An important problem when analyzing multilevel-structured data is the inherent violation of the independency assumption on which many traditional statistical methods are based. Teeth of a particular person share a common environment within the same oral cavity; therefore, the health status of these teeth may be related to each other. In disaggregation, individuals within a given dataset are approached as independent observations. If the data has a multilevel structure, it is ignored. In this case, a traditional statistical model will be incorrectly applied to a multilevel-structured dataset. One example of this kind of error would be applying the traditional analysis of variance model to correlate the relationship of multiple observations such as the correlation of multiple implants from the same patient. From a practical perspective, collecting information on 100 implants from 40 patients might require less effort and time than examining 100 implants from 100 patients would (assuming that each implant was randomly selected from each patient who might also have multiple implants). The amount of information collected from the 100 implants in 40 patients (correlated data) will likely be smaller than that from 100 implants in 100 patients (independent data). Therefore, if all other conditions are equal, the standard errors calculated from the correlated data will be larger than those from the independent data will be. In other words, if the correlated data is analyzed using the standard analytic methods that assume independence among individuals, a critical problem of underestimating the standard errors may lead to erroneously significant results.

In other cases, multilevel-structured dental data has frequently been treated as an aggregated form of averaged or summed scores. In the field of periodontal research, the gingival index or periodontal index is computed as a mean score of multiple teeth and/or multiple sites. In addition, the degree of dental caries can be operationalized by the decayed, missing, and filled teeth (DMFT) index, which is the sum of the total number of decayed, missing, and filled teeth. However, this aggregation method has demonstrated at least three shortcomings. First, a substantial loss of power is inevitable because a small number of aggregated values are used in the data analysis. For instance, each patient has only one DMFT value in the data analysis, instead of all of their observed records on dental caries experienced in all of their teeth. Second, there might be a loss of detailed observations. For example, a small number of deep pockets or a large number of shallow pockets can give the same averaged or summed periodontal index score, even though these data were obtained from very different measures status. Similarly, a high DMFT index score may imply that either the patient has many decayed teeth or many treated, filled teeth, which are quite different conditions from the viewpoint of treatment requirements. Third, it is impossible to estimate the status or the change in any conditions at the lower level such as at the teeth level. For example, evaluating the effectiveness of a periodontal treatment based on a specific change to the periodontal status around a tooth is impossible when only an aggregated score per subject is provided.

Three noteworthy examples of periodontal research that applied the multilevel mixed effects model are introduced in Table 1. Tu et al. [15,16] investigated the longitudinal relationships between the outcomes lifetime cumulative attachment loss (LCAL) and probing depth in relation to potential risk factors for periodontal disease progression. The risk factors of interest included site-level factors (supragingival calculus, subgingival calculus, and bleeding on probing), tooth-level factors (tooth position), and subject-level factors (number of sites with a LCAL>1 mm and smoking status). The multilevel mixed effects model was applied, and the results revealed a linear relationship for tooth position and a significant effect for subgingival calculus and bleeding on probing with both LCAL and probing depth. Pereira et al. [17] explored the association between plasmic human immunodeficiency virus viral load and subgingival microbiota measured at 12 sites in each patient with chronic periodontitis (six sites from a tooth with the highest probing depth and six with a tooth in good periodontal health). A two-level model for an ordinal outcome variable was constructed with sites as the first level and persons as the second level. Last, Guglielmetti et al. [18] aimed to compare the presence and number of periodontal pathogens in smokers and never-smokers. Using four subgingival plaque samples collected from each person, the presence and number of bacteria were analyzed using the multilevel mixed model logistic regression and multilevel mixed model linear regression, respectively.

Abuhussein et al. [19] investigated factors associated with apoptosis in serum, saliva, and gingival crevicular fluid (GCF) and their associations with periodontal disease severity and activity. Clinical assessments such as those testing for gingivitis, measuring the number of deep pockets, and categorizing patients into mild or moderate/severe chronic periodontitis groups were determined at six sites per tooth. In addition, the GCF sample was collected from the mesiobuccal site of each tooth. To adjust for the correlated multiple measures taken from each patient, the GEE was implemented. The outcomes of interest were the aforementioned clinical groups and the number of deep pockets. The main explanatory variables were the level of GCF DNA fragmentation and presence or absence of the apoptosis markers. In patients with chronic periodontitis, factors associated with apoptosis in GCF were reported after adjustment for the multiple observations (in the mesio-buccal site of each tooth) that were performed in each patient.

Fig. 2 depicts the collection framework for a multilevel-structured dataset with multiple repeated measurements taken at the person or community level. Table 2 lists specific examples of these kinds of data in periodontal research. Multiple repeated measures in the same individual are frequently used in an attempt to measure the variable accurately. For example, Monje et al. [20] measured the sinus lateral wall thickness in atrophic posterior maxillae at six different sites in each patient; therefore, multiple repeated observations were made at the person level (Fig. 2A). Because correlated repeated measures were made in the same person, a mixed effects model was applied to assess the effects of residual ridge height, sex, and age on sinus lateral wall thickness. After consideration of the repeated measurements, the authors found that sinus lateral wall thickness was influenced by residual ridge height, the presence of teeth, and age.

The multilevel structure is a general phenomenon in data obtained from society, which also has a natural, multilevel structure. Many aspects of the human society frequently form a multilevel structure, (e.g., the four-level structure of students (level 1), classes (level 2), schools (level 3), and districts (level 4). Vettore et al. [21] investigated the prevalence and geographical distribution of periodontal disease and its association with contextual and individual social inequalities. Contextual effects mean that a higher level (community level in the example) factor affects the relationship with the lower level (person level) factor and the outcome variables. In their study, social inequalities were assessed using the Human Development Index and the Gini Index of Income Inequality. A multilevel model was implemented to accommodate the multilevel structure of the data and evaluate the contextual relationship of periodontal disease state (person-level variable) with the second-level variables. The authors concluded that income inequality (the second-level, community variable) plays a significant role in the occurrence of severe periodontal disease (the first-level, personal variable).