Nurses' health study: log-incidence mathematical model of breast cancer incidence

In 1983, Pike et al. developed a mathematical model to quantify the effects of reproductive risk factors on the incidence of breast cancer. In 1994, we modified that model to correct some deficiencies in the original model, including a lack of terms for spacing of births and an inability to easily accommodate births after age 40 years. Our extended Pike model, while improving on the original, still has serious disadvantages, such as difficulty in translating model parameters into relative risks (RRs) and an incomplete fit to data that slightly overestimated incidence for premenopausal women with an early age at first birth and that underestimated incidence for post-menopausal women with a late age at first birth.

We undertook both the development of a new mathematical model to quantify the effects of reproductive risk factors on breast cancer incidence and validation of the model.

A new log-incidence model of breast cancer incidence was developed using nonlinear regression methods, and a study population consisting of 89,132 women in the Nurses' Health Study from which a total of 2249 incident cases of breast cancer were identified. Subjects were followed from the return of the 1976 Nurses' Health Study questionnaire until June 1, 1990, or until the last questionnaire was returned, until the development of any cancer, or until death, yielding 1,148,593 person-years of follow-up. The log-incidence models were fitted using iteratively reweighted least squares analysis.

The log-incidence model provided a better fit to that data than the extended Pike model, with parameter estimates interpretable in terms of RRs. This new model can be fitted using standard commercially available statistical software. In the model, younger parous women are generally at slightly higher risk than nulliparous women, which is true for both the observed and expected RRs, and older parous women, aged 55-64 years with an early age at first birth, are at lower risk than nulliparous women,while older women with a late age at first birth are at substantially higher risk than nulliparous women.

Log-incidence models, such as this one, provide an efficient framework for modeling the effect of lifestyle risk factors on breast cancer incidence that may be specifically targeted to certain time periods of a woman's reproductive life.