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Biological Interpretation of the Correlation of Emergence Times of Permanent Teeth
1 Department of Biostatistics, University of Aarhus, 6 Vennelyst Boulevard, DK-8000 Århus C, Denmark; Correspondence: * corresponding author, parner{at}biostat.au.dk
The eruption mechanism is not fully understood. It is known that the dental follicle is essential and that experimentally provoked denervation influence the process of eruption. Accordingly, the purpose of this study was to elucidate the eruption pattern in a human population and relate this pattern to the pattern of jaw innervation. The eruption pattern was evaluated from the correlation between the emergence times of different teeth in the permanent dentition based on longitudinal data from a large national registry (12,642 boys and 12,095 girls). Correlations coefficients were generally high (>0.5) and higher between teeth within the same tooth groups (i.e. incisors, canines and premolars, and molars) than between teeth from different tooth groups. It was shown that the correlation in emergence of teeth closely followed the pattern of innervation of the jaws. Thus the study supported the hypothesis concerning a possible association between eruption and innervation.
Key Words: emergence • permanent teeth • correlation • tooth innervation
Studies on correlations between emergence times of teeth may give important information on the biological processes underlying development of the dentition. Previous studies have described the correlations between the ages at which different teeth emerge in the same individual. Some of these studies, however, were either not clear on how the emergence time of a tooth was determined or were based on relatively small samples (Garn et al., 1960; Sturdivant et al., 1962; Kent et al., 1978; Garn and Smith, 1980). Other studies have determined the emergence time as the midpoint between the age when the tooth was last observed as not emerged and the age when it was first observed as emerged (Hamano and Hägg, 1988), a method which introduces bias, especially when correlations are studied (Parner, 2001). Moreover, in none of the previously published works has any attempt been made to explain the emergence patterns seen in the human dentition. If emergence patterns could be interpreted biologically, it might add to the understanding of the eruption mechanism. Experimentally, it has been shown that the dental follicle plays an essential role in eruption (Marks and Schroeder, 1996), that innervation occurs in the human follicle (Christensen et al., 1993), and that denervation performed experimentally influences the process of osteoclast appearance necessary for tooth movement (Yamashiro et al., 2000). Accordingly, we hypothesized that an association exists between eruption pattern and innervation pattern. The purpose of our present study was to examine correlations between the emergence times of different teeth in the permanent dentition on data from a large national database, using statistical methods appropriate for these types of data. In addition, we aimed to associate eruption patterns to the innervation patterns of the jaws (Kjær, 1997) and thereby possibly contribute to an understanding of the eruption process. Finally, we also wanted to assess to what extent knowledge of the emergence time of one tooth would increase the precision with which the emergence of another tooth could be predicted.
SCOR is a nationwide Danish registry of oral conditions among 3- to 18-year olds from the early 1970s to the present. As a part of the regular visit, the child's dentist carries out an oral examination according to written criteria from the National Board of Health. These oral registrations are made annually. [For further details on the SCOR database, see Parner et al.(2001).] For the present study, we considered tooth emergence data for children born in 1978 and with more than 11 records in the database, in total 12,642 boys and 12,095 girls. The emergence time for a given tooth, i.e., the age of the child when the tooth emerged, is known to lie in the interval determined by the age of the child at the last visit prior to emergence and the age at the first visit after emergence. Such data are called "interval-censored data" (see Lindsey and Ryan, 1998, for a review on the analysis of interval-censored data). When pairs of emergence times are considered, the data on each child are a pair of interval-censored observations, and the pair of emergence times is therefore known to lie only in a two-dimensional interval, i.e., a rectangle in the plane. In earlier studies, we showed that the distribution of emergence times is approximately Gaussian (Parner et al., 2001), and that the joint distribution of two emergence times indeed follows approximately a two-dimensional Gaussian distribution (Parner, 2001). Both of these papers used non-parametric methods for interval censoring, which requires only a minimum set of assumptions. This approach may be viewed as a generalization of the empirical distribution function to interval-censored data, and the appropriateness of Gaussian distribution can therefore be assessed. In the present analysis, the likelihood function for two emergence times was derived as the product of the probabilities of the observed rectangles based on a two-dimensional Gaussian distribution. We then obtained maximum likelihood estimates of the means, standard deviations, and correlations by maximizing the likelihood function. Standard errors of the means, standard deviations, and correlations were calculated as the inverse of minus the matrix of second numerical derivatives of the log-likelihood function. We used standard results about multivariate Gaussian distributions to derive the effect on the variance of the distributions of emergence times for a given tooth when the emergence times of other teeth were taken into account (Mardia et al., 1979, page 64). If the emergence time of just one other tooth were accounted for, the variance would thus be reduced by a factor equal to 1 minus the squared correlation coefficient between the two teeth. We used these results to study the effect of adjusting for the emergence times of other teeth on a reference interval for the emergence time of a given tooth.
