Mathematical Modeling for Breast Cancer Risk Assessment

For women at increased risk of breast cancer, important opportunities exist for primary and secondary prevention. Effective medical triage requires that risk be recognized and quantified. An extensive body of literature describes the hormonal/reproductive, family history, histologic, and demographic factors that contribute to breast cancer risk. The concept that clinicians should identify women at high risk for breast cancer has come of age. The justification for practicing breast cancer risk assessment encompasses the following reasons:

• The importance of maintaining a high level of suspicion for clinical diagnosis, despite the young age of a patient[1]
• The need to begin surveillance earlier than recommended by standard guidelines[2,3]
• Better information about the effectiveness of prophylactic mastectomy, the ideal surgical approach, and the optimal age at surgery[4-7]
• The opportunity for breast cancer chemoprevention[8]
• Recognition of the risks of additional preventable cancers, such as ovarian cancer in BRCA1 and BRCA2 carriers
• The chance to treat not only high-risk patients, but also the high-risk family.

Genetic counseling for inherited cancer syndromes has grown tremendously over the past several years, due in large part to the discovery of two genes, BRCA1 and BRCA2, mutations of which account for the majority of hereditary breast/ovarian cancer families.[9,10] Mutations in several other genes also confer susceptibility to breast cancer—namely, TP53 (aka p53) associated with Li-Fraumeni syndrome and PTEN associated with Cowden disease. These conditions account for less than 1% of hereditary breast cancer, and no available mathematical modeling incorporates them. Therefore, they will not be discussed further in this article.

Genetic testing for mutations in BRCA1 and BRCA2 can be thought of as a highly sophisticated method of risk assessment. However, for the majority of women, genetic testing is not useful in clarifying risk. Mathematical models can be used to identify families for whom testing may be beneficial and to estimate risk in the absence of genetic testing.

For most women at moderate risk (loosely defined as a non-Jewish family with one or two relatives with breast cancer and no ovarian cancer or male breast cancer), quantitative risk assessment alone may be sufficient for guiding medical decision-making about chemoprevention, surgical prevention, and assessment of the risk/benefit ratio for hormone replacement therapy. Using a case-based approach, we will summarize the major breast cancer risk assessment models, compare and contrast their utility, and illustrate the role of genetic testing in risk management.

Mathematical Models for Breast Cancer Risk Assessment

Breast cancer is a common disease—the most common cancer found among women and the second major cause of cancer death. Preliminary searches for the causes or risk factors for breast cancer have been population-based. After female gender, the most important risk factor is increasing age. Composite incidence projections derived from the Surveillance, Epidemiology, and End Results (SEER) registry of the National Cancer Institute (NCI) have enabled the determination of general age-related population risks for breast cancer.[11] The next largest risk factor is family history. Early quantification of this influence consisted of empiric prevalence tables based on various configurations of affected relatives.[12-14]

Relative risks and odds ratios for various characteristics have been derived from several studies; however, an individual woman’s risk is based on a combination of these factors. Therefore, statistical modeling that incorporates the relative weight of separate risk factors is necessary to approximate an individual’s unique risk. Ideally, the model is then validated in population studies. Of the models discussed here, only the Gail model[15] has been validated.[16-18]

Epidemiologic Models

The quantitative models currently used in breast cancer risk assessment can be loosely divided into two categories: epidemiologic and genetic. The Gail[15] and Claus[19] models are epidemiologic tools used to predict absolute breast cancer risk over specified intervals of time for women who have never had breast cancer. They are derived from large population-based datasets and, thus, apply to a broad range of women, particularly those without a strong family history of breast cancer (Table 1).

Genetic Models

The newest category of models estimates BRCA1 or BRCA2 mutation carrier status (and, indirectly, breast cancer risk), based entirely on family history of breast and ovarian cancer. These models were derived from small populations with a strong family history of these diseases. Specifically, the Couch (University of Pennsylvania),[20] Shattuck-Eidens,[21] and Myriad (Frank) models[22] were derived from logistic regression of risk factors predicting a positive mutation test outcome. The Berry-Parmigiani-Aguilar model (BRCAPRO)[23,24] is based on Bayesian calculations of the probability of carrying a BRCA1 or BRCA2 mutation, given the individual family pattern of affected and unaffected individuals.

The genetic models calculate mutation probabilities based on affected individuals. Risk can be adjusted by Mendelian extrapolation for unaffected relatives. Brief descriptions of each model are presented below and in Table 2; a detailed discussion of their derivations can be found elsewhere.[25]

Two other quantitative models of mutation carrier risk not detailed in this paper are worth noting. First, Ford et al provide tables predicting the probability of linkage to BRCA1 and BRCA2 for high-risk families with a minimum of four cases of breast cancer diagnosed prior to age 60 and various combinations of ovarian cancer and male breast cancer.[26] The probability of linkage (an indirect measure of whether the gene in question is involved) does not equate with the probability of finding a mutation, because a variety of mutation types are not identified even by complete DNA sequencing of the coding region and intron/exon boundaries. Genetic testing detected BRCA1 or BRCA2 mutations in only 63% of families with linkage scores suggesting involvement of these genes.

