Supplementary Material for: Fetal Biometry: A Method for Comparing Local Curve Populations with Those from Major Reference Standards

<b><i>Objectives:</i></b> This study aimed to present a statistical method for assessing potential differences between fetal growth standard curves and local curve population. <b><i>Methods:</i></b> This was an observational repeated measures longitudinal study. We used a simulation model to generate random distribution of the international population from the IG-21st for fetal AC using the original equations of means and standard deviations (SD) obtained by the fractional polynomial method. A general linear model (GLM) allowed us to calculate new equations originating from simulated intergrowth-21st data (SIM_IG21st) and to compare them, by visual inspection of the estimated coefficients and their 95% CI, with the original published. We used further GLMs for evaluating the goodness of fitting of our local curve and comparing the relative equations of means and SD with those of SIM_IG21st. Finally, the impact of percentile differences between the 2 curves was quantified. <b><i>Results:</i></b> SIM_IG21st data yielded very similar coefficients than those of IG-21st reference to such an extent that means and SD and percentiles of interest were identical to the original. The comparison between SIM_IG21st curve and local curves showed a nonsignificant intercept and a slight difference of the 2 slopes (GA and GA³) for the equations of the mean. As a result, the local curve resulted in greater AC values. A difference in the intercept but not in the slopes (GA², GA³, and GA³ * lnGA) was instead reported for the equations of the SD. In the percentile comparison, the local curve resulted in an overestimation of the 3rd and the 10th percentile that corresponded to the 4th and 12th percentiles of SIM_IG21st, respectively. <b><i>Conclusion:</i></b> This statistical method allows sonographers to assess potential differences between standard curves and local curve population, enabling a more proper identification of abnormal growth trajectories.

<b><i>研究目标:</i></b> 本研究旨在提出一种统计学方法，用于评估胎儿生长标准曲线与本地人群曲线之间的潜在差异。<b><i>研究方法:</i></b> 本研究为观察性重复测量纵向研究。我们采用模拟模型，结合通过分数多项式法获得的均值与标准差（standard deviation, SD）原始公式，生成源自IG-21st标准的国际胎儿腹围（Abdominal Circumference, AC）人群随机分布数据。借助广义线性模型（General Linear Model, GLM），我们从模拟的IG-21st数据集（SIM_IG21st）中推导得到全新公式，并通过可视化检视估计系数及其95%置信区间（95% Confidence Interval, 95% CI），将其与原始已发表公式进行对比。此外，我们还使用广义线性模型评估本地曲线的拟合优度，并将均值与标准差的对应公式与SIM_IG21st的相关公式进行比较。最后，量化两条曲线间百分位数差异所产生的影响。<b><i>研究结果:</i></b> SIM_IG21st数据集得到的系数与IG-21st参考标准的系数极为相似，以至于目标均值、标准差及百分位数与原始数据完全一致。SIM_IG21st曲线与本地曲线的对比结果显示：均值公式的截距无统计学显著性差异，但两条斜率（胎龄（Gestational Age, GA）与胎龄三次方GA³）存在细微差异。据此，本地曲线计算得到的腹围数值更高。研究结果显示，标准差的计算公式存在截距差异，但斜率（胎龄平方GA²、胎龄三次方GA³及胎龄三次方与胎龄自然对数的乘积GA³×lnGA）无显著差异。在百分位数对比中，本地曲线对第3百分位数及第10百分位数存在高估，其分别对应SIM_IG21st的第4百分位数与第12百分位数。<b><i>研究结论:</i></b> 本研究所提出的统计学方法可帮助超声医师评估标准曲线与本地人群曲线之间的潜在差异，从而能够更准确地识别异常生长轨迹。