title: A mathematical model to predict the risk of hepatitis B infection through needle/syringe sharing in mass vaccination.
abstract: BACKGROUND
  The Japanese Government settled a class litigation case with hepatitis B virus (HBV) carriers who claim to have been infected through needle/syringe sharing in childhood mass vaccination with a blanket compensation agreement. However, it is difficult to estimate how many of the present HBV carriers were infected horizontally from mass vaccination and how many were infected vertically from mothers.
  
  
  METHODS
  A mathematical model to predict the risk of infection through needle/syringe sharing in mass vaccination was proposed and a formula was developed. The formula was presented in a logarithmic graph enabling users to estimate how many people will be infected if a needle/syringe is shared by how many people for how many times under certain probability of infection. The formula was then applied to the historical data of mass tuberculin skin tests (TSTs) and BCG inoculation, from which a best estimate of how much needle/syringe sharing was practiced in different birth cohorts was determined.
  
  
  RESULTS
  For the oldest cohort born between 1951 and 1955, the prevalence of HBV carriers-0.65% at birth through vertical transmission-more than doubled in 1995 (1.46%) through horizontal transmission. If the probability of infection through needle/syringe sharing is assumed to be 10%, it is theoretically likely that an average of five or more people shared a needle/syringe four times to achieve the prevalence of HBV carriers in 1995. However, for the youngest cohort born between 1981 and 1985, the effects of needle/syringe sharing were negligible because the later prevalence of HBV carriers was lower than the prevalence at birth.
  
  
  CONCLUSIONS
  More than half of the HBV carriers born in the early 1950s might have contracted the disease by mass vaccinations. Japan's experience needs to be shared with other countries as a caution in conducting mass vaccination programs under scarce needle/syringe supply (291 words).
authors.affiliation: Department of Health and Welfare Service Research, National Institute of Public Health, Saitama 351-0197 2-3-6 Minami, Wako-shi, Japan. atoz@niph.go.jp.
authors.forename: Etsuji
authors.initials: E
authors.lastname: Okamoto