Predictors of Developmental Defects of Enamel in Primary Maxillary Central Incisors using Bayesian Model Selection

Abstract

Introduction

Localized non-inheritable developmental defects of tooth enamel (DDE) are classified as enamel hypoplasia (EH), opacity (OP) and post-eruptive breakdown (PEB) using the Enamel Defects Index. To better understand the etiology of DDE, we assessed the linkages amongst exposome variables for these defects during the specific time duration for enamel mineralization of the human primary maxillary central incisor enamel crowns. In general, these two teeth develop between 13–14 weeks in utero and 3–4 weeks’ postpartum of a full-term delivery, followed by tooth eruption at about 1 year of age.

Methods

We utilized existing datasets for mother-child dyads that encompassed 12 weeks’ gestation through birth and early infancy, and child DDE outcomes from digital images of the erupted primary maxillary central incisor teeth. We applied a Bayesian modeling paradigm to assess the important predictors of EH, OP, and PEB.

Results

The results of Gibbs variable selection showed a key set of predictors: mother’s prepregnancy body mass index (BMI); maternal serum concentrations of calcium and phosphorus at gestational week 28; child’s gestational age; and both mother’s and child’s functional vitamin D deficiency (FVDD). In this sample of healthy mothers and children, significant predictors for OP included the child having a gestational period > 36 weeks and FVDD at birth, and for PEB included a mother’s prepregnancy BMI < 21.5 and higher serum phosphorus concentration at week 28.

Conclusion

In conclusion, our methodology and results provide a roadmap for assessing timely biomarker measures of exposures during specific tooth development to better understand the etiology of DDE for future prevention.

1. Introduction

Three major types of localized non-inheritable developmental defects of tooth enamel (DDE) are classified in the Enamel Defects Index (EDI) as enamel hypoplasia (EH), opacities (OP) and post-eruptive breakdown (PEB) [1]. Prevalence data for these defects in the human primary dentition are scarce, and the results generally reflect global convenience samples with ranges of 4–99%, 2–98% and 6–50% for the three defects, respectively [2–6]. One of the consequences that these developmental defects can incur is dental treatment. For example, the enamel surface irregularities of EH can provide niches for cariogenic bacteria leading to dental caries and the subsequent need for dental treatment [7,8]. For OP, the treatment considerations generally revolve around esthetics; and for PEB, the treatment considerations can involve function and/or esthetics [9–11]. Dental treatment in these young children with DDE is challenging and expensive [12–16]; and 50% of the early childhood dental caries are found in the primary maxillary anterior dentition [11]. Prevention efforts for DDE are delayed by the lack of knowledge of the etiology and potentially modifiable exposures for DDE. The purpose of this study was to assess a set of exposure variables measured during specific tooth development to help inform knowledge of the predictors for each of the three DDE outcomes.

2. Methods

We focused our clinical study on the DDE of human primary central maxillary incisor teeth (PMCI). The PMCI enamel is estimated to develop between 13–14 weeks’ in utero and 3–4 weeks’ postpartum of a full-term delivery [17,18]. We used Bayesian methodology for a secondary analysis of data for 161 maternal-child dyads originating from a randomized controlled clinical trial (RCT) of vitamin D supplementation during pregnancy for healthy mothers, and also follow-up studies of the children. These 161 healthy mothers with singleton pregnancies were self-identified as 47 Caucasian, 57 African American and 57 Hispanic with a mean age of 27.5 years (SD 5.6yrs), a prepregnancy BMI of 28.6 (SD 7.0) and a 97% current nonsmoking status. The children had a mean gestational age of 38.7 (SD 2.2) weeks and a range of 27–43 weeks. Further details on this self-selected sample are available from published studies [19–21].

