Protection from prior natural infection vs. vaccination against SARS-CoV-2-a statistical note to avoid biased interpretation.

Introduction: The fight against SARS-CoV-2 has been a major task worldwide since it was first identified in December 2019. An imperative preventive measure is the availability of efficacious vaccines while there is also a significant interest in the protective effect of a previous SARS-CoV-2 infection on a subsequent infection (natural protection rate). Methods: In order to compare protection rates after infection and vaccination, researchers consider different effect measures such as 1 minus hazard ratio, 1 minus odds ratio, or 1 minus risk ratio. These measures differ in a setting with competing risks. Nevertheless, as there is no unique definition, these metrics are frequently used in studies examining protection rate. Comparison of protection rates via vaccination and natural infection poses several challenges. For instance many publications consider the epidemiological definition, that a reinfection after a SARS-CoV-2 infection is only possible after 90 days, whereas there is no such constraint after vaccination. Furthermore, death is more prominent as a competing event during the first 90 days after infection compared to vaccination. In this work we discuss the statistical issues that arise when investigating protection rates comparing vaccination with infection. We explore different aspects of effect measures and provide insights drawn from different analyses, distinguishing between the first and the second 90 days post-infection or vaccination. Results: In this study, we have access to real-world data of almost two million people from Stockholm County, Sweden. For the main analysis, data of over 52.000 people is considered. The infected group is younger, includes more men, and is less morbid compared to the vaccinated group. After the first 90 days, these differences increased. Analysis of the second 90 days shows differences between analysis approaches and between age groups. There are age-related differences in mortality. Considering the outcome SARS-CoV-2 infection, the effect of vaccination versus infection varies by age, showing a disadvantage for the vaccinated in the younger population, while no significant difference was found in the elderly. Discussion: To compare the effects of immunization through infection or vaccination, we emphasize consideration of several investigations. It is crucial to examine two observation periods: The first and second 90-day intervals following infection or vaccination. Additionally, methods to address imbalances are essential and need to be used. This approach supports fair comparisons, allows for more comprehensive conclusions and helps prevent biased interpretations.