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Trajectory Patterns of Dental Caries Experience in the Permanent
Dentition to the Fourth Decade of Life
J.M. Broadbent1,*, W.M. Thomson1, and R. Poulton2
1Department of Oral Sciences, Faculty of Dentistry, University of Otago, Dunedin, New Zealand 2Director,
Dunedin Multidisciplinary Health and Development Research Unit, Department of Preventive and Social
Medicine, Dunedin School of Medicine, University of Otago, Dunedin, New Zealand
Abstract
Dental caries is a chronic, cumulative disease, but no studies have investigated longitudinal patterns
of caries experience. The objective of this study was to identify and describe developmental
trajectories of caries experience in the permanent dentition to age 32. Longitudinal caries data for
955 participants in a longstanding birth cohort study were analyzed by trajectory analysis. Three
caries experience trajectories were identified by the SAS macro PROC TRAJ; these were categorized
as “high” (~ 15%), “medium” (~ 43%), and “low” (~ 42%) DMFS (Decayed, Missing, and Filled
Surfaces). All were relatively linear, although the higher trajectories were more “S-shaped”. This
effect disappeared following adjustment for the number of unaffected surfaces remaining at each
age, suggesting that, among individuals following a similar caries trajectory, caries rate is relatively
constant across time.
Keywords
longitudinal study; adult; trajectory analysis; caries
INTRODUCTION
Dental caries is a chronic, cumulative disease, and the caries status of an individual develops
over time. Caries occurs at any stage in life, provided that an individual has susceptible teeth
(and surfaces) remaining. Biological, behavioral, and environmental factors act upon the
dentition throughout life, suggesting that the life-course approach (Ben-Shlomo and Kuh,
2002) is relevant to dental caries epidemiology. However, dental caries epidemiology has rarely
been investigated from the life-course perspective (due, in part, to a paucity of appropriate
data), and statistical approaches to the analysis of such data have, correspondingly, been seldom
discussed in the dental literature. Analyzing differences in the accumulation of caries
experience over time among individuals can be challenging, and the interpretation of such data
is not always straightforward (Härkänen et al., 2002). In the past, many researchers have
defined groups to assist in data analysis on the basis of risk factors or other subjective
classifications; however, such an approach may fail to identify important developmental
patterns (Nagin, 2005).
Latent class analysis is a statistical approach used to group observations (or variables) into
strongly inter-related subgroups (or classes). Latent class analysis is relatively new in health
research, and appears to be a useful tool for evaluating complex developmental data. Thus, it
*corresponding author, jonathan.broadbent@stonebow.otago.ac.nz.
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Published in final edited form as:
J Dent Res. 2008 January ; 87(1): 69–72.
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provides a new and exciting option for identifying, summarizing, and describing the complex
patterns of findings often generated by life-course studies. While numerous statistical software
applications are available for conducting latent class analysis, not all can deal with longitudinal
data.
‘Group-based trajectory modeling’ is a specialized application of finite mixture modeling, and
can simplify longitudinal data by identifying developmental trajectory groups on a likelihood
basis. It approaches a set of individual trajectories by grouping those which closely resemble
one another (using a probability function). Essentially, the methodology assumes the existence
of unobserved (latent) subpopulations. While these groups do not (necessarily) exist per se,
their identification has applications in both the interpretation and further analysis of
longitudinal data. Dealing with a small number of groups of trajectories is less complicated
than analyzing several hundred individual trajectories (Nagin, 2005). Presentation of
longitudinal findings may be in the form of easily understood graphs and tables, and
determinants of group membership can be more readily investigated. Such data may be more
accessible for clinicians and other non-researchers.
While trajectory analysis is relatively new (Nagin and Land, 1993), it has already been used
extensively in longitudinal social research (Nagin and Tremblay, 2005). In psychology, the
term ‘developmental trajectory’ is used to describe the course of a behavior or outcome over
age or time. Such a term (or one such as ‘disease trajectory’) could also be applied to the
progression over time of a cumulative disease, such as dental caries.
