Analysis of tooth decay data in Japan using asymmetric statistical models

Kouji Yamamoto,¹ Sadao Tomizawa<sup>2

1</sup>Department of Medical Innovation, Osaka University Hospital, Osaka, ²Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan

Background: The aim of the present paper was to develop two new asymmetry probability models to analyze data for tooth decay from 363 women and 349 men aged 18–39 years who visited a dental clinic in Sapporo City, Japan, from 2001 to 2005.
Methods: We analyzed the probability relationship between grade of upper and lower tooth decay for men and women using the two new models, and tested goodness-of-fit for the models.
Results: The probability that a woman's (man's) grade of lower tooth decay is i (i = 1,2) and her (his) grade of upper tooth decay is j(>i), (j = 2,3) is estimated to be at most 13.52 (10.23) times higher than the probability that the woman's (man's) grade of upper tooth decay is i and grade of lower tooth decay is j.
Conclusion: From the data on tooth decay, decay of the upper teeth is worse than of the lower teeth in women and men, and the tendency becomes stronger as the numbers of decayed upper and lower teeth increase.

Keywords: distance-proportional symmetry, asymmetry, square contingency table, teeth