A randomized placebo-controlled trial in children showed that flu shots increased fivefold the risk of acute respiratory infections caused by a group of noninfluenza viruses, including coronaviruses. (Cowling et al, Clin Infect Dis 2012;54:1778) From Table 3, vaccine recipients had 20 noninfluenza virus-positive ARIs and 19 virus-negative ARIs; non-recipients had 3 noninfluenza virus-positive ARIs and 14 virus-negative ARIs. These figures yield an odds ratio of 4.91 (CI 1.04 to8.14).
Such an observation may seem counterintuitive, but it is possible that influenza vaccines alter our immune systems non-specifically to increase susceptibility to other infections; this has been observed with DTP and other vaccines. (Benn et al, Trends in Immunology, May 2013) There are other immune mechanisms that might also explain the observation.