Utilizing group-based trajectory analysis, we investigated the natural history of dental caries
experience in a birth cohort from childhood until the middle years of life. This research will
be particularly useful in determining whether (at the population level) high-risk periods for
dental caries exist—a ‘critical period’ of risk such as, for example, the teenage years (Carlos
and Gittelsohn, 1965)—or whether a cumulative increase in caries experience over time is
relatively constant, suggesting that risk does not vary with age (Ben-Shlomo and Kuh, 2002).
METHODS
The Dunedin Multidisciplinary Health and Development Study (DMHDS) is a longitudinal
study of a birth cohort of children who were born at the Queen Mary Hospital, Dunedin, New
Zealand, between 1st April 1972 and 31st March 1973 (Silva and Stanton, 1997). Perinatal
data were obtained, and the sample for the longitudinal study was first followed up at age 3
yrs (N = 1037), and again at ages 5, 7, 9, 11, 13, 15, 18, 21, 26, and, most recently, at 32 yrs.
The current study uses data collected from dental examinations at ages 5, 9, 15, 18, 26, and 32
yrs. The Otago Ethics Committee granted ethics approval for each assessment phase. Over
90% of the cohort self-identify as being of European origin. Study participants gave informed
consent prior to inclusion.
Measurement of Dental Caries
At each age, dental examinations for caries and missing teeth were conducted by calibrated
examiners. Before each examination, recording sheets were adjusted to account for teeth that
had been missing at the previous assessment. Teeth were examined for dental caries and
restorations, with 4 surfaces (buccal, lingual, distal, and mesial) being considered for canines
and incisors, and a fifth surface (the occlusal) included for premolars and molars. In a small
number of cases where a surface could not be visualized by the examiner, the surface was
excluded from the examination (and later analyses). We obtained an estimate of accumulated
tooth loss due to caries by observing the presence or absence of each tooth, and by ascertaining
the reason for its absence at that age by asking the participant at the time of each examination.
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Repeat examinations were not possible, because of the logistical constraints imposed by the
tightly scheduled assessment that study participants underwent. Dental examiners were not
aware of study participants’ socio-economic status (SES) or questionnaire responses at the time
of the examinations. Further information on these assessments is available in previous
publications (Suckling et al., 1985; Thomson et al., 2000; Broadbent et al., 2006).
Data Analysis
We used surface-level dental examination data to compute DMFS (Decayed, Missing, and
Filled Surfaces). For the ‘M’ component of DMFS, a minimum of 3 surfaces was assigned as
having been carious for each extracted tooth (Broadbent and Thomson, 2005). Where more
than 3 surfaces (4 or 5) were known to have been carious at the most recent assessment prior
to the extraction of the tooth, this number was used. For example, DMFS scores for teeth which
were missing at age 26 due to caries were adjusted by their surface status at age 18 (if present),
while teeth which were missing due to caries at age 32 were adjusted by their surface status
only from age 26. In this study, only teeth which had been lost because of caries are included
in the estimations of tooth loss due to caries, and in the ‘M’ component of DMF scores.
Group-based trajectory analysis was performed with the PROC TRAJ macro in SAS version
9.1 (Jones et al., 2001). To enable a single measure of dental caries experience to be used for
the trajectory model, the modified DMFS was used, as described above. The modified measure
is preferable in this instance to either DFS or generally accepted DMFS (where each missing
tooth is presumed to have been completely decayed prior to extraction), since it is very likely
that those measures provide under- and overestimates of true caries experience, respectively
(Broadbent and Thomson, 2005). Data analysis was restricted to those study participants for
whom dental data were available from at least 3 assessment ages. The PROC TRAJ macro
assumes that missing data are missing completely at random, and the model is adjusted so that
missing observations do not contribute to the sample size or analytical outcome.
