A total of 126 STORK and 14,817 STARR babies were initially considered in this analysis (Supplemental Fig. 1). After excluding values per protocol, 97 (77.0%) STORK and 14,695 (99.2%) STARR babies had sufficient measurements to be included in the weight analyses. For height, examined only in STARR, 11,655 (78.7%) babies had sufficient measurements to be included in the height analyses.
The sex of infants was similar in both STORK and STARR. STORK babies were slightly heavier than STARR babies both at birth (p = 0.002) and at approximately 36 months (p = 0.05) (Table 1). For the 97 STORK babies, weight values were spread fairly consistently across the 36 months due to the study design; no height measures were obtained. For the 14,695 STARR babies, the number of weight and height timepoints per subject was quite variable (range: weight: 5–15; height: 5–13).
Table 1
Characteristics of STORK and STARR babies
| | STORK | STARR |
| | N | Statistic a | N | Statistic |
Babies in weight analyses | | 97 | | 14,695 | |
Babies in height analyses | | NA | | 11,655 | |
Female | | 49 | 50.5 | 7162 | 48.7 |
Birthweight (kg) | | 96 | 3.42 (0.46) | 14,695 | 3.28 (0.50) |
Birth length (cm) | | NA b | | 11,655 | 50.23 (2.58) |
Weight at ~ 36 months c (kg) | | 35 | 15.48 (2.76) | 3,117 | 14.72 (1.84) |
Height at ~ 36 months (cm) | | NA | | 2,514 | 95.88 (3.79) |
Weight measures overall | | 796 | 9 (3) [5–10] | 133,732 | 9 (4) [5–14] |
Weight measures for ages (months) | 0–12 13–24 25–36 | 280 267 249 | 3 (1) [3–5] 3 (1) [1–4] 3 (1) [0–5] | 86,705 31,809 15,218 | 6 (0) [4–8] 3 (2) [0–4] 1 (2) [0–4] |
Height measures overall | | NA | | 107,586 | 10 (3) [5–13] |
Height measures for ages (months): | 0–12 13–24 25–36 | NA | | 68,927 26,221 12,438 | 6 (1) [3–8] 3 (1) [0–4] 1 (2) [0–3] |
Ethnicity | Hispanic/Latino Non-Hispanic Unspecified | | | 1,026 8,418 5,373 | 6.9 56.8 36.3 |
Race group | Asian Black Native American Pacific Islander White Other Unspecified | | | 3,220 255 18 42 3,911 1,858 5,513 | 21.7 1.7 < 1 < 1 26.4 12.5 37.2 |
a Percent or mean (standard deviation [sd]) or median (interquartile range [IQR]) [range]. |
b NA: not applicable in STORK (neither birth length nor height values were ascertained at household visits). |
c +/- 2 months. |
Weight models
The Michaelis-Menten model was successfully fitted to 94 STORK babies (95.9%) and 14,596 STARR babies (99.3%). Distributions of the model parameters a1 and b1 were right-skewed; the c1 parameter followed a normal distribution and approximated birthweight (Spearman Rho correlation: 0.79, 0.84 and 0.87 for STORK boys, STORK girls and both STARR boys and girls, respectively; difference between median c1 values and median birth weight: 0.27, 0.03, 0.05 and 0.04 kg in STORK boys, STORK girls, STARR boys and STARR girls, respectively) (Supplemental Fig. 2, Supplemental Table 1).
Visual inspection of plots of infant weights over time, along with the fitted curves indicated a good fit with this Michaelis-Menten model for both STORK and STARR babies (Fig. 1, A-D). Accuracies of model fit were high, as measured by low RMSE, particularly in STARR babies (median RMSE, for boys and girls: in STORK: 0.47 and 0.43 kg; in STARR: 0.22 and 0.20 kg; 90% RMSE, for boys and girls, in STORK: 0.65 and 0.74 kg, in STARR: 0.43 and 0.39 kg) (Fig. 2A and B, Supplemental Table 1). Overall, a total of only 11 (0.08%) babies had RMSE values above 1.0 kg (Supplemental Fig. 3); whether these outliers reflect errors in weight value data entry or measurement, or weight loss and gain that deviates from a more typical growth curve, is unknown. The different ethnic and racial groups had similar RMSE values (Table 1, Supplemental Fig. 4). The effect of age on RMSE over time showed a slight increase across three years (Supplemental Fig. 5).
