Improving the sensitivity of stereotactic core biopsy to diagnose ductal carcinoma in situ of the breast: a mathematical model.

Stereotactic core biopsy (SCB) is performed on mammographically suspicious, non-palpable lesions of the breast. Reported sensitivities of SCB for the detection of ductal carcinoma in situ (DCIS) vary from 41% to 93%. We have developed a simple mathematical model to predict the probability of retrieving at least one diagnostic core from a focus of DCIS. We make recommendations of the number of samples needed for different sized areas of microcalcification. The sensitivity of SCB is affected by needle placement accuracy, diameter of the area of microcalcification (d), histological density of DCIS (x) (calculated as 7.5% by previous studies) and number of core samples (n) removed. The probability of achieving at least one representative core sufficient for diagnosis (P(core)) is defined as: P(core) = 1-(1 + p ([1- (x/100)]d - 1 ))n, where rho is the probability of a SCB accurately targeting the area of microcalcification. At least seven core samples should be removed in small foci (<5 mm) of DCIS to achieve a 0.75 probability of an accurate diagnosis. The probability of a diagnostic biopsy of larger areas of DCIS (>10 mm) is 0.95 when five cores are removed. This formula serves as an explanation to patients why SCB may fail to diagnose DCIS, and justifies the retrieval of more core samples to increase the probability of an accurate diagnosis and to reduce the chance of a non-representative core. In the absence of sufficient samples, a wire-guided open biopsy is necessary to exclude DCIS.