Exposure to ionizing radiation has been testified to have harmful effects on the developing human brain, particularly in the highly vulnerable period of 8-15 weeks after ovulation as an incereased frequency of severe mental retardation. However, the distribution of cases of severe mental retardation suggests a threshold in the low dose region. Data are composed of a binary (1,0) for mentally retarded or normal individuals. The statistical approaches with a threshold are conceivable for a simple, odds, logistic and Gompertz regression models. Estimation of threshold and 100(1-α)% confidence limits are derived from the maximum likelihood technique based on a profile approach.