Second, Myriad Genetic Laboratories, Inc, provides and updates a set of penetrance tables on their website (www.myriad.com), reporting the frequency of BRCA1 and BRCA2 mutations for various constellations of family history, including Jewish and non-Jewish ancestry. The data in these tables were not obtained in a controlled research study and have not been statistically modeled. Moreover, family history was not collected in a systematic, verifiable fashion. Nevertheless, the dataset includes several thousand individuals who have undergone genetic testing and is quite impressive.

Gail Model

Using multivariate logistic regression, the following risk factors for developing breast cancer were identified in the Breast Cancer Detection Demonstration Project (BCDDP) population: age at menarche, age at first live birth, number of previous breast biopsies, number of first-degree relatives with breast cancer, and current age of the individual.[27] In addition to these characteristics, the demonstration of atypical hyperplasia on biopsy is incorporated into the original Gail model as another multiplication factor. Relative risk estimates were calculated for each of these parameters, and a woman’s composite relative risk is obtained by multiplying the numbers associated with each relative risk factor. Absolute risk—defined as the probability of developing breast cancer over a specified time—is computed by multiplying the composite relative risk by the baseline proportional hazards estimation derived from the BCDDP population.

The NCI website contains a breast cancer risk assessment tool in Windows format (http://bcra.nci.nih.gov/brc/) based on a revised version of the Gail model[28] that was used to determine eligibility for the Breast Cancer Prevention Trial.[8] It provides 5-year and lifetime risks for developing breast cancer and differs from the original model in that (1) it predicts invasive cancer only (the original predicted both invasive and in situ cancers), (2) the baseline incidence is derived from SEER data (the original Gail model used baseline data from the BCDDP population), and (3) it includes a separate baseline incidence for black women (the original applied only to white women).

The Gail model is routinely used in cancer risk counseling to derive a preliminary breast cancer risk estimate for unaffected women. It is not applicable to women who have already had either in situ or invasive cancers. Although the model has been formally validated in three studies[16-18] and can accurately predict the rate of breast cancer development in populations, it tends to overestimate risk for young women and underestimate risk for older women. Some of the overprediction in younger women results from the fact that the model was based on a population of women who were undergoing annual screening mammography.

From the standpoint of genetic risk assessment, the main limitations of the Gail model are that it does not incorporate breast cancer history for more than two first-degree relatives and does not consider age at onset of cancer. Furthermore, because second-degree relatives are not included, paternal family history is ignored. It should also be pointed out that although risk models may be accurate for populations, risk predictions for individuals may be of limited accuracy.[29]

Claus Model

A second epidemiologic model used to estimate a woman’s risk of developing breast cancer over time is the Claus model.[19] Using segregation analysis on data obtained from the Cancer and Steroid Hormone Study (CASH), tables were constructed that predict cumulative probabilities for the occurrence of breast cancer at different ages, depending on both the presence of breast cancer in various combinations of first- and second-degree relatives and age at onset of cancer. Although the Claus model is only useful for the subset of women with one or two relatives with breast cancer, it may be more accurate than the Gail model for this cohort, particularly in the setting of premenopausal breast cancer and minor nonfamilial risk factors, and especially when there is a paternal family history of breast cancer.

In general, the Gail and Claus models should be avoided in individuals with a strong family history of cancer and used only with caution when genetic testing has produced negative results.

Couch Model

The Couch model[20] is based on data from 169 women who were assessed at a high-risk clinic and tested for mutations in the BRCA1 gene. Risk is based on the average age at diagnosis of breast cancer in a woman’s family, ethnicity (Ashkenazi Jewish descent or not), the presence of familial breast cancer only or familial breast and ovarian cancer, and whether any individual has had both breast and ovarian cancer. Risks are provided in tables.

Shattuck-Eidens Model

The Shattuck-Eidens model[21] is based on a subset of 593 women with either breast or ovarian cancer who were evaluated in 20 familial risk clinics and underwent full-sequence mutation analysis for BRCA1. Risk factors included in the final model are based on the characteristics of both the proband and her family. For the proband, the risk factors are breast or ovarian cancer status including age at onset and Ashkenazi Jewish ancestry. For the family, risk factors include breast or ovarian cancer status, but not age at onset or degree of relatedness.

Cancer status for both the proband and family members are categorized according to the presence of breast cancer alone, ovarian cancer alone, or both cancers in the same individual. Bilaterality is also considered for the proband, who must be affected for the model to be applicable. Limited risk values are provided in graphs, but it is necessary to calculate the regression equation for many families.