Appendix 2

The meta-analysis of penetrance was based on the Bayes theorem and stratified by cancer type (breast or ovarian), risk group (average, moderate, and high), and age. The penetrance of BRCA mutations is the probability of developing cancer given that a clinically significant BRCA mutation is present. Let D⁺ denote "individual has cancer," D¯ denote "individual does not has cancer," G denote "individual has a clinically significant BRCA mutation," penetrance is then denoted as P(D⁺|G) By the Bayes theorem, penetrance is given by:

where P(D¯) = 1 - P(D⁺). In our analysis, we assume P(D⁺) is fixed. For the average-risk group, the estimate of P(D⁺) from Surveillance, Epidemiology, and End Results (SEER) data using DevCan software⁵² is used in the calculation of penetrance. When family history is present, the estimate of P(D⁺) is obtained by multiplying the SEER estimate by the relative risk for cancer with a positive family history. P(G|D⁺) and P(G|D¯) are the prevalences of BRCA mutations from the cancer-affected and cancer-unaffected populations, respectively, and are estimated from different studies in a meta-analysis by using a randomeffects model.⁵³

The 95% CI of P(D⁺|G) is calculated as follows. Modifying equation (1), we have:

Assuming that P(G|D⁺) and P(G|D¯) are independent with each other, standard calculation using delta-method shows:

Usually, logit(P(D⁺|G)) is assumed to be normally distributed and the 95% CI of logit(P(D⁺|G)) is given as

where Z_0.975 is the 97.5% quantile of the standard normal distribution. The 95% CI of P(D⁺|G) is obtained by converting the above interval back to the original scale.

For some risk groups, there are no data from genetic testing studies with which to estimate P(G|D¯), and we used the best point estimates available in the literature. However, SEs associated with the point estimates are usually not available. Under such conditions, the second part of equation 3 on the right side would be zero, and the 95% CI for the penetrance would be underestimated.

Equation 1 provides the formula to calculate penetrance in general. It is easy to extend equation 1 to calculate penetrance of BRCA mutations by a particular age or with a positive family history. For example, if we are interested in penetrance of BRCAmutations by age x, we substitute D⁺ by D⁺ by age x, denoted by D⁺/_x, in equation (1), which gives

In this analysis, we assume

In our analysis, we calculated penetrance of breast cancer to ages 40 and 75 years and ovarian cancer to ages 50 and 75 years to be consistent with how age was considered by the studies. For penetrance of BRCA mutations when a positive family history is present,

We conducted a sensitivity analysis in the average-risk groups by calculating penetrance 2 ways: including and excluding studies of women with family history of breast or ovarian cancer. Calculation of 95% CI for penetrance in equations 4 and 5 is similar to that described above, with appropriate substitution of terms.

---

Return to Contents
Proceed to Next Section