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

Abstract

Abstract 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.