Thesis: Computed tomography (CT) has been used increasingly over the last decades. However, concerns have been raised about potentially radiation-related cancer risks, particularly after exposure to CT in childhood, due to the greater radiation sensitivity of children. The French CT cohort includes almost 100,000 children who received at least one CT between 2000 and 2011 in one of the 21 participating university hospitals. Examinations and radiological protocols were retrieved to estimate cumulative absorbed doses. The aim of this work is to estimate accurate cancer risks following CT scans (i.e. central nervous system tumors, leukemia and lymphoma) and their related uncertainties from the French CT cohort data. A first analysis showed a statistically significant positive association between the absorbed organ dose and the incidence of central nervous system tumors and leukemia. However, several sources of uncertainty in the calculation of organ dose exist but have not been accounted for in risk estimates. Bayesian hierarchical models were proposed and compared to simultaneously account for several sources of dose uncertainty when estimating the risk of childhood cancer following CT scans. Finally, we aimed at quantifying the effect of childhood CT exposure on the estimation of the cumulative incidence function of each radiation- induced cancer of interest. For this purpose, we proposed an original Bayesian mixture model accounting for competing risks, a time-dependent exposure covariate and a weak signal in the data.