All correlation coefficients are larger than 0.5, indicating that a substantial part of the variation in the emergence times is a characteristic of the child rather than of the specific tooth (Table). A distinct feature of the correlation coefficients is the high correlation between teeth of the same type, especially between teeth in a pair of homologous teeth in the same jaw (antimeres). This is clearly seen in a display of correlations between an index tooth in the right upper jaw and all other teeth (Fig. 1  ). Within the same side of the jaw, the correlation decreases with distance from the index tooth; for teeth in the opposite side of the upper jaw, a similar pattern is seen, since the correlation decreases with distance from the homologous index tooth. The correlations between the index tooth and the teeth in the lower jaw show the same pattern, but the correlation coefficients are generally smaller. The results for girls and boys are remarkably similar.
The correlations are estimated with a high degree of precision. The estimated standard errors of the correlations ranged between 0.000001 and 0.009, with a median standard error of 0.007.
In both jaws, the largest correlation between pairs of neighboring teeth is seen between the two central incisors (Fig. 2
The estimated correlations may be used for calculating improved reference intervals of the emergence times. As an example, we consider calculating 95% reference intervals for the emergence time of tooth 17 (Fig. 3 ). The gray area in the Fig. gives a 95% reference interval for the emergence time of tooth 17 based only on information on this tooth. If the time of emergence of tooth 16 is available, the reference interval for tooth 17 is given as the interval between the two tilted lines for the particular value of x, the emergence time of tooth 16.
The results of the present study concerning eruption pattern are in general agreement with the results of previous studies on the correlation of emergence times for permanent teeth. However, the correlations found by, for example, Hamano and Hägg (1988) were consistently lower than those found in our study and gave a different pattern for boys and girls, probably due to the small sample size and the statistical method used. In many studies concerning the eruption of permanent teeth, the emergence time is approximated by the midpoint of the intervals determined by the age prior to and after the emergence of the tooth. In the present study, a consequence of this procedure is that two teeth will either emerge at exactly the same time or with a difference of approximately one year, two years, etc. Thus, the distribution of these midpoint data is far from a bivariate Gaussian distribution, and bias is introduced when the correlations are estimated. The size of this bias may be considerable: When the emergence times in the present data were approximated by midpoints, the bias ranged from 9% to 57%, with a median bias of 40%. The largest bias was seen for tooth pairs emerging at approximately the same age. In the present study, which is based on a very large dataset, it has been shown that there is a high correlation in emergence times between teeth in the dental arch that are homologous, i.e., that belong to the same group of teeth. On the other hand, there is a lower correlation in emergence times between teeth from different tooth groups. In that connection, it is worth noticing that tooth groups are innervated separately. For instance, nerve supply to molars and premolars is not the same (Kjær, 1995; Chavéz-Loméli et al., 1996). This suggests that innervation may have an important influence on emergence times. This hypothesis is supported by the relatively high correlation coefficients between teeth with the same nerve supply, while teeth from different tooth groups show lower correlation in emergence times, even though the teeth are adjacent to one another, e.g., the first molar and the second premolar. The fact that the correlation in emergence times between a given index tooth and the teeth in the same jaw segment is generally higher compared with the correlation between the same index tooth and teeth in the contralateral part of the jaw can also be explained by the pattern of innervation. Considering that the two bilateral parts of the jaw are innervated from two bilateral and different trigeminal ganglia, it is reasonable to assume a higher correlation in emergence times between teeth belonging to the same ganglion than between teeth innervated from different ganglia. It is commonly assumed that the inferior alveolar nerve supplies all the teeth in the mandible. Recent studies, however, have shown that the inferior alveolar nerve is a large bundle of nerve fibers whose individual nerve branches grow out at different times to innervate different tooth groups (Chavéz-Loméli et al., 1996). The correlation of emergence times that is documented in the present study can thus be presumed to visualize the innervation patterns of both maxilla and mandible. That the pattern is more distinct in the maxilla than in the mandible may be related to the fact that the courses of the nerve branches are more separate in the maxilla (naso-palatine nerve to the incisors, maxillary nerve to canines/premolars, palatine nerve to molars) than in the mandible (inferior alveolar nerve with a common bundle of individual nerve branches). General factors and local factors (e.g., caries history of the predecessors) are known to influence eruption. The present theory concerning influence from the peripheral nervous system exemplifies a general factor. The credibility of this present biological interpretation is indirectly supported by the fact that other explanations seem less consistent with the results. For instance, different types of teeth emerging about the same age do not show a particularly high correlation. Concerning the deciduous dentition, the innervation paths are similar to those of the permanent dentition, but the correlations of these emergence times have not yet been analyzed. Therefore, comparisons with similar studies in the deciduous dentition cannot be performed.
Due to the large sample size and the high precision of the estimates of correlations, results from our study could be useful in the diagnosis of the delayed eruption of permanent teeth, such as, for example, upper canines, and thus assist in the decision as to whether radiographic examination is needed. Another example could be delayed eruption of lower second molars, which is often vaguely defined as "emergence beyond the time when it should normally erupt" (Varpio and Wellfelt, 1988). Consider, e.g., the emergence of tooth 17. The 95% reference interval for the age at emergence of this tooth is (9.97, 14.67) yrs (Fig. 3
The study was supported by the Danish Dental Association and by the Aarhus University Research Foundation (grant no. 1-79 2824 9501). Received for publication August 14, 2001. Revision received May 6, 2002. Accepted for publication May 15, 2002.
Journal of Dental Research, Vol. 81, No. 7,
451-454 (2002) Related articles in Journal of Dental Research:
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