Results

Descriptive analysis

The collected sample consisted of 112 fourth right ribs, collected during the autopsies performed at the Institute of Legal Medicine of the University of Rome “Tor Vergata,” between July 2017 and September 2023. The sample consisted of 74 male and 38 female subjects. The mean age was 53.4 years (SD: 14.1) for males, and 58.0 (SD: 23.8) for females. The sample distribution, by phase, is detailed in Table 2. Several ribs could correspond to many phases, as Iscan’s age ranges are notoriously wide and overlapping. Two observers (L. F. and A. M.) observed the 112 ribs twice each, for a total of 448 observations. For each phase, the mean and standard deviation are reported in Table 2.

Gender | Phase | N of ribs (compatible within phase) | Expected n by each operator | Observed n by OP 1 | OP 1 mean | OP 1 SD | Observed n by OP 2 | OP 2 mean | OP 2 SD
Female | 1 | 0 | 0 | 3 | 17.00 | - | 6 | 19.67 | 4.62
2 | 2 | 4 | 9 | 22.00 | 3.32 | 8 | 24.50 | 4.04
3 | 2 | 4 | 10 | 45.60 | 18.80 | 6 | 50.00 | 23.52
4 | 6 | 7 | 16 | 53.50 | 17.72 | 6 | 60.00 | 20.41
5 | 22 | 15 | 4 | 59.00 | 1.41 | 21 | 62.58 | 21.30
6 | 21 | 14 | 6 | 62.33 | 13.32 | 13 | 76.29 | 8.2
7 | 22 | 15 | 19 | 76.90 | 9.75 | 8 | 69.80 | 8.47
8 | 17 | 16 | 9 | 85.80 | 4.66 | 8 | 77.60 | 16.88
Male | 1 | 1 | 1 | 2 | 18.00 | - | 2 | 18.00 | -
2 | 1 | 1 | 19 | 38.40 | 12.53 | 12 | 38.00 | 8.06
3 | 7 | 5 | 24 | 43.92 | 12.49 | 18 | 39.36 | 10.72
4 | 9 | 6 | 20 | 55.20 | 6.83 | 27 | 52.93 | 8.55
5 | 30 | 20 | 25 | 53.62 | 10.62 | 31 | 56.00 | 13.24
6 | 60 | 40 | 26 | 60.38 | 11.75 | 26 | 58.73 | 11.44
7 | 57 | 38 | 26 | 60.00 | 7.97 | 22 | 59.92 | 10.09
8 | 57 | 38 | 6 | 77.33 | 4.62 | 10 | 63.83 | 11.99

Agreement and reliability

Intra-operator agreement was found to be almost perfect for both operators, with weighted Cohen’s kappa values of 0.98 (Op.1) and 0.92 (Op.2); inter-operator agreement was substantial, both in the first (kappa = 0.75) and in the second (kappa = 0.76) session of scoring. The P-values were < 0.001 for all estimations.

The success rate for phase assignment was found to be 46.9% for Observer 1 and 48.2% for Observer 2. The Kolmogorov-Smirnov test showed no significant difference between the distributions of success rates (KS = 0.036, P = 0.999), indicating that the two observers performed similarly in assigning rib phases. Overall success rates are depicted in Fig. 4.

Fig. 4: Success rate by operator. Scatter points represent the success rates for each observed case, with Observer 1 shown as upward triangles and Observer 2 as downward triangles. Dashed lines represent logistic regression fits for each observer

Figure 5 shows the Prior and Posterior KDE Density Distributions for the Iscan CT classification. Prior probability is overrepresented in phases 6 and higher, with Posterior distributions shifted rightward, indicating a tendency toward higher-phase assignments. Differences are minimal in phases 3 to 5, where Prior and Posterior distributions align more closely. The largest discrepancy occurs in phase 8, where the Posterior density is more dispersed, suggesting greater classification variability.