The parameters for the trajectory model were determined on a maximum-likelihood basis by
a general quasi-Newton method (Dennis et al., 1981; Jones and Nagin, 2005). In the interests
of parsimony, a three-group trajectory analysis model was defined (Table). The Bayesian
Information Criterion (BIC) is a tool which is often used in model selection; however, in
trajectory analysis, the BIC does not always clearly identify a preferred number of groups.
Selection of that number must balance the interests of parsimony with the objective of reporting
the distinctive developmental patterns in the data. The objective of model selection is not the
maximization of some statistic of model fit; rather, it is to summarize the distinctive features
of the data in as parsimonious a fashion as possible (Nagin, 2005).
We defined the order of the two resultant groups with the greatest experience of dental caries
over time as having cubic trajectories, while the group with the lowest disease experience was
allocated a linear trajectory. This combination was determined by visual inspection of the
shapes of the trajectory plots, and by adjustment of the parameters to maximize the BIC within
the three-group model.
Since it is not yet possible to fit models in PROC TRAJ according to the zero-inflated negative
binomial (ZINB) distribution, the zero-inflated Poisson (ZIP) model was used instead as a
reasonably acceptable alternative (Lewsey and Thomson, 2004). The degree of zero-inflation
for the ZIP model was determined with the BIC. At all ages, the analysis was restricted to the
permanent teeth, since the primary teeth constitute a discrete dentition. Age-5 dental data were
included, because 46 of the 878 participants at that age had had at least 1 permanent tooth
erupted, but none had yet experienced caries. Thus, age 5 served as a ‘zero point’ for dental
caries experience.
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Plot data were generated by means of the macro ‘TRAJPLOT’. To reinforce the model and
trajectory plots produced, we calculated 95% confidence intervals through the macro
‘TRAJPLOTNEW’. Standard errors for the mean trajectories were calculated according to a
first-order Taylor series expansion (Jones and Nagin, 2005). Plot data were exported into (and
plotted in) Intercooled Stata 8.0 (Stata Corporation, College Station, TX, USA). The percentage
of caries-affected surfaces was computed at each age within each trajectory group, and this
was also plotted.
RESULTS
Participation rates in the Dunedin Study have remained high, with 972 study individuals (96%)
participating at age 32 yrs, and 932 (92%) participating in the dental examination. Dental caries
data were available for 955 individuals at 3 or more of the 6 dental assessment ages, and the
following analyses are restricted to those individuals. The 82 excluded individuals included
48 males (9.0%) and 34 females (6.8%).
The individual caries trajectories were plotted (Fig. 1), and through the trajectory group
assignment based on the PROC TRAJ macro, 384 participants (40.2%) were assigned to ‘group
1’, 427 (44.7%) to ‘group 2’, and 144 (15.1%) to ‘group 3’. These were designated the ‘low’,
‘medium’, and ‘high’ trajectory groups, respectively. When DMFS data by trajectory group
were plotted against age, the mean DMFS scores of trajectory groups were seen to diverge with
increasing age (Fig. 2). By age 32, the mean DMFS was 5.4 (SD 3.7) in group 1, 18.6 (SD 6.8)
in group 2, and 42.3 (SD 12.7) in group 3. On average, 36.9% of tooth surfaces in trajectory
group 3 had been affected by caries by age 32. At the group level, the plot of the percent of
caries-affected surfaces (of those permanent teeth present in the mouth) revealed no period of
rapid increase in DMF (Fig. 3).
The prevalence of tooth loss was greatest in the two higher trajectory groups. None of the
participants had lost teeth due to caries by the age of 18 yrs. By age 26, 0.6% of participants
in the low DMFS trajectory, 13.2% in the medium DMFS trajectory, and 33.3% in the high
trajectory for DMFS had lost teeth due to caries, with a mean 0.0, 0.3, and 0.7 teeth lost,
respectively. By age 32 yrs, the prevalence of tooth loss due to caries had increased in all
groups, to 5.9% in the low trajectory, 28.4% in the medium, and 53.8% in the high trajectory,
with a mean 0.1, 0.7, and 2.2 teeth lost, respectively.