The existing datasets included maternal data from 12 weeks of gestation through birth; child data at birth, at 4–6 weeks’ early infancy and from digital photographic images of the facial surface of the child’s erupted PMCI teeth at about 2 years of age or older. Maternal variables included: mother’s age, pre-pregnancy body mass index (BMI), and total count of months of antacid use during pregnancy weeks 12–36; serum circulating concentrations at weeks 12, 28 and 36 for calcium (Ca), phosphorus (P), intact parathyroid hormone (iPTH), 25-hydroxyvitamin D (25(OH)D) and 1,25-dihydroxyvitamin D (1,25(OH)₂D). Three time points during pregnancy were chosen for maternal blood chemistry data because of their previously published trajectory of change: week 12 (starting point), week 28 (elbow point), and week 36 (ending point) [21]. Child variables included: gestational age; cord blood serum concentrations for Ca, P, iPTH, 25(OH)D, 1,25(OH)₂D and vitamin D binding protein (VDBP) genotype (focusing on 1s, 1f, and 2 genotypes as the three most common VDBP alleles); early infancy diet (determined as whether or not the child had received formula by 4–6 weeks post-partum or was exclusively fed breastmilk); and scores for DDE from dental images.

Case definitions for the DDE outcome variables were from the Enamel Defects Index (EDI) as follows: for EH, as a reduced thickness of enamel, translucent or opaque; OP as an alteration in translucency of enamel, smooth and with either a diffuse or demarcated border; and PEB as the loss of surface enamel after tooth eruption [1,22]. Defects were scored from digital photographic images taken of the facial surfaces of the two PMCI teeth (51 and 61). Each facial surface was divided into 3 nonoverlapping regions (incisal, middle, and cervical) and the presence of each defect was scored for each region, resulting in child scores as status (binary) and extent (count, with a range of 0–6 per defect type for the 2 teeth per child) [21]. Decayed, restored and missing teeth or regions (due to dental caries, trauma or exfoliation) were scored using the index for cavitated, non-cavitated lesions and excluded from these analyses [23–25].

2.1. Variable Transformations

We log-transformed the mother’s BMI before model fitting. We used the concurrent serum 25(OH)D and iPTH ratio to identify maternal and child functional vitamin D deficiency (FVDD). The FVDD case definition was that a serum 25(OH)D < 20ng/mL (deficiency) and iPTH > 65 pg/mL (abnormal, elevated) provided a definitive ratio i.e., ≤ 0.308 to identify as FVDD or not [26]. The FVDD group was assigned for the mothers at the three time points during pregnancy (_12, _28, and _36 weeks) and for the children at birth. The child’s VDBP genotype variable was included as 6 levels (1s, 1f or 2 homozygous or 1s/1f, 1f/2 or 1s/2 heterozygous).

2.2. Bayesian Hierarchical Modeling and Variable Selection

We approached the analysis of DDE by using regression models with fixed and random effects (mixed) models. These models were fitted to the defect outcomes using standard Bayesian strategies [27]. The models are regression models with observed predictors and additional random effects included to allow for unobserved confounding in the outcome. To find the best model, we used a Gibbs variable selection (GSV) [28]. This strategy searches through all possible variables to find the best fitting model. It does this by using an indicator (π) to allow all predictors to be included. For any given model, the included predictors have p = 1 whereas those excluded have p = 0. As the model fitting proceeds, this parameter is estimated to be 0 or 1.

The regression function used was of the form:

$$g(\cdot )={\sum }_{i=1}^p{\pi }_i{X}_i{\beta }_i,$$

Where X_i is the i th predictor and β_i is the coefficient for the i^th predictor. In Bayesian modeling it is usual to assume prior distributions for the parameters. The prior distribution of the indicator was assumed to be:

$${\pi }_i~\mathit{\text{Bernoulli}}\left(p_i\right),$$

With the probability p_i given a beta distribution

$$p_i~\mathit{\text{Beta}}(1,1).$$

This represents a uniform prior for the selection probability. This allows different predictors to have different probabilities of being included in the models without any prior bias in the choice. For the binary outcomes, EH status, OP status, and PEB status, we applied the logistic regression with random effects as the following:

$$Y_i^{\mathit{\text{status}}}~\mathit{\text{Bernoulli}}\left(f_i\right),$$

$$\mathit{\text{logit}}\left(f_i\right)={\sum }_{i=1}^p{\pi }_i{X}_i{\beta }_i+r_i,$$

