The linear excess relative risk (ERR) is the most commonly reported measure of association in radiation epidemiological studies, when individual dose estimates are available. While the asymptotic properties of the ERR estimator are well understood, there is evidence of small sample bias in case-control studies of treatment-related radiation exposure and second cancer risk. Cohort studies of cancer risk after exposure to low doses of radiation from diagnostic procedures, e.g., computed tomography (CT) examinations, typically have small numbers of cases and risks are small. Therefore, understanding the properties of the estimated ERR is essential for interpretation and analysis of such studies. We present results of a simulation study that evaluates the finite-sample bias of the ERR estimated by time-to-event analyses and its confidence interval using simulated data, resembling a retrospective cohort study of radiation-related leukemia risk after CT examinations in childhood and adolescence. Furthermore, we evaluate how the Firth-corrected estimator reduces the finite-sample bias of the classical estimator. We show that the ERR is overestimated by about 30% for a cohort of about 150,000 individuals, with 42 leukemia cases observed on average. The bias is reduced for higher baseline incidence rates and for higher values of the true ERR. As the number of cases increases, the ERR is approximately unbiased. The Firth correction reduces the bias for all cohort sizes to generally around or under 5%. Epidemiological studies showing an association between radiation exposure from pediatric CT and cancer risk, unless very large, may overestimate the magnitude of the relationship, while there is no evidence of an increased chance for false-positive results. Conducting large studies, perhaps by pooling individual studies to increase the number of cases, should be a priority. If this is not possible, Firth correction should be applied to reduce small-sample bias.