Quantifying cancer patient survival from the perspective of cure is clinically relevant. However, most cure models estimate cure assuming no competing causes of death. We use a relative survival framework to demonstrate how flexible parametric cure models can be used in combination with competing-risks theory to incorporate noncancer deaths. Under a model that incorporates statistical cure, we present the probabilities that cancer patients (1) have died from their cancer, (2) have died from other causes, (3) will eventually die from their cancer, or (4) will eventually die from other causes, all as a function of time since diagnosis. We further demonstrate how conditional probabilities can be used to update the prognosis among survivors (eg, at 1 or 5 years after diagnosis) by summarizing the proportion of patients who will not die from their cancer. The proposed method is applied to Swedish population-based data for persons diagnosed with melanoma, colon cancer, or acute myeloid leukemia between 1973 and 2007.