Comparison of additive and multiplicative models for reproductive risk factors and post-menopausal breast cancer

The mathematical multistage model of carcinogenesis proposed by Breslow and Day indicates that if hormonal risk factors for breast cancer are late-stage carcinogens then the use of an additive model (excess absolute risk) should be preferrable to the present standard use of the multiplicative model (excess relative risk). To test different models, information from a large prospective study of 431,604 women aged 45-74 years in 1970 with follow-up to 1985 on reproductive factors and post-menopausal breast cancer mortality was used to compute goodness-of-fit statistics. The relative risk function, ranging from multiplicative to additive, was explored by changing the exponent in a power transformation. The analysis found evidence of better fit by the additive compared with the multiplicative models, consistent with the proposed mathematical model.