Fig. 5: Prior and Posterior KDE Density Distribution of Phase Assignments: This figure compares the expected (Prior, blue dashed line) and observed (Posterior, red solid line) phase assignments using Kernel Density Estimation (KDE) for phases 2 to 8. The Prior distribution reflects the theoretical classification based on the Iscan method, while the Posterior distribution represents actual phase assignments made by two independent observers. The degree of misalignment between the two curves highlights potential biases in phase estimation: Rightward shifts in the red curve indicate overestimation of that phase. Leftward shifts suggest underestimation. Phase 1 was omitted as no observation had a prior probability of being phase 1

To highlight differences in accuracy, we investigated the tendency to under- or over-estimate, by gender, according to the specimen age. A depiction of each method’s misclassification tendency, distinct by gender, is available in Fig. 6. The method showed a tendency to underestimate both sexes.

Fig. 6: Kernel Density Estimation (KDE) plots illustrating estimation errors for males (top) and females (bottom). The X-axis represents the actual age of individuals, while the Y-axis reflects the estimation error. Each point corresponds to a single observation, with colors indicating the type of error: blue for underestimation, green for correct classification, and red for overestimation. In the background, the KDE heatmap represents the density of observations. Darker regions indicate a higher concentration of cases, helping to visualize where errors are more frequent. The color scheme (blue for males and red for females) is purely stylistic and does not indicate error magnitude. The position of denser regions along the Y-axis provides insight into error trends: Regions shifting upward indicate grade and tendency toward overestimation; Regions shifting downward suggest grade and tendency toward underestimation; The closer a region is to the center, the more accurate the classification

Relation between score and age, and implementation of sclerosis score

To evaluate the relationship between age and observation on the ribs, for each sex, two linear regression models were tested. The first model was based solely on the CT Iscan phase classification, treating it as an ordinal variable. The second model incorporated both the CT Iscan phase and the degree of sclerosis as independent variables, aiming to assess whether the latter could refine age estimation. Each observation was considered individually.

Males

The tests were based on a total of 296 observations (74 male individuals × 4 observations each). The first model, using only the CT Iscan phase, explained 39% of age variability (R² = 0.39) with a mean squared error (MSE = 119.28 years²). The second model, incorporating the sclerosis score, improved explanatory power (R² = 0.49) and reduced prediction error (MSE = 99.42 years²). However, the 95% confidence interval width increased from 3.43 to 3.78 years, indicating slightly greater variability in individual predictions. The analysis of residuals with the Shapiro-Wilk test indicated slight deviations from normality (W = 0.98). Given the W statistic values very close to 1 the observed deviations are minimal and practically negligible, especially considering the relatively large sample size. Therefore, the assumptions underlying the linear regression model can be regarded as sufficiently satisfied for the purposes of this study.

Table 3 shows the predicted 95% confidence intervals for age estimation in both models and sexes, highlighting the effect of integrating the sclerosis score. The confidence intervals for the CT Iscan Phase model are generally broader, while the CT Iscan Phase + Sclerosis Score model refines the estimates by reducing the interval width for most phases. Figure 7 visually represents these confidence intervals using box plots, illustrating the variability in estimated age ranges across phases and sclerosis scores. As the overall width increases slightly from 3.43 to 3.78 years, suggesting that individual-level variability increases in some phases, this effect is not uniform. In the middle phases, where the model has the highest predictive accuracy, sclerosis refines age estimates. For instance, in Phase 5, the confidence interval shifts from 53 to 55 years in the CT Iscan Phase model to 50–53 years for a sclerosis score of 0 and 57–61 years for a sclerosis score of 1, indicating a more precise classification. In contrast, for older individuals (Phases 6–8), the confidence intervals widen, as seen in Phase 6, where the range extends from 55 to 58 years (sclerosis score 0) to 68–75 years (sclerosis score 2).

