An analytic approach that provides explicit estimates of risk on cataract and epilation data is evaluated by reasonableness of conceivable relative risk models regarding a simple, odds, logistic or Gompertz regression method, assuming a binomial distribution. In these analyses, we apply relative risk models with two thresholds between epilators and nonepilators from a highly characteristic lesion of which radiation cataract does not occur around 2 gray for a single acute exposure. The risk models are fitted to the data assuming 10 as a constant relative biological effectiveness of neutron. The likelihood of observing the entire data set in these models fitted is evaluated by an individual binary-response array. Estimation of a threshold with or without severe epilation and the 100 ($1-alpha$)% confidence limits are derived from the maximum likelihood approach. The relative risk model with two thresholds can be expressed as a formula with structure of Background $ imes$ RR, where RR includes threshold models with or without epilation. The radiosensitivity of ionizing radiation to cataracts has been examined for the relationship between epilators and nonepilators.