Appendix. How the standard Gail Model method was modified and implemented in the halls.md breast cancer risk calculator.
Here are the statistical details, the technical stuff, describing the inner workings of the halls.md Breast Cancer Risk Calculator. My summary is: I’ve made some modifications to the published Gail Model method, but my calculator works very well and it can do a few things that other calculators can’t.
Firstly, the standard Gail model
Table 1 shows the relative risk values for Gail model1 in column X, as published in reference 1. These are also the same relative risks described for NSABP model 2 in reference 5. However, when I tried to implement a NSABP model2 calculator using column X figures, the results didn’t match the output of the NCI’s Breast Cancer Risk Assessment Tool. But when I modified the relative risk values to column Z, then my NSABP model2 calculator results closely emulated the results from the NCI‘s Breast Cancer Risk Assessment Tool.
I suspect that my column Z’s relative risk values have incorporated the mathematical effects of h*I(t) and F(t) into them (and also into the absolute risk curves that I use), whereas those terms are handled by separate mathematical operations in the NCI’s Breast Cancer Risk Assessment Tool.
Note that B. Number of Biopsies column Z uses different values for lifetime risk calculation versus 5-year risk calculation, only for ages under 50, 1 or more biopsies. Although this seems peculiar, using these numbers helps my calculator emulate the NCI’s Tool’s output.
|A. Age at menarche in years|
| 14 or
| 11 or
|B. Number of Biopsies|
|Age under 50 years||life||5-yr|
|2 or more||2.88||1.647||2.750|
|Age 50 years or older|
|2 or more||1.62||1.539|
| C. Number of first degree
relatives with breast cancer
| Age at first live birth < 20
|2 or more||6.80||6.168|
|Age at first live birth 20-24 years|
|2 or more||5.78||5.318|
|Age at first live birth 25-29 years|
|2 or more||4.91||4.591|
|Age at first live birth 30 + years|
|2 or more||4.17||3.953|
|D. Biopsy with atypical hyperplasia?|
| Not applicable
| No atypical
| Yes, atypical
Next, are shown a series of additional relative risk modifiers. These came from different published studies, for example, about mammographic density, or about taking tamoxifen, or drinking alcohol, etc. If the studies were legitimate and big and provided good reliable relative risk values published, I encorporated them into the calculator.
|E. Mammographic Density|
|1% to 24%||0.636|
|25% to 49%||1.000|
|50% to 74%||1.121|
|75% to 100%||1.761|
Most people aren’t on this particular medicine, but for those who are, it reduces risk.
|F. Taking Tamoxifen?|
|yes, age under 50 yrs||0.56|
|yes, age 50 to 60 yrs||0.49|
|yes, age over 60 yrs||0.45|
LCIS – a biopsy that showed Lobular carinoma in situ
Another thing most people don’t have, a history of a suspicious biopsy with LCIS.
|H. LCIS on biopsy?|
|biopsy at age < 40||8.70|
|biopsy age 40-44||6.80|
|biopsy age 45-49||5.60|
|biopsy age 50-54||4.50|
|biopsy age >54||3.10|
Is drinking a lot of alcohol bad? Yes. But suprisingly, not at low amounts.
|G. Alcohol use|
|< 1.5 grams/d||1.07|
|< 5 grams/d||0.99|
|< 15 grams/d||1.06|
|60 or more||1.31|
Birth Control Pills
|I. Used Oral Contraceptives?|
Age at first use
|< 20 yr||1.59|
|Last use 1-4 years ago||Last use 10-14 years ago|
Age at first use
|< 20 yr||1.49||
Age at first use
|< 20 yr||1.13|
|20-24 yr||1.15||20-24 yr||0.93|
|25-29 yr||1.09||25-29 yr||1.06|
|>29 yr||1.11||>29 yr||0.95|
|Last use 5-9 years ago||Last use 15 years or longer|
Age at first use
|< 20 yr||1.07||
Age at first use
|< 20 yr||1.14|
|20-24 yr||1.09||20-24 yr||1.01|
|25-29 yr||1.01||25-29 yr||1.01|
|>29 yr||1.18||>29 yr||0.99|
Summary Relative Risk is calculated using this formula:
Summary Relative Risk = A x B x C x D x E x F x G x H x I
For example, a 30 year old woman with menarche at age 12, one benign biopsy, no relatives with breast cancer, no atypical hyperplasia, mammographic density unknown, not taking tamoxifen, not drinking alcohol, no LCIS, no oral contraceptives:
Summary Relative Risk = 1.10 x 1.70 x 1.00 x 0.93 x 1.00 x 1.00 x 1.00 x 1.00 x 1.00 = 1.7391
After calculating summary relative risk, then the absolute risk is determined using polynomial equations. For example, the equation: Y = -0.0102*X2 + 1.619*X + 0.1418 describes the black part of the curve shown below. For the Gail model1 calculator, there are separate curves for 10-year, 20-year and 30-year absolute risk, for ages 20, 30, 40 and 50. For the NSABP model2 calculator, there are separate curves for 5-year and lifetime absolute risk, for ages 20, 30, 40, 50, 60 and 70.
