Mathematical Modeling for Breast Cancer Risk Assessment

Mathematical Modeling for Breast Cancer Risk Assessment

Breast and ovarian carcinomas pose major public health problems in most
Western countries. Countless attempts have been made to better understand a
patient’s lifetime risk of breast cancer. The most significant etiologic risk
is increasing age, followed by family history. In addition, hormonal and
reproductive factors—ie, early menarche and later age at menopause,
nulliparity (and, therefore, a greater number of ovulations over the patient’s
lifetime), and late age at first pregnancy (greater than age 30 years)—also
increase a patient’s breast cancer risk.

Obesity (perhaps due to the more affluent high-fat, low-fiber, high-caloric
diet) and irradiation of the chest, particularly early in life, have also been
incriminated as risk factors for breast cancer. On the other hand, early age at
first full-term pregnancy, particularly under age 20, is protective against
breast cancer.

Epidemiologic Models

Rubinstein et al provide a critical appraisal of several mathematical models
for calculating breast cancer risk. The so-called epidemiologic models, based on
population studies, include the Gail model[1] and the Claus model.[2] Models
derived from logistic regression of risk factors that are better predictors of a
genetic etiology are the Shattuck-Eidens,[3] Myriad (Frank),[4] and Couch
models.[5] The BRCAPRO (Berry-Parmigiani-Aguilar) model[6,7] is based on
Bayesian calculations to assess the probability of a BRCA1 or BRCA2 mutation in
concert with the family configuration of affected and unaffected individuals.
These genetic models calculate mutation probabilities based on affected family
members, and risk is adjusted by Mendelian extrapolation for unaffected

The Gail model’s main value is its ability to predict the rate of breast
cancer in large populations. However, as Rubinstein et al note, this approach
tends to overestimate breast cancer risk for young women and underestimate it
for older women. Its limitations from the standpoint of genetic risk assessment
are the inability to incorporate breast cancer history for more than two
first-degree relatives and its failure to consider age at onset of cancer. Also,
it does not take second-degree relatives into consideration, thereby ignoring
paternal family history.

The Claus model employs segregation analysis on data obtained through the
Cancer and Steroid Hormone (CASH) study. This model is useful for the subset of
women who have one or two relatives with breast cancer, and it may be more
accurate than the Gail model for this particular cohort, especially when there
is a paternal family history of breast cancer. Rubinstein et al appropriately
suggest that the Gail and Claus models should not be employed in individuals
showing a strong family history of cancer. Rather, they should be used
cautiously when genetic testing has been performed and the result is negative.

Modified Nuclear Pedigree


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