use at least one blood pressure-lowering medicine (adjusted OR 1·42, 95% CI 1·25–1·62; p<0·0001), combination therapy (1·26, 1·08–1·47; p=0·0038), and have their blood pressure controlled (1·13, 1·00–1·28; p=0·0562) than were those unable to afford the medicines. Interpretation: A large proportion of communities in low-income and middle-income countries do not have access to more than one blood pressure-lowering medicine and, when available, they are often not affordable. These factors are associated with poor blood pressure control. Ensuring access to affordable blood pressure-lowering medicines is essential for control of hypertension in low-income and middle-income countries. Funding: Population Health Research Institute, the Canadian Institutes of Health Research, Heart and Stroke Foundation of Ontario, Canadian Institutes of Health Research Strategy for Patient Oriented Research through the Ontario SPOR Support Unit, the Ontario Ministry of Health and Long-Term Care, pharmaceutical companies (with major contributions from AstraZeneca [Canada], Sanofi Aventis [France and Canada], Boehringer Ingelheim [Germany amd Canada], Servier, and GlaxoSmithKline), Novartis and King Pharma, and national or local organisations in participating countries