Bootstrap confidence interval estimation in generalized nonlinear models

The excess relative risk (ERR) model is a statistical model commonly used in radiation epidemiology to estimate the increased risk of cancer associated with radiation exposure. Generally, the parameters of the ERR model are estimated using the maximum likelihood estimation in generalized nonlinear models (GNMs) with a log-linear link function. One of the key challenges in applying GNMs is the evaluation of model uncertainty. We investigated likelihood-based approaches (Wald and profile likelihood methods) and various bootstrap confidence interval estimation methods to evaluate the statistical uncertainty of the model parameter estimators. In addition, we compared nonparametric and parametric resampling techniques in a GNM setting. Numerical studies were conducted on the normal, Poisson, and Bernoulli random variables of the responses given covariates. We applied the proposed methods to the ERR models used in the Life Span Study at the Radiation Effects Research Foundation and the Korean diagnostic medical radiation workers cohort.