In 1723 English physician and scientist James Jurin published A Letter . . . Containing, a Comparison Between the Mortality of the Natural Small Pox and that Given by Inoculation. In this work, which is one of the earliest applications of statistics to a particular socio-medical problem, Jurin proved statistically that the fatality of inocculated smallpox is very much less than the fatality of natural smallpox.
J. Norman (ed.) Morton's Medical Bibliography 5th ed (1991) no. 1689.