# Estimation of Age in Humans Using Dental Translucency of Permanent Teeh: An Experimental Study
## 2 Materials and Methods
### Statistical Analysis  
An a priori power analysis was conducted to ensure that the number of participants was representative for the purposes of this study using the program G*Power (3.1.9.2, Universitat Kiel, Kiel, Germany). A two-independent Pearson correlation was selected, imputing an \(\alpha\) error probability =0.05 and a (1 - \(\beta\)) = 0.95; the effect size was q =0.6. The outcomes parameters thus calculated detected a total sample size of 128 teeth. Moreover, to calculate the a priori sample size required for the regression analysis, we used [PERSON]'s rule of thumb (medium effect), which indicated a required total sample size of 105 teeth. Additional subjects were included to ensure the availability of data. Descriptive statistics were performed through mean and standard deviation for the continuous variables and percentage for the categorical variables. For statistical comparisons, we divided the sample into three age classes (<40; between 40 and 59; \(\geq\)60 years) [22]. Comparisons between sexes were performed through independent sample _t_-tests, whereas comparisons between the three age classes were through analysis of variance (ANOVA). A Tukey post hoc test was also performed. All the teeth were independently measured by the same operator (A) in two independent measurement sessions one month apart (A1 and A2) and independently by a second operator (B). The first operator was an expert in the field of biological anthropology, whereas the second operator was a master's student. Intra-operator and inter-operator reliability was assessed by Intraclass Correlation Coefficient (ICC) by comparing the results obtained by the same operator (A1 vs. A2) and the two independent operators (A1 and B), respectively. ICC is based on a two-way model considering single measures and the same rater for all subjects. To prevent bias, both operators were blind to the other's result and the chronological age (CA) of the subject. Values of ICC below 0.5 indicate poor reliability, between 0.5 and 0.75 moderate reliability, between 0.75 and 0.9 good reliability, and any value above 0.9 indicates excellent reliability [23]. Pearson correlation was performed between CA and the three dental measures (RH, PH, and RHT). We then proceeded to test the different equations of the literature estimating the age of each tooth by applying the formulas of [PERSON] and [PERSON] [19], [PERSON] et al. [6], [PERSON] and [PERSON] [8], [PERSON] et al. [17], [PERSON] and [PERSON] [20], [PERSON] et al. [11], and [PERSON] et al. [21] (Table 1). Each equation has been applied only on teeth with RHT > 0 and for [PERSON]'s formula only on RHT \(\geq\) 3. For each equation, we calculated the Bias (mean error: [\(\Sigma\)(estimated age - chronological age)]/n), the precision (standard deviation of the mean error), and the inaccuracy (mean absolute error: [\(\Sigma\)(estimated age - chronological age)]/n) [22]. In addition, the number (and percentage) of estimates with errors \(\leq\)\(\pm\)5, \(\leq\)\(\pm\)10 years, and \(\geq\)\(\pm\)15 years was also calculated. [PERSON] and [PERSON] [24] have categorized the former as \"acceptable\" and designated the latter as \"unsatisfactory\" in forensic age estimation. The second step was to create a specific regression equation based on the Italian sample. For comparison purposes, we selected randomly from the whole sample (N = 155) a holdout sample of 20 individuals (10 males and 10 females). Data from this subsample were excluded from the database used to develop new formulas for age estimation. Thus, the study sample used consisted of 135 teeth (M = 53; F = 82). To minimize the bias, every holdout group for each sex comprises 3 single-rooted teeth (1 with an age < 40; 1 with an age comprised between 40 and 59 years; 1 with an age > 60 years); 3 multi-rooted teeth (1 with an age < 40; 1 with an age comprised between 40 and 59 years; 1 with an age > 60 years); 4 teeth randomly selected among all the teeth typology and age.