How cancer at the primary site and in the lymph nodes contributes to the risk of cancer death

Abstract

This article describes the synthesis and characterization of hydroxyl tailored, molecularly defined biodegradable cooligomers capable of chelating rhenium for potential radiopharmaceuticals. New insights were gained during the synthesis of lactide based on dimethylaminopyridine‐catalyzed transesterification. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011

Why cancer at the primary site and in the lymph nodes contributes to the risk of cancer death

“…We have observed that, when information is available only on tumor size, a simple expression, the SizeOnly equation, accurately captures the relation between primary tumor size and lethality, as observed from our data on patients with breast carcinoma, renal cell carcinoma, and melanoma [1][2][3][4] (for the SizeOnly equation, see Equation 1 from the accompanying article 4 ). We also have observed that the relation between tumor size and the risk of cancer in the lymph nodes is captured well by a variant of the SizeOnly equation, the NodalSizeOnly equation (see Equation 1n in the accompanying article 4 ), as indicated by data from patients with breast carcinoma and patients with melanoma. In addition, we have observed that the relation between tumor size and the risk of death for patients with lymph node-negative melanoma and or breast carcinoma is captured by another variant of the SizeOnly equation, the PrimarySizeOnly equation.…”

“…of the probabilities of lethal spread of breast carcinoma from the primary site to the periphery using tumor size/survival data for all patients and of the lethal spread of breast carcinoma from the primary site to the periphery with tumor size/survival data for lymph node-negative patients using Equation 13 from the accompanying article. 4 Note that, in both cases, the correlation between the probability of spread and tumor size is well fit by a power function. Tumor sizes groups examined included 1 mm to 10 mm, 11 mm to 20 mm, 21 mm to 25 mm, 26 mm to 30 mm, and 31 mm to 35 mm.…”

“…leading to death in lymph node-negative patients (p primary-to-periphery ); or from the primary site to the periphery, leading to death in patients as a whole (p overall or p, which is the aggregate of all of these probabilities) ( More precisely (see derivation in the accompanying article in this series 4 ), the probability of the spread of a cancer cell, p x , can be calculated with the expression we call the ProbabilityEstimation equation:…”

“…The mathematical framework for the binary-biologic model of cancer metastasis is outlined in the accompanying article in this issue of Cancer. 4 In this report, we demonstrate that applying this framework to actual data will allow us to determine how cancer at the primary site and in the lymph nodes contributes to lethality.…”

“…We also have observed that, for breast carcinoma, each positive lymph node is associated with an approximately 6% risk of death, and each millimeter of primary tumor greatest dimension is associated with an approximately 1% risk of death; whereas, for melanoma, each positive lymph node is associated with an approximately 23% risk of death and, each millimeter of primary tumor greatest dimension is associated with an approximately 8% risk of death. 4 For both cancers, the overall risk of death is the sum of the risks of death from the lymph nodes and the primary site, which takes the form of a pair of linked equations, the SizeþNodes method. 5 In the current report, we examine the underlying basis for these observations.…”