The number distribution for involved lymph nodes in cancer

The number of involved lymph nodes exhibits considerable heterogeneity within populations. Here, the implications of population heterogeneity are explored with respect to the kinematics of nodal metastases. Data from the National Cancer Institute's Surveillance, Epidemiology, and End Results program for 224656 breast, 12404 gastric, 18015 rectal, 4117 cervical and 2443 laryngeal cancers as well as 9118 melanomas were used to construct frequency distributions for the number of involved nodes which were then fitted to the negative binomial distribution. The negative binomial distribution described the heterogeneity in nodal involvement well. The patterns of nodal involvement can be explained by either of two models: one where involved nodes could seed further nodal metastases, the other where the number of nodal metastases in any individual was randomly distributed, with the deviations between patients accounted for by population heterogeneity. Since the number of sampled nodes similarly approximated a negative binomial distribution, random involvement with superimposed population heterogeneity would more credibly explain both sets of observations.