BAYESIAN ANALYSIS OF LYMPHATIC SPREADING PATTERNS IN CANCER OF THE THORACIC ESOPHAGUS

AKIFUMI YAFUNE^{1}, TOSHIKI MATSUBARA^{2} AND MAKIO ISHIGURO^{3}

1The Kitasato Institute, 5-9-1 Shirokane, Minato-ku, Tokyo 108, Japan 2Cancer Institute Hospital, 1-37-1 Kami-Ikebukuro, Toshima-ku, Tokyo 170, Japan

3The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

(Received November 25, 1991; revised February 3, 1993)

Abstract. For the treatment of patients with cancer of the thoracic esophagus, lymphatic spreading is one important factor to infer how advanced their cancer is. We introduced a one-dimensional scale based on lymphatic spreading patterns, the stage of cancer, to express how advanced their cancer is, and we proposed a method to infer each patient’s stage from his lymphatic spreading pattern by applying a Bayesian model. Our Bayesian model was built based on the assumption that lymphatic spreading in cancer could be explained as what was brought about by the advance of stage. In the modeling, we introduced the probability of what stage each patient was in as a prior distribution. We also introduced distribution functions of Weibull distributions to express the relation between the advance of stage and the increase of the probability of metastasis. Our model was applied to the data of nodal involvement obtained from 103 patients with cancer of the thoracic esophagus and the parameters were estimated with the maximum likelihood method. AIC was used to check that the data had enough information to be divided into the stages of a clinically reasonable number. With the estimated parameters, we inferred the probability of metastasis to each lymph node in each stage and calculated by Bayes’ theorem with 31 new patients the probability of what stage they were in. The results well represented some characteristics of the lymphatic spreading and suggested the appropriateness of our approach.

Key words and phrases: Cancer of the thoracic esophagus, lymphatic spreading pattern, Bayesian model, Bayes’ theorem, Weibull distribution, AIC.