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Updated: May 29, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Breast cancer risk in atomic bomb survivors from multi-model inference with incidence data 1958-1998
J C Kaiser1, P Jacob, R Meckbach
1Helmholtz-Zentrum München, German Research Centre for Environmental Health, Institute of Radiation Protection, 85764, Neuherberg, Germany. christian.kaiser@helmholtz-muenchen.de
Abstract:
Breast cancer risk from radiation exposure has been analyzed in the cohort of Japanese a-bomb survivors using empirical models and mechanistic two-step clonal expansion (TSCE) models with incidence data from 1958 to 1998. TSCE models rely on a phenomenological representation of cell transition processes on the path to cancer. They describe the data as good as empirical models and this fact has been exploited for risk assessment. Adequate models of both types have been selected with a statistical protocol based on parsimonious parameter deployment and their risk estimates have been combined using multi-model inference techniques. TSCE models relate the radiation risk to cell processes which are controlled by age-increasing rates of initiating mutations and by changes in hormone levels due to menopause. For exposure at young age, they predict an enhanced excess relative risk (ERR) whereas the preferred empirical model shows no dependence on age at exposure. At attained age 70, the multi-model median of the ERR at 1 Gy decreases moderately from 1.2 Gy(-1) (90% CI 0.72; 2.1) for exposure at age 25 to a 30% lower value for exposure at age 55. For cohort strata with few cases, where model predictions diverge, uncertainty intervals from multi-model inference are enhanced by up to a factor of 1.6 compared to the preferred empirical model. Multi-model inference provides a joint risk estimate from several plausible models rather than relying on a single model of choice. It produces more reliable point estimates and improves the characterization of uncertainties. The method is recommended for risk assessment in practical radiation protection.
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