Enhancing a Somatic Maturity Prediction Model

We evaluated potential overfitting using the original Pediatric Bone Mineral Accrual Study (PBMAS; 79 boys and 72 girls; 7.5-17.5 yr). We assessed change in R and standard error of the estimate (SEE) with the addition of predictor variables. We determined the effect of within-subject correlation using cluster-robust variance and fivefold random splitting followed by forward-stepwise regression. We used dominant predictors from these splits to assess predictive abilities of various models. We calibrated using participants from the Healthy Bones Study III (HBS-III; 42 boys and 39 girls; 8.9-18.9 yr) and Harpenden Growth Study (HGS; 38 boys and 32 girls; 6.5-19.1 yr).

Change in R and SEE was negligible when later predictors were added during step-by-step refitting of the original equations, suggesting overfitting. After redevelopment, new models included age × sitting height for boys (R, 0.91; SEE, 0.51) and age × height for girls (R, 0.90; SEE, 0.52). These models calibrated well in external samples; HBS boys: b0, 0.04 (0.05); b1, 0.98 (0.03); RMSE, 0.89; HBS girls: b0, 0.35 (0.04); b1, 1.01 (0.02); RMSE, 0.65; HGS boys: b0, -0.20 (0.02); b1, 1.02 (0.01); RMSE, 0.85; HGS girls: b0, -0.02 (0.03); b1, 0.97 (0.02); RMSE, 0.70; where b0 equals calibration intercept (standard error (SE)) and b1 equals calibration slope (SE), and RMSE equals root mean squared error (of prediction). We subsequently developed an age × height alternate for boys, allowing for predictions without sitting height.