where $Y_i^{\mathit{\text{status}}}$ represents either EH status, OP status, or PEB status. Here r_i is the random effect that allows for a random intercept for each subject under a normal prior distribution with mean 0 and variance τ². For the counted outcomes, EH extent, OP extent, and PEB extent, we applied the truncated Poisson regression with random effects as the following:

$$Y_i^{\mathit{\text{extent}}}~\mathit{\text{TPoisson}}\left({\lambda }_i;7\right),$$

$$\mathit{\text{log}}\left({\lambda }_i\right)={\sum }_{i=1}^p{\pi }_i{X}_i{\beta }_i+r_i,$$

where 7 represents the upper limit of the count (based on 6 tooth regions and including zero), and r_i is the random effect, as defined above.

The variable selection was carried out using a posterior sampling algorithm where the parameters and their indicators were sampled over a large number of iterations. This allows for a range of possible models to be evaluated. The Gibbs variable selection produces estimated average indicators for each predictor. If the averages exceed 0.5, then the predictor is assumed to be important and should be selected for inclusion in the final model [29]. We applied a slightly smaller threshold criterion (0.3 in the first step and 0.4 in the following steps) to allow more variables entering the model in the early stage of analyses. We did this because the maternal blood chemistry predictors from 3 time points were used in our model and their mutual correlation could impact the indicator’s significance. Following that, the final model was fitted again using only the selected predictors to obtain the corresponding coefficients. The software used was the OpenBUGS platform and the samplers were run for 5000 iterations for burn-in and 10000 iterations for the final sample [30].

2.3. Variable Imputation and Multinomial Regression

For missing values and outliers in some predictors, we assumed a prior distribution for each to impute values automatically when model fitting. An example of variable imputation is provided for VDBP genotype, a multi-level categorical predictor (6 levels) with some missing values. We considered a Bayesian structure to impute VDBP values with mother’s race/ethnicity as the predictor, as previous studies showed a strong association between race/ethnicity (or genotype) and the VDBP types [31]:

$$\mathit{\text{VDBP}}~\mathit{\text{Multinomial}}\left(v_1,v_2,v_3,v_4,v_5,v_6\right),$$

$$v_i=\frac{a+b\cdot {\mathit{\text{Race}}}_i}{{\sum }_{i=1}^{6}a+b\cdot {\mathit{\text{Race}}}_i}$$

where a and b are the coefficients in the multinomial regression. These coefficients were estimated by Bayesian multinomial regression with priors chosen:

$$a~N\left(0,{\sigma }_a^2\right),b~N\left(0,{\sigma }_b^2\right)$$

$${\sigma }_a~\mathit{\text{Unif}}(0,1),{\sigma }_b~\mathit{\text{Unif}}(0,1)$$

2.4. Fractional Polynomial Selection

In the process of model building, we considered the inclusion of alternative non-linear relations between selected predictors and outcomes. To this end we considered non-linear patterns based on fractional polynomial models [32–34]. Fractional polynomial models are simple and flexible models for regression relations that allow non-linear effects (curved and non-monotone relations). For this a range of power values were assumed for the predictor

$$x_i^{*}=x_i^p\mathit{\text{where\hspace{0.17em}}}p=[a,b,c,d,e,f,g].$$

The candidate power set was the commonly used:

$$\text{power}=\left[-2,-1,-0.5,0,0.5,1,2\right]$$

In particular, the power equals 0 means the logarithm transformation. The selection of the most appropriate power was done by comparing values of the deviance information criterion (DIC), and the model with the smallest DIC value was chosen.