This example graph shows the absolute 10-year risk curve for a 30 year old (for Gail model1) The black part of the curve comes from reference 1, and the gray part of the curve is my own estimate of the curve extended for higher relative risks, which might occur if many high risk modifiers were selected. (The vast majority of women will have Summary Relative Risk values within the black part of the curve). From this curve, if Summary Relative Risk was 20, then the Absolute Risk of developing breast cancer within 10 years, for a woman age 30, would be 28.4%.
For ages that fall in-between the decade values of 20,30,40,50,60, and 70, a simple linear equation scales the absolute risks. For example, a 35 year old women would be assigned an absolute risk value half-way between age 30 and 40.
After determining absolute risks using the curves available, linear equations estimate any missing values. For Gail model1, the 5-year and lifetime risk are estimated by linear interpolation from the 10-year, 20-year and 30-year risks. For NSABP model2, the 10-year, 20-year and 30-year risks are estimated by linear interpolation from the 5-year and lifetime risks.
Back to the actual Breast Cancer Risk Calculator.
- Benichou J, Gail MH, Mulvihill JJ, Graphs to estimate an individualized risk of breast cancer. J Clin Oncol 1996; 14:103-110.
- Gail MH, Brinton LA, Byar DP, Corle DK, Green SB, Chairer C, Mulvihill JJ, Projecting individualized probabilities of developing breast cancer for white females who are being examined annually. J Natl Cancer Inst 1989; 81:1879-1886.
- Spiegelman D, Colditz GA, Hunter D, et al.: Validation of the Gail et al. model for predicting individual breast cancer risk. J Natl Cancer Inst 1994; 86:600-607.
- Bondy ML, Lustbader ED, Halabi S, et al.: Validation of a breast cancer risk assessment model in women with a positive family history. J Natl Cancer Inst 1994; 86: 620-625.
- Costantino JP, Gail MH, Pee D, Anderson S, Redmond CK, Benichou J, Wieand S, Validation studies for models projecting the risk of invasive and total breast cancer incidence. J Natl Cancer Inst 1999; 91:1541-1548.
- Byrne C, Schairer C, Wolfe J, Parekh N, Salane M, Brinton LA, Hoover R, Haile R, Mammographic features and breast cancer risk: Effects with time, age and menopause status. J Natl Cancer Inst 1995; 87:1622;1629.
- Fisher B, Costantino JP,Wickerham DL at al, Tamoxifen for prevention of breast cancer: Report of the national surgical adjuvant breast and bowel project P-1 study. J Natl Cancer Inst 1998; 90:1371-1388.
- Spiegelman D, Colditz GA, Hunter D, Hertzmark E. Validation of the Gail et al. model for predicting individual breast cancer risk. J Natl Cancer Inst 1994; 86:600-607.
- Smith-Warner SA, Spiegelman D, S Yaun, et al. Alcohol and breast cancer in women: A pooled analysis of cohort studies. JAMA 1998; 279:535-540.
- Bodian CA, Perzin KH, Lattes R, Lobular Neoplasia. Long term risk of breast cancer and relation to other factors. Cancer 1996:78:1024-1034.
- Collaborative Group on Hormonal Factors in Breast Cancer. Breast cancer and hormonal contraceptives: collaborative reanalysis of individual data on 53 297 women with breast cancer and 100 239 women without breast cancer from 54 epidemiological studies. Lancet 1996; 347:1713-1327.
These published medical journal articles should be available to the public in most medical libraries at medical schools, major hospitals, cancer treatment centers, etc.