COVID-19 Test Positivity Rate as a marker for hospital overload

The use of antigen tests for the diagnosis of COVID-19 in Italy has risen sharply in autumn 2020. Although, Italian regions like Alto Adige, Veneto, Toscana, Lazio, Piemonte and Marche did a large use of these tests for screening and surveillance purposes or for implementing diagnosis protocols, in addition to molecular tests, they were not reported in the statistics in the last months of 2020. As a consequence of this situation the test positivity rate (TPR) index, defined as the number of new positive cases divided by the number of tests, has lost in accuracy. Only in the recent days, starting from the 15th of January 2021, antigen tests have become part of the statistics for all the Italian regions. Despite the lack of data, we have noticed that TPR has a strong correlation with the number of patients admitted in hospitals, and that TPR peaks in general precede the peaks of hospitalized people which occur on average about 15 days later. In this paper, we have deepened this intuition, analysing the TPR course and its relationship with the number of hospitalized people. To conduct the study we have defined a novel version of the TPR index which takes into account the number of tests done with respect to the population (considering both molecular and antigen tests), the number of infected individuals, and the number of patients healed. Successively, starting from a limited set of data which were made available in November 2020, we have reconstructed the antigen tests time series of four Italian regions, and we computed the TPR index for them. The results show that TPR peaks precede peaks of hospitalized people in both the first and the second phases of the pandemic in Italy, provided that antigen tests are considered. Moreover, the TPR index trend, can be used to deduct important information on the course of the epidemic, and on the impact of COVID-19 in the health care system, which can be monitored in advance.