3. Results

3.1. DDE outcome information

Of the 161 mother-child dyads, the final cohort sizes were 145 for EH, 144 for OP and 143 for PEB. Table 1 displays the children’s DDE of their PMCI teeth by both status and extent. Cohort sizes varied because of missingness in the children’s outcome measures, however the patterns for missingness were not systematic. In addition to Table 1, the following results further describe the severity of the defects amongst those children with the defect. The defect, number of children with the defect, mean (standard deviation) and range of counts of defective tooth regions per child were as follows: EH, n=60, 1.8 (1.1) 1–4; OP, n=45, 2.3 (1.2) 1–6; and PEB, n=69, 1.9 (1.0) 1–5. Additional tables of child cord blood chemistries by DDE status are available in Supplementary Tables A1–3.

Table 1.

Children’s DDE by status and by extent of PMCI tooth regions

	Status		Extent
		Counts
EH	Yes	60 (41.4%)	Mean (Std)	0.72 (1.04)
	No	85 (58.6%)	Range	0 – 4
OP	Yes	45 (31.2%)	Mean (Std)	0.65 (1.18)
	No	99 (68.8%)	Range	0 – 6
PEB	Yes	69 (48.3%)	Mean (Std)	0.75 (1.01)
	No	74 (51.7%)	Range	0 – 5

3.2. Bayesian variable selection

For each DDE outcome, the selected variables in the status and extent models look similar, though not the same (shown in Table 2). In general, among the three outcomes (EH, OP and PEB), we found that maternal FVDD was selected for both EH and OP, and mother’s BMI was selected for both EH and PEB. Maternal P_28 was selected only for PEB, and child’s gestational age and FVDD were selected only for OP.

Table 2.

The selected variables in the final models (Intercept is fixed for all models).

Models	Variable Selection
EH Status	Intercept + mombmi1 + momCa_282
EH Extent	Intercept + mombmi1 + momFVDD_283
Opacity Status	Intercept + gestage4 + childFVDD5 + momFVDD_126
Opacity Extent	Intercept + gestage4 + childFVDD5
PEB Status	Intercept + mombmi1 + momP_287
PEB Extent	Intercept + mombmi1 + momP_287

¹mombmi: mother’s prepregnancy BMI value.

²momCa_28: mother’s calcium concentration at gestational week 28.

³momFVDD_28: mother’s FVDD condition at gestational week 28.

⁴gestage: gestational age in weeks at birth.

⁵childFVDD: child’s FVDD condition at birth.

⁶momFVDD_12: mother’s FVDD condition at gestational week 12.

⁷momP_28: mother’s phosphorus concentration at gestational week 28.

3.3. Effect of predictors using linear modeling

3.3.1. Enamel hypoplasia defects

For both EH status and extent models, predictors maternal BMI, Ca_28 and FVDD_28 were negatively associated with the EH outcome, though not significantly under the 0.05 criterion (shown in Supplementary Tables B1–2).

3.3.2. Opacity defects

For OP status, the coefficient of child gestational weeks had a 95% credible interval above 0, suggesting a significant and positive association with the outcome i.e., a longer gestation time was associated with a higher risk of having opacity defects in the child’s PMCI (shown in Fig. 1a). A 1 unit increase in the gestation week increased the odds ratio to e^0.36 = 1.43. Likewise for OP extent, gestational weeks showed a significant and positive association; a 1 unit increase in the gestational weeks increased the mean count (λ) to e^0.4 = 1.49 times the baseline (shown in Fig. 1b).

Fig. 1.

Predicted OP status (a) and OP extent (b) by gestational weeks with 95% credible interval.

The child’s FVDD at birth was also associated with OP status; however, the association was weak and only marginally approached the 0.05 level, resulting in overlaps between the two groups (shown in Fig. 2a). The child’s FVDD at birth was associated with a higher risk of OP extent with the average OP extent score (λ) as high as e^1.1 = 3.00 times compared to the non-FVDD group (shown in Fig. 2b). See Supplementary Tables C1 and C2 for more detailed comparisons.

Fig. 2.

Predicted OP status (a) and OP extent (b) by the child’s FVDD group with 95% credible interval.

