Lymph Node Ratio after Neoadjuvant Chemotherapy for Stage II/III Breast Cancer: Prognostic Value Measured with Gini’s Mean Difference of Restricted Mean Survival Times

Abstract

Restricted mean survival time (RMST), recommended for reporting survival, lacks a tool to evaluate multilevel factors. The potential of the Gini’s mean difference of RMSTs (Δ) is explored in a comparison of a lymph node ratio-based classification (LNRc) versus a number-based classification (ypN) applied to stage II/III breast cancer patients who received neoadjuvant chemotherapy and underwent axillary dissection. Number of positive nodes ( npos) classified patients into ypN0, npos = 0, ypN1, npos = [1,3], ypN2, npos = [4,9], and ypN3, npos ⩾ 10. Ratio npos/( number of nodes examined) of 0, (0,0.20], (0.20,0.65], and >0.65, classified patients into Lnr0 to Lnr3, respectively. Unadjusted and Cox-adjusted RMSTs were computed for the ypN and LNRc’s. At a follow-up time horizon of 72 months for 114 node-negative and 254 node-positive patients, unadjusted ypN0-ypN3 RMSTs were 62.4-41.4 months, Δ = 11.9 months (95%CI: 7.4-16.9), and Lnr0-Lnr3 62.4 to 36.3 months, Δ = 14.0 months (95%CI: 10.1-18.1). Cox models’ ypN1-ypN3 hazard ratios were 1.81-3.30, and Lnr1-Lnr3 1.52-4.39. Δ from Cox-fitted survival were ypN 8.1 months (95%CI: 5.9-10.5), LNRc 10.5 months (95%CI: 8.4-12.8). In conclusion, Gini’s mean difference is applicable to well established data in keeping with the literature on LNRc. It provides an alternative view on the improvement gained with a lymph node ratio-classification over using a number-classification.

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

“…The model was checked on the original non-imputed data to ascertain that there was no untoward discrepancy (column HR non-imputed). Lastly, the hazard ratios were compared with the confounder model published from the data set from the Seoul National University Hospital (column SNUH) 16 .…”

“… The novelty is in combining the components, in applying the GMD to the RMST to create a new measure. At the time of this writing, a search of Pubmed finds out of 33 million articles only one paper that applied GMD as a survival metric 16 . The GMD of the RMST provides a fresh perspective in survival analysis.…”

“…Fortunately, the limitation has just been lifted. Authors from Korea and Martinique demonstrated that Gini's mean difference (GMD) was applicable to analyze the RMSTs of any number of groups 16 . They showed that the GMD applied to RMST generalized the 2-groups comparison.…”

“…For a set of n "observations" X 1 , …, X n , the Gini's mean difference Δ is the mean absolute difference between any two distinct "observations" 15 , 16 : …”

“…Searching along Royston and Sauerbrei's concept of prognostic separation 13 , Gini's mean difference (GMD), the mean of absolute difference between all distinct pairs of quantities 14 , 15 , was found to express well the concept of separation. Application of the GMD to RMST has been presented for the first time in a study with disease-free survival endpoint from the Seoul National University Hospital (SNUH) 16 .…”