The model failed to fit 4.1% of STORK babies and 0.7% of STARR babies, generally because a1 and b1 parameters increased without bound; these babies tended to show linear, rather than non-linear growth (Supplemental Fig. 6).
Height models
The model parameters a1 values were slightly left-skewed while the b1 values were right-skewed, with both showing a small number of large outliers; the c1 parameter again had a normal distribution and was correlated with birth length (Spearman Rho: 0.92 and 0.91 for boys and girls, respectively; difference between mean c1 value and birth length: 0.3 cm and 0.5 cm for boys and girls, respectively) (Supplemental Table 1, Supplemental Fig. 7).
Visual inspection of the fitted data for height indicated excellent fit (Fig. 1, E-F) and RMSE values were low for these models, with both median and 90% values under 1 cm (median: 0.93 and 0.91 for boys and girls, respectively; <90%: 0.998 for boys and girls). A total of only five subjects (0.043%) had RMSE over 3 cm (Supplemental Fig. 8). Again, RMSE values were similar across racial and ethnic groups (Supplemental Fig. 4). The effect of age on RMSE over time again showed a slight increase across three years (Supplemental Fig. 5).
Very few subjects (0.25%) failed to fit the model as a1 and b1 parameters increased without bound; these babies showed either very linear growth, or had very large height values that were likely data entry errors rather than aberrant growth (e.g. substantial loss of height) (Supplemental Fig. 9).
Imputation Tests
In testing critical time points for weight or height imputation, the removal of visit 1 (birth weight or length) increased RMSE more than the removal of any other visit (Supplemental Table 2). When imputing values in the first year alone (visits 1–7), visit 7 at approximately 1 year of age had the second largest impact on model fit. Considering years 1–3, the removal of the final data point alone, visit 12, had a much more modest impact on RMSE, as did the removal of other visits besides visit 1. Most combinations of visits could be dropped, with exceptions: removal of visit 1 in combination with other visits, particularly visits during year 1, led to a sizable increase in RMSE, as did removal of consecutive visits at the final time points (visits 5, 6, and 7 for the year 1 subset; visits 10, 11, and 12 for the years 1–3 subset). The RMSE could be rescued to some degree for missing visit 1 birth data, but not missing final time point data (e.g. visit 7 for year 1 data), by increasing the initial a1 and b1 parameters to higher values (e.g. a1 = 15, b1 = 500).
Prediction
For weight prediction modeling, a total of 4,829 STARR infants (48.8% female) had at least five time points in Y1 and two in each of Y2 and Y3; of these, 1.8% were dropped due to the inability of the model to fit their growth values (Supplemental Fig. 1). RMSE values were low for the full model (median RMSE: 0.33 and 0.30 kg for STARR boys and girls; Supplemental Table 3). The median RMSE increased to 1.13 and 1.08 kg (boys and girls) when the model predicted Y3 data points using Y1 + Y2 data (Supplemental Fig. 10). Median RMSE increased further to 1.37 and 1.34 kg (boys and girls respectively) when only Y1 data was used to predict fitted data for Y2-Y3.
As with weight data, we tested the Michaelis-Menten equation to predict future heights using models created from Y1 or Y1 + Y2 data (Supplemental Fig. 11). A total of 3,963 STARR infants (49.3% female) had sufficient time points. A small number (0.58%) failed to fit a growth model. Median RMSE values were slightly over 1 cm for complete data fitting (1.14 cm for boys, 1.08 cm for girls) (Supplemental Table 4). Prediction of Y3 data from Y1 + Y2 yielded a RMSE of 2.91 and 2.68 cm for boys and girls, respectively. Median RMSE values for Y2 + Y3 data predicted from Y1 alone were 5.38 cm and 5.63 cm for boys and girls, respectively.