The analysis of categorized algorithms was made by assessing the mean absolute percentage error and the fraction of estimated birth weight within ±10% and ±15% of the actual birth weight. The lowest and the highest mean absolute percentage errors were respectively produced by the head-abdomen-femur (HAF) and femur (F) groups of equations, with mean±standard error of the mean of 8.09±0.32% and 9.85±0.38% (Fig. 3A). Algorithms that rely on femur length only provided the poorest results, with less than 60% of predictions within the 10% of difference (Fig. 3B). No significant differences were found for accurate predictions (within 10% of mean absolute error) between the group of women who underwent ultrasonography with intact and ruptured membranes or between cephalic and noncephalic presentations in each group of categorized algorithms (data not shown). The performance of all groups was very high for actual birth weights between 3,000 and 3,500 g, with about 80% of predictions within 10% of error (range 73.8–82.5%, Fig. 4). Similar accuracy was found for all groups but the femur (F) group, which demonstrated a very disappointing ability to predict birth weight for infants weighing less than 3,000 g and more than 4,000 g. It is interesting that the abdomen-femur (AF) group showed the highest accuracy for newborns who had a birth weight of more than 3,500 g (P<.01). All five groups showed a parabolic trend in six birth weight groups (Fig. 5), with a tendency to underestimate large fetuses with about 11% of mean error and only 40% of estimates with ±10% of error (data not shown). The mean discrepancy was definitively acceptable (within 150 g) up to 4,000 g, although the standard deviation (SD) of about 300 g has also to be considered. In fact, the analysis of standard deviations (using Bartlett’s test) suggested that the differences among SDs were extremely significant (P<.001), with higher variations as the actual birth weight increased (from 146.6 g for actual birth weight less than 2,000 g to 359.4 g for actual birth weight more than 4,000 g). This can be explained by technical difficulties in obtaining reproducible and accurate biometric parameters for large fetuses (observational error).
This study shows that most formulas for the estimated fetal weight give an acceptable estimate of birth weight, although the accuracy of the different methods of predicting fetal weight depends on the range of birth weights under study. All formulas showed the same tendency to underestimate large fetuses and overestimate the small ones, regardless of the ultrasonographic parameters they rely on. Remarkably, the formulas of Ferrero et al,11 Hadlock et al,12 and Warsof et al13 that are based on abdominal circumference and femur length (identified in the article as the AF group) provided the best predictions of birth weights over 3,500 g. It is intuitive that body weight derives from height and fatness, which can be indirectly measured by femur length and abdominal circumference, respectively. Besides, other formulas that also incorporate also head measurements (HAF group) had a lower percentage of good predictions in the same intervals of birth weight, although they add another biometric parameter to the formula. This confirms that, at least in these cases, another variable (head) is poorly informative. This can be explained by the fact that the presence of multiple variables in a formula increases the risk of multi-collinearity and enhances the internal error of each measurement. Besides, large fetuses occur in pregnancies at term when the head is deep into the pelvis and its measurements cannot be taken properly due to fetal head engagement.
The deviation of estimated birth weight from actual birth weight can roughly be estimated as half due to the measurement error and half arising from the intrinsic properties of the formula.36 The first is compromised by significant intra- and interobserver variability of ultrasonographic measurements.37,38 As for the analysis of algorithms, an observation has to be made. According to the Bayes Theorem, when different parameters predict the same event (ie, birth weight), the consideration of all of them improves the accuracy.39 This is true only for independent variables because they add new information to the algorithm, whereas mutual dependency between variables enhances the internal error of each measurement (multi-collinearity). Formulas for estimated birth weight combining more than two parameters are deemed more reliable and accurate than those with one or two measures,40 although a hidden linear correlation (interdependency) between biometric parameters is at least intuitive. Therefore, the error due to the equations is likely to be the largest source of disagreement between predictions and actual birth weights.
The accuracy of predicting birth weight by different formulas has been studied extensively under different points of view. The key weaknesses of all studies were the lack of details on ultrasonographers’ experience, small study populations, need for mathematical adjustments for scan-to-delivery interval, and the study design (most of them are retrospective). The experience of the examiners plays a leading role in the accuracy of predictions because measurement of suboptimal images is a factor of interobserver variability and a major bias for the estimation of fetal weight.38,41 It is important to highlight that all mathematical modifications of biometrical parameters add further biases to intra- and interobserver variability of ultrasound measurements, making the estimated fetal weight mathematically less reliable.
Our study was to assess the reliability of algorithms for estimated birth weight according to the variables they rely on. We tested 35 formulas, although only a few of them are widely used in clinical practice over the different centers. The aim of this study was not to test the ability of each formula to accurately predict birth weight but to assess the performance of different classes of algorithms over different intervals of birth weight. The strength of our study is that 1) all scans were made by experienced physicians; 2) only fetuses born within 48 hours of the ultrasonography were considered for the study; 3) the actual number of observations entered into the analysis was 15,435 because 35 estimates of birth weight were calculated for all fetuses (n=441); 4) the prospective design allowed us to use estimated birth weight instead of actual birth weight as reference (independent variable) to assess the accuracy of the studied formulas because actual birth weight is clinically less useful than the ultrasonographic estimation in that the birth weight is unknown until after birth; 5) each class of algorithms included at least two formulas. Indeed, this study presents some limitations, such as a whole white population of women with singleton pregnancies and the relatively small number of newborns weighing 2,000 g or less and 4,000 g or more (n=55). Nevertheless, the primary purpose of this study was not to evaluate the ability of formulas for the estimated birth weight to correctly identify small or large infants.
The limited accuracy of ultrasonographic estimated birth weight at extremes of birth weight has been recognized for a long time. Our findings seem to suggest a specific approach for future research that is to focus on measurements of the fetal soft mass, mainly for macrosomic fetuses. In fact, if formulas based on femur length and abdominal circumference perform best in fetuses weighing more than 3,500 g, a combination of ultrasonographic assessment of fat and lean mass and the estimation of fetal height may improve the accuracy of the estimated birth weight. A similar approach was proposed by using 3D ultrasonography to derive fractional arm and thigh volumes as fetal soft tissue parameters for assessment of growth and weight estimation.42,43
Clinically, our findings provide evidence that most formulas have good accuracy at predicting birth weight up to 3,500 g, whereas all estimations beyond that weight have to be carefully considered (clinical evaluation) because all algorithms tend to underestimate large fetuses.
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