Statistical kinematics of axillary nodal metastases in breast carcinoma

The number of involved lymph nodes in individuals with breast cancer is highly variable, and of both prognostic and therapeutic importance. A statistical description for the frequency distribution of the numbers of involved nodes in an affected population could potentially reveal mechanisms of axillary metastasis, and eventually facilitate predictive models for tumor control and axillary sampling. A meta-analysis of 15 studies involving 24,757 axillary dissections was performed, including conventional dissections, sentinel node dissections and studies of occult metastases. Frequency histograms for the numbers of involved axillary lymph nodes from the populations were tested for clustering and they were fitted, as a first approximation, to a negative binomial distribution. Although the number of involved nodes per individual was quite variable, some individuals sustained more involved nodes than could be expected from a random (Poisson) distribution. The negative binomial distribution, however, provided acceptable descriptions for the distributions of involved nodes in all populations studied. Two mechanisms could explain these observations: (1) an apparent contagion model, where involved nodes seeded further nodal metastases, and (2) a spurious contagion model where the number of involved nodes per individual was randomly (Poisson) distributed and population heterogeneity accounted for the more severe cases. Both models were consistent with the hypothesis that the nodal metastasis is a chance event, with the probability of involvement greatest for nodes contiguous to the primary tumor and proportioned by lymphatic flow.