Relative excess risk due to interaction (RERI) has been used to quantify the joint effects of 2 exposures in epidemiology. However, the construction of confidence intervals (CIs) for RERI is complicated by sparse cells. Assuming that the data contain no zero cells, here we propose constructing CIs for RERI using nonparametric and parametric bootstrap methods with a continuity correction, and compare these proposed methods to existing methods using 3 empirical examples and Monte Carlo simulations. Our results show that, when cell counts are not sparse, CIs resulting from the explored bootstrap methods are generally acceptable in terms of CI coverage and length, although computationally more demanding than existing methods. However, when cell counts are sparse, the proposed bootstrap methods using a continuity correction outperform existing methods and continue to provide acceptable CIs. The continuity correction is needed for the explored bootstrap methods to provide acceptable CIs because resampled data sets may contain zero cells even when the observed data do not.