DISCUSSION
The Dunedin Study remains the only dental study to have followed a group of individuals from
birth to adulthood. Our use of group-based trajectory analysis appears to be a valid approach
to exploring developmental trajectories; the technique has the added advantage of being simple
to interpret. The trajectory groupings are a useful statistical device for capturing the essential
features of the underlying complex reality of the longitudinal caries data-set.
A possible weakness of this study is that we have chosen to limit our analyses of possible
determinants of trajectory group membership (at this stage), and have not yet considered any
potential confounding variables. From an analytical standpoint, it is important to remember
that the trajectory ‘groups’ do not exist in the real sense; they are an analytical convenience.
Furthermore, several alternative programs are available for estimation of such latent classes
(PROC TRAJ, MPlus, and LatentGold), and the outcomes of latent class analyses may differ
according to the precise estimation parameters that are specified. PROC TRAJ (which we have
used) does not consider growth factor variances within trajectory classes, while the alternative
program MPlus does. This consideration is important theoretically, since it may affect the
trajectory group membership of a few cases; however, it is unlikely that including such
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variation would materially affect the overall outcome (and associated inferences) of the
analysis.
Trajectory analysis appears to be a useful and valid descriptive tool in the investigation of
caries experience across the life-course, and can aid in the recognition of patterns (or
trajectories) of caries experience over time. In this study, the two higher trajectory plots were
S-shaped (or cubic), while the lowest trajectory was linear. Teeth were lost at a proportionally
greater rate among participants following higher trajectories, thus decreasing the number of
surfaces available and ‘at risk’ to caries in the mouth over time. The rate of increase in %-
DMFS appeared to be linear in all trajectory groups, with no apparent drop-off in the rate of
increase in %-DMFS with increasing age. Thus, analysis of our data does not support the
commonly held belief among dentists that childhood and adolescence are periods of special
risk for dental caries, or that caries ‘immunity’ may be acquired during late adolescence or
early adulthood (Carlos and Gittelsohn, 1965). In this population at least, new caries appears
to be occurring at a relatively constant rate, implying that for greatest benefit, caries-preventive
measures are necessary at all stages of the life-course.
Acknowledgements
Jonathan Broadbent and the dental study are supported by Grant R01 DE-015260-01A1 from the National Institute
of Dental and Craniofacial Research, National Institutes of Health, Bethesda, MD 20892, USA. We thank study founder
Phil Silva, Harvey Brown, and all those involved in the administration of the Study. The Dunedin Study would not
be possible but for the ongoing participation of the Study members. The Health Research Council of New Zealand
(previously the Medical Research Council), the New Zealand Department of Education, the New Zealand Department
of Health, the National Children’s Health Research Foundation, and the Dental Research Foundation of New Zealand
provided funding for the assessments.
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Figure 1.
Simple join of DMFS scores by age (from the Dunedin Multidisciplinary Health and
Development Study database).
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Figure 2.
Trajectory plot of mean DMFS scores for three-group caries trajectory analysis model.
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Figure 3.
Plot of mean percentage of at-risk surfaces affected by caries over time for three-group caries
trajectory analysis model.
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Broadbent et al. Page 10
Table
Trajectory Model Selection Criteria
BIC*Percent Change in BIC for +1 Group AIC
1 group −19528 −19512
2 groups −13165 −32.6 −13126
3 groups −11669 −11.4 −11607
4 groups −11026 −5.5 −10941
5 groups −10850 −1.6 −10743
6 groups −10748 − 0.9 −10618
7 groups −11401 +6.1 −11248
8 groups −11339 −0.5 −11163
9 groups −11378 +0.3 −11180
*BIC, Bayesian Information Criterion; AIC, Akaike Information Criterion.
J Dent Res. Author manuscript; available in PMC 2008 February 25.