3.3.3. Post Eruptive Breakdown Defects

For the PEB status and extent models, the coefficient of mother’s pre-pregnancy BMI was strongly and negatively associated with the outcome under a 95% credible interval (shown in Fig. 3a, 3b), indicating that a mother’s higher BMI value was associated with a lower risk of having PEB defects in the child’s PMCI. For a 1 unit increase from a BMI of 21.5, the odds ratio for PEB status decreased by 11%. For PEB extent, 1 unit increase from 21.5 in BMI decreased the average score (λ) as much as e^{−1.43×(log(22.5)−log(21.5))} = 0.93 or 7%.

Fig. 3.

Predicted PEB status and extent by maternal log(BMI) levels (a, b) with 95% credible intervals and by maternal phosphorus concentration at week 28 (c, d) with 95% credible intervals.

Also, the maternal serum P_28 was strongly and positively associated with both PEB status and extent (95% credible interval). A 1 unit increase in maternal P_28 increased the odds ratio as much as e^1.02 = 2.77 or 177% for PEB status and increased the average score (λ) to 1.57 (shown in Fig. 3c, 3d). See Supplementary Tables D1 and D2 for more detailed comparisons.

3.4. Fractional Polynomial Models

To verify the effect of the predictors we used a comparative non-linear approach of fractional polynomial models. For EH status models, the main effects selected were maternal BMI and maternal Ca_28. We tested the fractional polynomial powers on these two predictors. However, the minimum DIC was only slightly improved compared with the linear model (DIC = 202.8 vs 205.4, shown in Supplementary Table E). For EH extent, the main effects selected were maternal BMI and maternal FVDD_28. The latter one was a categorical predictor, so we tested the fractional polynomial on the maternal BMI only. Like the status model, DIC values indicated the linear trend was a good fit and was kept due to simplicity. Similarly, the other four models -- OP status, OP extent, PEB status and PEB extent -- showed the non-linear terms were not necessary. Though non-linear trends were found by mean trajectory plots, e.g., OP status versus mother’s BMI, we kept the linear trend for simplicity.

3.5. Effect of predictors with models with interaction terms

For all 6 parallel models we checked the need to add possible interaction terms with the main effects fixed. Results were that the coefficients of the interaction terms all had a 95% credible interval including 0 (shown in Supplementary Table F). The DIC values for these models were slightly larger or the same compared with the models without interaction effects. Thus, we did not need to build the models with interaction terms.

4. Discussion/Conclusion

To shed light on the etiology of localized DDE, our Bayesian model selection identified maternal and child predictors for the outcomes of EH, OP and PEB in the child’s PMCI teeth. Key predictors from 12 weeks’ gestation through 4–6 weeks early infancy were the mother’s pre-pregnancy BMI, serum Ca_28 and P_28, and FVDD at 12 and 28 weeks of pregnancy; and the child’s gestational age in weeks and FVDD at birth.

Implications of identifying similarities in predictors for EH and PEB that were distinct from predictors for OP relate to both etiologies and case definitions of indices. A current limitation for studies, especially prevention studies of DDE, is that the case definitions are visual and tactile descriptions of the outcomes and not necessarily based in etiology. The Developmental Defects of Enamel (DDE) Index proposed in 1982 by the FDI (modified in 1989 and 1992) is an epidemiological index for descriptive surveys [35–37]. Likewise, the EDI is another epidemiological index not based in etiology. We chose the EDI for this study because the index includes not only the two major categories of DDE – EH as localized lack of enamel (quantitative) and OP as alterations in enamel translucency (qualitative) -- but also includes PEB defined as the loss of surface enamel after tooth eruption [1, 22]. The DDE Index does not distinguish PEB from EH. Our results using the EDI, found a common predictor for EH and PEB that provides preliminary evidence that supports a shared etiology (as reflected in the DDE Index) but also a difference because of the significant direct relationship of PEB with the maternal serum phosphorus at 28 weeks of pregnancy, not identified with EH.

