Appendix. How the standard Gail Model method
was modified and implemented in the breast cancer risk calculator.

Here are the juicy boring details, where the rubber meets the road. This is pretty 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.

Table 1  (along the right) 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. As discussed above, 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. Additional relative risk modifiers are listed below. E. Mammographic Density   Not Specified 1.000 0% fatty 0.405 1% to 24% 0.636 25% to 49% 1.000 50% to 74% 1.121 75% to 100% 1.761   F. Taking Tamoxifen?   no 1.00 yes, age under 50 yrs 0.56 yes, age 50 to 60 yrs 0.49 yes, age over 60 yrs 0.45   H. LCIS on biopsy?   Not applicable 1.00 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 G. Alcohol use   Not specified 1.00 none 1.00 < 1.5 grams/d 1.07 < 5 grams/d 0.99 < 15 grams/d 1.06 <30 grams/d 1.16 <60 grams/d 1.41 60 or more 1.31

Table 1. X Z A.  Age at menarche in years             14 or older 1.00 1.000         12-13 1.10 1.098         11 or younger 1.21 1.188       B.  Number of Biopsies        Age under 50 years   life 5-yr         0 biopsies 1.00 1.000 1.000         1 biopsy 1.70 1.278 1.683         2 or more  2.88 1.647 2.750    Age 50 years or older             0 biopsies 1.00 1.000         1 biopsy 1.27 1.237         2 or more 1.62 1.539       C.  Number of first degree        relatives with breast cancer        Age at first live birth  < 20 years             0 relatives 1.00 1.000         1 relative 2.61 2.560         2 or more 6.80 6.168    Age at first live birth 20-24 years             0 relatives 1.24 1.240         1 relative 2.68 2.640         2 or more 5.78 5.318    Age at first live birth 25-29 years             0 relatives 1.55 1.550         1 relative 2.76 2.705         2 or more 4.91 4.591    Age at first live birth 30 +  years             0 relatives 1.93 1.930         1 relative 2.83 2.779         2 or more 4.17 3.953       D.  Biopsy with atypical hyperplasia?             Not applicable or unknown 1.00 1.00         No atypical hyperplasia 0.93 0.93         Yes, atypical hyperplasia 1.82 1.82

 

I. Used Oral Contraceptives?
				Current user
Never used		1.00		Age at first use	< 20 yr	1.59
					20-24 yr	1.17
					25-29 yr	1.16
					>29 yr	1.25
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.