Not currently relevant, but an example of balancing risk and benefit and deciding to stop vaccinating against smallpox. Wikipedia

There are side effects and risks associated with the smallpox vaccine. In the past, about 1 out of 1,000 people vaccinated for the first time experienced serious, but non-life-threatening, reactions, including toxic or allergic reaction at the site of the vaccination (erythema multiforme), spread of the vaccinia virus to other parts of the body, and to other individuals. Potentially life-threatening reactions occurred in 14 to 500 people out of every 1 million people vaccinated for the first time. Based on past experience, it is estimated that 1 or 2 people in 1 million (0.000198 percent) who receive the vaccine may die as a result, most often the result of postvaccinial encephalitis or severe necrosis in the area of vaccination (called progressive vaccinia).[38]

Given these risks, as smallpox became effectively eradicated and the number of naturally occurring cases fell below the number of vaccine-induced illnesses and deaths, routine childhood vaccination was discontinued in the United States in 1972, and was abandoned in most European countries in the early 1970s.[5][40] Routine vaccination of health care workers was discontinued in the U.S. in 1976, and among military recruits in 1990 (although military personnel deploying to the Middle East and Korea still receive the vaccination.[41]) By 1986, routine vaccination had ceased in all countries.[5] It is now primarily recommended for laboratory workers at risk for occupational exposure.[20]