Breast Cancer Risk in Atomic Bomb Survivors from Multi-Model Inference

*Jan Christian Kaiser, Helmholtz Zentrum München, Institute of Radiation Protection 

Keywords: Multi-model inference, breast cancer, radiation risk, mechanistic modelling

Risk studies in radio-epidemiology often produce several plausible models which describe the data comparably well. It is common practice to select a single model of choice for risk assessment and neglect information that is offered by the remaining models. To partly adjust for the model selection bias, a recent study on leukemia mortality (1) in the life span study (LSS) cohort of Japanese A-bomb survivors has used a number of descriptive risk models to derive a joint risk estimate by multi-model inference (MMI). This method has been applied successfully in other fields of research such as physics, biology or environmental science but has received little attention in radio-epidemiology so far. Here the application of MMI is demonstrated to estimate the radiation risk of female breast cancer in the LSS cohort (2). The pool of candidate models that may qualify for joint risk inference includes both descriptive models (3) and biologically-based models.

The LSS cohort data do not contain enough detail for a realistic representation of complex events on the path to cancer. Hence, phenomenological assumptions for the stages of carcinogenesis, which are adapted to the details available, appear justified in biologically-based risk models. In the 1980s the mechanistic two-step clonal expansion (TSCE) model was applied to sporadic breast cancer incidence data from cohorts in the U.S., Europe and Japan (4). Typical age-specific trends were explained with simple representations of cell mutations during organ growth at puberty and of cell division and inactivation controlled by changes in hormone levels due to menopause. A recent study of the Swedish hemangioma cohort (5) with a TSCE model indicated that the initial cell mutation rate is permanently enhanced even after radiation exposure has stopped. This effect has been attributed to radiation-induced genomic instability. The modeling approaches of Moolgavkar et al. (4) for the baseline risk and of Eidemüller et al. (5) for the mechanistic radiation response have been combined in TSCE models for the LSS cohort. Together with mechanistic models, descriptive models have been applied to pursue two objectives. Firstly, descriptive models and mechanistic models can benefit from mutual appraisal. Mechanistic models explain epidemiological data based on concepts derived from the current understanding of biological processes. A comparison could boost the search, implementation and adaptation of relevant mechanistic effects. Descriptive models are not confined by biological constraints. This flexibility may yield better fits to the data. But, like mechanistic models, they can profit from a revision to avoid the inclusion of spurious features which may lack biological feasibility. Secondly, plausible mechanistic models introduce valuable additional input for the inference of a joint risk derived from several plausible models.

To mix descriptive models with mechanistic TSCE models, a model selection protocol has been developed based on a series of pair-wise likelihood ratio tests between nested models (2). It was motivated by a balance between scarce deployment of parameters and accurate approximation of the epidemiological data. After subjecting candidate models to the protocol three mechanistic models with different radiation responses and a descriptive model of the excess relative risk (ERR) survived. The four models were ranked according to the information criterion of Akaike which penalizes the Poisson deviance Dev with twice the number of model parameters (5). The lowest pertained to the descriptive ERR model with nine parameters and a linear dose response modified by a power function of attained age. The three TSCE models had lower deviances but higher AIC values caused by 2-3 additional parameters. To each model an AIC-related weight is assigned which determines its impact on the joint risk.

For exposure at young age, the TSCE models predict an enhanced ERR whereas the preferred descriptive ERR model shows no dependence on age at exposure. The multi-model median for the ERR at 1 Gy and attained age 70 drops from 1.2 Gy-1 (90% CI 0.72; 2.1) for exposure in the mid-twenties by almost 30% for exposure in the mid-fifties. Where model predictions diverge, uncertainty intervals from MMI grow by up to a factor of two compared to the preferred descriptive model.

The assignment of weights to a combination of an ERR model and an EAR model is already practiced to transfer site-specific cancer risks from the LSS cohort to western populations. In view of this practice, preferred models of both the EAR and ERR for breast cancer in the LSS cohort have been compared to the corresponding models of the Swedish hemangioma cohort and consequences for risk transfer are discussed.

In the past parameter parsimony was not a key issue but consideration of the matter may yield benefits. For a hypothetical example Walsh et al. (7) showed that models, which contain parameters with weak statistical support, may cause misleading point estimates. In other examples over-parametrized models may have little impact on point estimates but can still inflate uncertainty ranges artificially. Finally, MMI appeals to demands for risk assessment in practical radiation protection. For a decision to accept a certain dose from a diagnostic examination, i.e. a computer tomography scan at young age, the risk should be well known from the outset. Compensation claims for cancer, i.e. from occupational exposure, are often based on the probability of causation. In the U.S. the 99% confidence interval of this probability, which can be calculated with the IREP tool (8), is applied in court cases. In both areas the credibility of risk assessment is improved by MMI, which combines predictions of several plausible models rather than relying on a single model of choice. It produces risk estimates with enhanced support of the epidemiological data and provides a more comprehensive characterization of uncertainties.

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