A key biomarker in the study of differentiated thyroid cancer is thyroglobulin. Measurements of the levels of this protein in the blood are determined using laboratory instruments that cannot detect very small concentrations below a threshold, generating left-censored measurements. In the presence of censoring, ordinary least-squares regression models generate biased parameter estimates; therefore, it is necessary to resort to more complex models that consider the censored observations and the behavior of the distribution of the response variable, such as censored and mixed regression models. These techniques were used to model the relationship between thyroglobulin levels in individuals with differentiated thyroid cancer before and after treatment with radioactive iodine (I-131). Log-normal, log-skew-normal, log-power-normal, and log-generalized-gamma probability distributions were used to model the behavior of errors in the adjusted models. Log-generalized-gamma distribution yielded the best results according to the established model selection criteria.