Errors in the estimation of exposures or doses are a major source of uncertainty in epidemiological studies of cancer among nuclear workers. This paper presents a Monte Carlo maximum likelihood method that can be used for estimating a confidence interval that reflects both statistical sampling error and uncertainty in the measurement of exposures. The method is illustrated by application to an analysis of all cancer (excluding leukemia) mortality in a study of nuclear workers at the Oak Ridge National Laboratory (ORNL). Monte Carlo methods were used to generate 10,000 data sets with a simulated corrected dose estimate for each member of the cohort based on the estimated distribution of errors in doses. A Cox proportional hazards model was applied to each of these simulated data sets. A partial likelihood, averaged over all of the simulations, was generated; the central risk estimate and confidence interval were estimated from this partial likelihood. The conventional unsimulated analysis of the ORNL study yielded an excess relative risk (ERR) of 5.38 per Sv (90% confidence interval 0.54-12.58). The Monte Carlo maximum likelihood method yielded a slightly lower ERR (4.82 per Sv) and wider confidence interval (0.41-13.31).