This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure doses Overview of risk models realized in program package EPICURE Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident Elements of estimating equations theory Consistency of efficient methods Efficient SIMEX method as a combination of the SIMEX method and the corrected score method Application of regression calibration in the model with additive error in exposure doses