An Analysis of the Caries Process by Finite Absorbing Markov Chains

¹ Department of Biostatistics, University of Oregon Dental School

If the presence or absence of caries on the five surfaces of a tooth is considered, there are 32 possible patterns of decay for each tooth. The caries process may be considered as a finite absorbing Markov chain, with the pattern where all surfaces were carious as the absorbing state.

Four permanent teeth, the maxillary and mandibular second and first molars, were analyzed, based on data collected from 266 school children. It was found that the pattern occupancies of these four teeth were quite selective. The first molars each occupied 20 patterns with 15 patterns in common, and the second molars each occupied 10 patterns with 8 patterns in common.

The conditional probabilities of the caries process entering a pattern S_j given that it leaves pattern S_i were calculated. From this information, the probabilities of any path along which the caries process may proceed could be calculated. By viewing the different probabilities associated with different paths, we gain some insight of the workings of the caries process.

The probabilities of the process ever entering a pattern before absorption were also calculated. By setting the diagonal elements of this matrix, and summing over the rows, the row totals gave the average number of patterns the process may enter before absorption.

The average number of times (hence the average length of time) the process may stay in each pattern S_j were calculated. The row totals of this matrix gave the average number of steps (or the length of time) required for a tooth to reach absorption from a non-absorbing pattern. The standard deviations corresponding to each average were also calculated.

It is pointed out that the findings are useful in public health and dental insurance programs.

The need of extensive information of this kind for different groups and regions was discussed.