Infant bone age estimation based on fibular shaft length: model development and clinical validation

Abstract

Background

Bone age in infants (<1 year old) is generally estimated using hand/wrist or knee radiographs, or by counting ossification centers. The accuracy and reproducibility of these techniques are largely unknown.

Objective

To develop and validate an infant bone age estimation technique using fibular shaft length and compare it to conventional methods.

Materials and methods

We retrospectively reviewed negative skeletal surveys of 247 term-born low-risk-of-abuse infants (no persistent child protection team concerns) from July 2005 to February 2013, and randomized them into two datasets: (1) model development (n = 123) and (2) model testing (n = 124). Three pediatric radiologists measured all fibular shaft lengths. An ordinary linear regression model was fitted to dataset 1, and the model was evaluated using dataset 2. Readers also estimated infant bone ages in dataset 2 using (1) the hemiskeleton method of Sontag, (2) the hemiskeleton method of Elgenmark, (3) the hand/wrist atlas of Greulich and Pyle, and (4) the knee atlas of Pyle and Hoerr. For validation, we selected lower-extremity radiographs of 114 normal infants with no suspicion of abuse. Readers measured the fibulas and also estimated bone ages using the knee atlas. Bone age estimates from the proposed method were compared to the other methods.

Results

The proposed method outperformed all other methods in accuracy and reproducibility. Its accuracy was similar for the testing and validating datasets, with root-mean-square error of 36 days and 37 days; mean absolute error of 28 days and 31 days; and error variability of 22 days and 20 days, respectively.

Conclusion

This study provides strong support for an infant bone age estimation technique based on fibular shaft length as a more accurate alternative to conventional methods.

Appendix

Distribution of error estimates

The histograms of the estimated absolute errors from the knee and proposed fibular shaft length methods (with and without discretization) show the non-normal distribution of the data (Fig. 12), thus leading to the use of the non-parametric test for comparison.

Fig. 12

Histograms of the distribution of the absolute errors. The distribution of the absolute errors for the fibular shaft length-based estimates without discretization (a) and following discretization (b), in comparison to the distribution of the absolute errors for the knee method-based estimates (c)

Discretization of fibular shaft length method for fair comparison to the hand/wrist method

This method discretizes bone age at 0 months, 3 months, 6 months, 9 months and 12 months, with four intervals between these five ages. For each reader’s fibular shaft length-based estimates, a histogram was computed with four equally spaced bins (five bin edges). The median (across readers) center for each bin was used for the discretization. If an estimate was lower than the first bin center, bone age was set to 0. If it was between the first and second centers, second and third, third and fourth, or greater than the fourth center, it was set to 90 days, 180 days, 270 days and 360 days, respectively. The discretization was done separately for each reader as well as for the reader-averaged data. In the first case, the estimated histogram bin centers were 26.6 days, 111.4 days, 195.8 days and 280.2 days. Median bin width was 82 days. For the reader-averaged data, the histogram bin centers were at 41.2 days, 123.6 days, 206.1 days and 288.5 days.

Discretization of fibular shaft length method for comparison to the knee method

This method discretizes ages in the first 14–15 months of age unevenly at 0.03, 0.23, 0.5, 2.2, 5, 7.5, 11 and 15 months for girls, and 0.03, 0.33, 1, 3, 6, 9 and 14 months for boys.

Skeletal survey testing dataset

The minimum chronological age in this dataset was 5 days, which falls in the interval 0.03–0.23 month for girls and the interval 0.03–0.33 months for boys; and maximum chronological age was 364 days, which falls in the interval 11–15 months for girls and the interval 9–14 months for boys. Thus the 15-month and 14-month age points were included. A discretization of seven intervals for eight age points was selected for girls, six intervals for seven age points for boys. Bin edges were (in days) 0.0, 6.0, 14.0, 65.1, 149.1, 224.1, 329.1 and 449.1 days for girls; and 0.0, 9.0, 29.1, 89.1, 179.1, 269.1 and 419.1 days for boys. Corresponding bin centers were at 3.0, 10.1, 39.6, 107.1, 186.6, 276.6 and 389.1 days for girls, and 4.5, 19.1, 59.1, 134.1, 224.1 and 344.1 days for boys.

Normal infant validation dataset

The minimum chronological age in this dataset was 17 days, which falls in the interval 0.5–2.2 months for girls and the interval 0.33–1 month for boys; and maximum chronological age was 364 days, which falls in the interval 11–15 months for girls and the interval 9–14 months for boys. Thus the 15-month and 14-month age points were included. A discretization of five intervals for six age points was selected for girls, five intervals for six age points for boys. Because the scale in this method uses unequal intervals, estimated ages were also discretized using unequal intervals. For each reader, the ranges of model-based ages were used to estimate six edges of five bins for girls and boys, respectively. The median (over readers) edges were selected for the discretization. Resulting bin edges were (in days) 27.1, 78.1, 162.1, 237.1, 342.1 and 462.1 days for girls; and 27.2, 47.3, 107.3, 197.3, 287.3 and 437.3 days for boys. Corresponding bin centers were at 52.6, 120.1, 199.6, 289.6 and 402.1 days for girls; and 37.3, 77.3, 152.3, 242.3 and 362.3 days for boys.