Beginning in January 1997, American immunization policy allowed parents and physicians to elect one of three approved infant vaccination strategies for preventing poliomyelitis. Although the three strategies likely have different outcomes with respect to prevention of paralytic poliomyelitis, the extreme rarity of the disease in the USA prevents any controlled comparison. In this paper, a formal inferential logic, originally described by Donald Rubin, is applied to the vaccination problem. Assumptions and indirect evidence are used to overcome the inability to observe the same subjects under varying conditions to allow the inference of causality from non-randomized observations. Using available epidemiologic information and explicit assumptions, it is possible to project the risk of paralytic polio for infants immunized with oral polio vaccine (1·3 cases per million vaccinees), inactivated polio vaccine (0·54 cases per million vaccinees), or a sequential schedule (0·54–0·92 cases per million vaccinees).