Mutual relationships between SARS-CoV-2 test numbers, fatality and morbidity rates

Background The number of SARS-CoV-2 tests conversely to other factors, such as age of population or comorbidities, influencing SARS-CoV-2 morbidity and fatality rates, can be increased or decreased by decision makers depending on the development of the pandemic, operational capacity, and financial restraints. The key objective of this study is to identify and describe, within the probabilistic approach, the relationships between SARS-CoV-2 test numbers and the mortality and morbidity rates. Methods The study is based on a statistical analysis of 1058 monthly observations relating to 107 countries, from six different continents, in an 11-month period from March 2020 to January 2021. The variable utilised can be defined as the number of tests performed in a given country in 1 month, to the number of cases reported in a prior month and morbidities and mortalities per 1 million population. The probabilities of different mortality and morbidity rates for different test numbers were determined by moving percentiles and fitted by the power law and by the three-segment piecewise-linear approximation based on Theil Sen trend lines. Results We have identified that for a given probability the dependence of mortality and morbidity rates on SARS-CoV-2 test rates follows a power law and it is well approximated by the three Theil Sen trend lines in the three test rate ranges. In all these ranges Spearman rho and Kendall tau-b rank correlation coefficients of test numbers and morbidity with fatality rates have values between − 0.5 and − 0.12 with p -values below 0.002. Conclusions According to the ABC classification: the most important, moderately important, and relatively unimportant ranges of test numbers for managing and control have been indicated based on the value of the Theil Sen trend line slope in the three SARS-CoV-2 test rate ranges identified. Recommendations for SARS-CoV-2 testing strategy are provided.