Analysis of the Number of Tests, the Positivity Rate and Their Dependency Structure during COVID-19 Pandemic

Recent advances in medical instruments, information technology, and unprecedented data sharing allowed scientists to investigate, trace, and monitor the COVID-19 pandemic faster than any previous outbreak. This extraordinary speed makes COVID-19 a medical revolution that causes some unprecedented analyses, discussions, and models. Modeling the dependence between the number of tests and the positivity rate is one of these new issues. Using four classes of copulas (Clayton, Frank, Gumbel, and FGM), this study is the first attempt tom model the dependency. The estimation of the parameters of the copulas is obtained using the maximum likelihood method. To evaluate the goodness of fit of the copulas, we calculate AIC. The computations are conducted on Matlab R2015b, R 4.0.3, Maple 2018a, and EasyFit 5.6. Findings indicate that at the beginning of a typical epidemic, the number of tests is relatively low and the proportion of positivity is high. As time passes, the number of tests increases, and the positivity rate decreases. The epidemic peaks are occasions that violate the stated general rule -due to the early growth of the number of tests. Also, during both peak and non-peak times, the rising number of tests is accompanied by decreasing the positivity rate. We find that the proportion of positivity is more proportional than the number of tests to the number of infected cases. Therefore, the changes in the positivity rate can be considered a representative of the level of the spreading. Approaching zero positivity rate is a good criterion to scale the success of a healthcare system in fighting against an epidemic. Accordingly, the number and accuracy of tests can play a vital role in the quality level of epidemic data.