Abstract
Grasping the intricacy and diversity of complex systems dealing with ever-growing amounts of data is essential to public and private institutions' continuous improvement. Composite indicators (CIs) emerge as aggregators of key performance indicators, providing a single measure that reflects those multidimensional performance aspects. One way to build such measures is based on the use of data envelopment analysis (DEA). Several DEA models can be used to generate CIs. Still, not many of them can deal concurrently with desirable and undesirable outputs, and incorporate the decision-making actors' preference information. Based on the directional 'Benefit-of-the-Doubt' model, we propose a novel approach consisting of the simultaneous use of weight restrictions and an artificial target reached via a range directional vector. The resulting CI assesses the Portuguese public hospitals' performance under two perspectives of hospital activity: users and providers. In the end, managerial and policy implications are withdrawn from the results of this study conducted in cooperation with the Portuguese Ministry of Health.

Abstract
Convergence in productivity examines if entities in an industry get closer to the best practices or if the gap between the frontiers of the best and worst performers decreases over time. In a multi-input multioutput setting, the assessment of sigma- and beta-convergence can be measured with the use of non-parametric frontier techniques, such as data envelopment analysis. We propose an innovative approach to estimate convergence in the context of performance assessments resting on composite indicators, accounting for desirable and undesirable indicators. This methodology rests on 'Benefit-of-the-Doubt' models, specified with a directional distance function. It is applied to the Member States of the World Health Organization (WHO) in order to study their convergence in terms of the United Nations' Sustainable Development Goal (SDG) 'Good health and well-being'. We collected data for all years since the proposal of the SDGs, covering the period between 2016 and 2020. The results show that all WHO regions are (beta) over cap -divergent, especially because of the generalised decline of the Worst Practice Frontier (WPF), alongside an improvement at a lower rate of the Best Practice Frontier (BPF). The regional analysis also revealed (sigma) over cap -convergence in the Region of the Americas and the Eastern Mediterranean Region; the South-East Asia and African Regions exhibited (sigma) over cap -divergence; the Western Pacific and European Regions remained stable in terms of the performance spread regarding the BPF. At the worldwide level, we also observed an increase of the gap between the BPF and the WPF, although the performance spread around the worldwide BPF remained relatively stable.

Abstract
Health systems are complex organisations that attempt to deliver health services to meet the needs of the population. Regardless of the degree of access to and quality of those health services, the systems' sustainability has been the object of special attention by governments worldwide. To ensure their adequate functioning in light of the accountable and transparent facets of New Public Governance, one must resort to regulatory mechanisms, such as sunshine regulation. By publicly displaying the results of benchmarking assessments, sunshine regulation embarrasses operators with poor performances in an effort to force them to correct such divergences. Thus, in this paper, we propose a sunshine regulatory model to the public hospitals in Portugal using multi-criteria decision analysis. In particular, we created a five-star rating that categorises those operators according to their performances, by means of the outranking method ELECTRE TRI-NC. As a result, we provide evidence of the existence of a majority of providers assigned to the `Average' category of Three stars and the nonexistence of providers with unique extreme category assignments (One star or Five stars), both of which are supported by extensive stability and robustness analyses, and discussed in terms of policy implications for relevant stakeholders.

Abstract
Seeking to "ensure availability and sustainable management of water and sanitation for all" is an admirable Sustainable Development Goal and an honourable commitment of the United Nations and its Member States regarding the human right to safe drinking water and sanitation services (WSSs). However, the majority of countries are not on target to achieve this by 2030, with several of them moving away from the best practices. Brazil is one of these cases, given, for example, the existing asymmetries in the access to water supply and sanitation service networks. For this reason, we propose a benchmarking exercise using a two-stage Data Envelopment Analysis to measure the technical and scale efficiency of the Brazilian municipalities' WSSs, noting their contextual environment. Our results point towards low mean efficiency scores, motivated by the existence of significant scale inefficiencies (the vast majority of municipalities are operating at a larger than optimal scale). Furthermore, the Water source was found to be a statistically significant efficiency predictor, with statistically significant differences found in terms of Ownership and Geography. Ultimately, we suggest policy-making and regulatory possibilities based on debureaucratization, the implementation of stricter expenditure control policies, and investment in the expansion of WSSs.

Abstract
Nowadays, public health and sustainable development go hand in hand towards the renovated percep-tion of the former. Indeed, "ensuring healthy lives and promoting the well-being for all at all ages", which established one of the United Nations (UN) Sustainable Development Goals (SDGs), seeks to ensure that this conception is not only reinforced, but also that saving lives takes into account the physical, mental, and social well-being of populations whose "development meets the needs of the present without com-promising the ability of future generations to meet their own needs". Accordingly, it is useful to interpret and convey information pertaining to this multidimensional concept in a way that encapsulates all its facets. Since this can be achieved through a composite indicator (CI), we propose a sustainable public health index framework, based on the 13 targets of the UN's SDG 3 between 2016 and 2020. For this rea-son, using the popular CI-generating 'Benefit-of-the-Doubt' approach while considering desirable and undesirable indicators, we apply this framework to 181 World Health Organization Member States. We show that, from 2016 to 2020, less than 28% of them remained efficient and the European Region clearly dominated the remaining regions, which tended to decrease their performance, on average. Finally, we also reveal the global efforts towards improving the Proportion of births attended by skilled health personnel and the Density of medical doctors per 10,000 population, and the failure in achieving an acceptable Neonatal mortality rate, Under-five mortality rate, and a Number of people requiring interven-tions against neglected tropical diseases.

Abstract
The ongoing outbreak of SARS-CoV-2 has been deeply impacting health systems worldwide. In this context, it is pivotal to measure the efficiency of different nations' response to the pandemic, whose insights can be used by governments and health authorities worldwide to improve their national COVID-19 strategies. Hence, we propose a network Data Envelopment Analysis (DEA) to estimate the efficiencies of fifty-five countries in the current crisis, including the thirty-seven Organisation for Economic Co-operation and Development (OECD) member countries, six OECD prospective members, four OECD key partners, and eight other countries. The network DEA model is designed as a general series structure with five single-division stages - population, contagion, triage, hospitalisation, and intensive care unit admission -, and considers an output maximisation orientation, denoting a social perspective, and an input minimisation orientation, denoting a financial perspective. It includes inputs related to health costs, desirable and undesirable intermediate products related to the use of personal protective equipment and infected population, respectively, and desirable and undesirable outputs regarding COVID-19 recoveries and deaths, respectively. To the best of the authors' knowledge, this is the first study proposing a cross-country efficiency measurement using a network DEA within the context of the COVID-19 crisis. The study concludes that Estonia, Iceland, Latvia, Luxembourg, the Netherlands, and New Zealand are the countries exhibiting higher mean system efficiencies. Their national COVID-19 strategies should be studied, adapted, and used by countries exhibiting worse performances. In addition, the observation of countries with large populations presenting worse mean efficiency scores is statistically significant.