###
BAYESIAN ANALYSIS OF LYMPHATIC SPREADING PATTERNS

IN CANCER OF THE THORACIC ESOPHAGUS

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

^{1} *The Kitasato Institute, 5-9-1 Shirokane, Minato-ku, Tokyo 108, Japan*

^{2} *Cancer Institute Hospital, 1-37-1 Kami-Ikebukuro, Toshima-ku, Tokyo 170, Japan*

^{3} *The 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.

**Source**
( TeX ,
DVI ,
PS )