Uncertain Malmquist productivity index: An application to evaluate healthcare systems during COVID-19 pandemic

Evaluation of healthcare systems, as a key organization providing different health services, is essential. This issue becomes more crucial when occurring crises such as a pandemic. They need to keep track of their success in the face of the crisis to assess the effects of policy changes and their capability to respond to new challenges. The Malmquist Productivity Index (MPI) is measured to analyze the causes of productivity change between two periods of time. The estimation of the traditional MPI requires reliable and detailed information on the inputs and outputs of decision-making units. However, there are a lot of situations where input and/or output may be imprecise. It is not manageable to reliably measure certain measurement indices, such as quality of treatment or system flexibility. For such cases, experts are invited to model their opinion. Uncertainty theory is a mathematical branch rationally dealing with belief degrees. The primary objective of this study is to apply MPI concept in the nonparametric approach of data envelopment analysis to calculate the efficiency of systems over different periods of time under uncertain conditions. Accordingly, we consider the MPI when inputs and outputs are belief degrees of experts. Furthermore, the sensitivity of the model is analyzed to determine the reliability of the results to the variation of variables. Finally, as an illustrative example, we explore longitudinal efficiency of healthcare systems during COVID-19 pandemic. According to the results of our model, the majority of the countries have improved in the second period which can be the result of efforts to improve pandemic preparedness. The decomposition of MPI into efficiency changes and technical changes indicates that the rise in productivity is entirely related to the progressive change of the production frontier related to policymaking. This application attempts to demonstrate how crucial it is to take uncertainties into account when comparing the performance of different systems over periods of time. The developed model enables us to consider the uncertainty existing in COVID-19 pandemic. The proposed model can handle more accurately the uncertainty during the pandemic. Thus, the result could be more reliable, which can benefit decision-makers in regard to performance improvement.