Gini's mean difference and the long-term prognostic value of nodal quanta classes after pre-operative chemotherapy in advanced breast cancer

Gini's mean difference (GMD, mean absolute difference between any two distinct quantities) of the restricted mean survival times (RMSTs, expectation of life at a given time limit) has been proposed as a new metric where higher GMD indicates better prognostic value. GMD is applied to the RMSTs at 25 years time-horizon to evaluate the long-term overall survival of women with breast cancer who received neoadjuvant chemotherapy, comparing a classification based on the number (pN) versus a classification based on the ratio (LNRc) of positive nodes found at axillary surgery. A total of 233 patients treated in 1980-2009 with documented number of positive nodes (npos) and number of nodes examined (ntot) were identified. The numbers were categorized into pN0, npos = 0; pN1, npos = [1,3]; pN2, npos = [4,9]; pN3, npos ≥ 10. The ratios npnx = npos/ntot were categorized into Lnr0, npnx = 0; Lnr1, npnx = (0,0.20]; Lnr2, npnx = (0.20,0.65]; Lnr3, npnx > 0.65. The GMD for pN-classification was 5.5 (standard error: ± 0.9) years, not much improved over a simple node-negative vs. node-positive that showed a GMD of 5.0 (± 1.4) years. The GMD for LNRc-classification was larger, 6.7 (± 0.8) years. Among other conventional metrics, Cox-model LNRc's c-index was 0.668 vs. pN's c = 0.641, indicating commensurate superiority of LNRc-classification. The usability of GMD-RMSTs warrants further investigation.