Analysis of Lymph Nodal Metastases in Malignant Melanoma Using the Poisson Probability Paradigm and Bayes Rule

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This article deals with and formalizes 2 notions common to the practice of pathology. The first is that the number of lymph nodes found positive for metastasis relates directly to the total number of lymph nodes examined. The second is that for any patient, there is a chance that the absence of lymph node metastases is a false-negative result. I introduce the Poisson probability density function to deal with the first notion and the Bayes probability rule to deal with the second. To illustrate the insight these 2 models provide, I apply them to data regarding lymph nodal metastases in malignant melanoma. In this preliminary study, the results of these 2 models correlate well with observed survival probabilities in patients with stage N0 melanoma and with observed rates of false-negative results in sentinel lymph node biopsy technology. With further development, the combination of these models should provide a way to estimate the probability of nodal metastasis when, in fact, none have been observed. Thus, these models might provide useful tools for evaluating patients with stage N0 malignant neoplasms.

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