New and significant findings of this DDE study were that a maternal higher serum phosphorus at week 28 and a lower maternal prepregnancy BMI predicted PEB, and that a child’s longer gestational age, especially beyond 36 weeks predicted OP. There are no directly comparable results found in the literature to explain these findings. At best, these predictors do follow a general timeline of enamel formation of secretion through maturation [38, 39]. The predictors for the quantitative defects EH and PEB occur earlier in pregnancy for the PMCI, whereas the predictors for qualitative OP occur later in pregnancy.

Introduced in this study was the novel predictor FVDD, determined as the ratio of 25(OH)D:iPTH [26]. FVDD is an indicator of the both the direction and interplay of 25(OH)D and iPTH, and provides a more sensitive indicator of the ongoing metabolic processes. Using this FVDD grouping also helped to reduce the number of predictors and presented a clearer pattern that iPTH dominated the effect of 25(OH)D towards the defects, compared to our previous study that used 25(OH)D and iPTH concentrations only as independent variables [21]. Comparable dental studies of FVDD during enamel development are not available for discussion.

Also novel in this study was our use of the child’s vitamin D binding protein (VDBP) genotype as a predictor for DDE. Differences in bound and available 25(OH) vary by VDPB genotype, and we were able to use the child’s VDBP as a predictor for the child’s DDE outcome [31]. We did impute some missing values for child VDBP by using the mother’s race/ethnicity as African American, Caucasian, or Hispanic. In future studies, collapsed groupings of the genotypes and/or larger sample sizes are needed to more fully describe the relationship of child’s VDBP genotype, vitamin D and DDE.

A major strength of this study was the measurement of maternal and child biomarkers of key components of enamel (Ca, P, 25(OH)D, and iPTH) that had the biological and temporal plausibility to impact enamel development of the PMCI. By extending the timeline for variables through 4–6 weeks early infancy, we included the impact of early infancy feeding habits to encompass the full extent of time for completion of PMCI enamel formation. However, infant early diet did not appear to impact the presence of DDE.

We scored the defects from digital photographs as the literature supports the accuracy and reliability of using digital photographs when compared to clinical exam [40–42]. Our intra-examiner agreement for EH was determined as “substantial” at the child level by a comparative rescore of the 6 tooth regions for 15% of the children (κ = 0.78) [43].

Limitations for generalizability of our study results include the selection bias of our very healthy population of mothers with no preexisting calcium, parathyroid, chronic hypertension or active thyroid disease conditions; and who also did not require diuretic or cardiac medications, including calcium channel blockers. These mothers then self-selected for the follow-up studies with the children [19, 21]. The DDE rates found in this study are not directly comparable to those in the published literature in part because of our healthy sample, our use of the EDI and our including only the facial surfaces of 2 teeth rather than e.g. a full primary dentition.

In consideration of sample size and the impact of outliers, we found that the risk of OP changed slowly when the child gestational age was less than 36 weeks, and then the risk for OP increased dramatically beyond 36 weeks. Thus, we are more likely to state the effect of gestational age as positive when the value of gestational week was relatively very high. Similar ideas related to this effect of outliers may also explain the impact of the mother’s BMI and serum chemistry predictors. One possible explanation is that the range of our predictors were concentrated within a small interval, making the extreme values likely to have a greater leverage effect on the results.

There is also the potential confounding in our results because of the mothers’ participation in an RCT of vitamin D supplementation during pregnancy [19]. However, the mothers’ characteristics by treatment group were similar and also our key variables were made from serum circulating blood chemistries, rather than vitamin D intake.

In conclusion, our methodology and results provide a roadmap for assessing timely biomarker measures of exposures during specific tooth development to better understand the etiology of DDE for future prevention. Our results showed similar predictors for EH and PEB, as compared to OP. This kind of distinction provides evidence to support that DDE case definitions implicate a basis in differing etiologies. A more clear understanding of maternal and early infancy exposures that result in DDE of the PMCI is needed for prevention research. Our ongoing studies continue to examine the interrelationships among these developmental defects and their exposome to better understand the in utero, birth and early infancy development of these enamel defects in the PMCI.

Data Availability Statement

All data generated or analyzed during this study are not yet publicly available due to ongoing study. Further inquiries can be directed to the corresponding author.