Gender | MODEL1:CT Iscan Phase only | CI Lower bound | CI Upper bound | MODEL2:CT Iscan phase + sclerosis score | CI Lower bound | CI Upper Bound
Male | 1 | 32 | 37 | 1 − 0 | 31 | 36
2 | 37 | 42 | 2 − 02 − 1 | 3643 | 4048
3 | 42 | 46 | 3 − 03 − 13 − 2 | 414854 | 445262
4 | 48 | 51 | 4 − 04 − 1 | 4653 | 4857
5 | 53 | 55 | 5 − 05 − 15 − 2 | 505763 | 536170
6 | 58 | 60 | 6 − 06 − 16 − 2 | 556268 | 586575
7 | 62 | 66 | 7 − 07 − 17 − 2 | 596672 | 637079
8 | 66 | 71 | 8 − 08 − 18 − 2 | 637077 | 687584
Female | 1 | 18 | 28 | 1 − 0 | 19 | 28
2 | 28 | 36 | 2 − 0 | 28 | 36
3 | 38 | 44 | 3 − 03 − 1 | 3740 | 4347
4 | 48 | 52 | 4 − 04 − 14 − 2 | 454950 | 515561
5 | 57 | 61 | 5 − 05 − 15 − 2 | 535960 | 606268
6 | 65 | 71 | 6 − 06 − 16 − 2 | 606668 | 687176
7 | 74 | 80 | 7 − 07 − 17 − 2 | 687376 | 788084
8 | 82 | 90 | 8 − 08 − 18 − 2 | 758084 | 878993

Fig. 7: Boxplots representing the 95% confidence intervals (CI) for age estimation. The left plot shows the CI for the model 1, which estimates age using only CT-derived phase classification. The right plot displays the CI for the model 2, which integrates sclerosis scoring to refine age estimation. Each box represents the range between the lower and upper CI bounds, with whiskers extending to the full interval

Additionally, the inclusion of sclerosis modifies the relative positioning of age estimates across phases, leading to overlapping and exceeding effects. In Phase 6, individuals with a sclerosis score of 2 have an estimated age range of 68–75 years, surpassing the 62–66 years observed in Phase 7 with a sclerosis score of 0. Similarly, in Phase 3, the range for a sclerosis score of 2 (54–62 years) exceeds that of Phase 4 with sclerosis 0 (46–48 years). The overlapping and exceeding effects indicate that sclerosis modifies age distribution within phases, shifting estimated ranges beyond those of the subsequent phase with sclerosis 0.

Females

The tests were based on a total of 152 observations (38 female individuals × 4 observations each). The first model, using only the CT Iscan phase, explained 64% of age variability (R² = 0.64) with a mean squared error (MSE = 200.78 years²). The second model, incorporating the sclerosis score, minimally improved explanatory power (R² = 0.65) and reduced prediction error (MSE = 195.51 years²). However, the 95% confidence interval width increased from 6.25 to 7.60 years, indicating slightly greater variability in individual predictions.

The analysis of residuals with the Shapiro-Wilk test indicated slight deviations from normality (W = 0.95). Given the W statistic values close to 1, the observed deviations are minimal and practically negligible, especially considering the relatively large sample size. Therefore, the assumptions underlying the linear regression model can be regarded as sufficiently satisfied for the purposes of this study.

Table 3 presents the 95% confidence intervals for age estimation in both models, illustrating, for females, the effect of integrating the sclerosis score. Compared to males, the impact of sclerosis follows a more linear pattern, with fewer overlapping and exceeding effects. Figure 7 visually represents these confidence intervals using box plots, showing the distribution of estimated age ranges across phases and sclerosis scores.

Unlike the male sample, the effect of widening of confidence interval in the second model is more evenly distributed across phases, without strong deviations in specific age groups. While the overall trend of age estimation remains progressive and structured, the introduction of sclerosis still leads to moderate adjustments in estimated age ranges within phases. However, these adjustments do not significantly disrupt the sequential progression of CT Iscan phases. The pattern observed in males, where individuals with high sclerosis in a lower phase could exceed the estimated range of the next phase, is less prominent in females. Instead, sclerosis appears to act as a gradual modifier, refining age estimates without altering the overall phase-based progression.