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Estimation of Birth Weight by Two-Dimensional Ultrasonography: A Critical Appraisal of Its Accuracy

Scioscia, Marco MD; Vimercati, Antonella MD, PhD; Ceci, Oronzo MD; Vicino, Mario MD; Selvaggi, Luigi E. MD

doi: 10.1097/01.AOG.0000296656.81143.e6
Original Research

OBJECTIVE: To assess the accuracy and characterize two-dimensional ultrasonographic formulas for the estimation of birth weight according to the type of fetal biometric parameters these formulas rely on to make fetal weight predictions.

METHODS: A prospective recruitment of 589 pregnant women was carried out for this cross-sectional study. Different biometric parameters were taken ultrasonographically to estimate birth weight using 35 different formulas. Only those patients who delivered within 48 hours were considered for the analysis (n=441). Differences between the estimated and actual birth weight were assessed by percentage error, accuracy in predictions within ±10% and ±15% of error, and use of the Bland-Altman method. All formulas were assessed individually and clustered on the basis of the type of fetal biometric information that they incorporate.

RESULTS: Twenty-nine formulas provided an overall mean absolute percentage error less than or equal to 10%, with overall predictions within ±10% and ±15% of the actual birth weight (69.2% and 86.5%, respectively). Twenty formulas showed a good accuracy (bias 0.50 or less) and low variability (mean standard deviation 1.2). Among the categorized algorithms, formulas based on head-abdomen-femur measurements showed the lowest mean absolute percentage error. Upon stratification for birth weight, the group of formulas that rely on abdomen and femur measurements performed best for fetuses weighing more than 3,500 g (P<.01).

CONCLUSION: Our findings show that most formulas are relatively accurate at predicting birth weight up to 3,500 g, and all algorithms tend to underestimate large fetuses.


Best-performing formulas for ultrasonographic estimation of birth weight in fetuses weighing more than 3,500 g are those based on femur length and abdominal circumference.

From the Department of Gynaecology, Obstetrics and Neonatology, University of Medical Science of Bari, Bari, Italy.

The authors thank Dr. Massimo Lorusso, Obstetrics and Gynecology Fellow, Policlinico Hospital, Bari, for help with data acquisition.

Corresponding author: Dr. Marco Scioscia, Department of Gynaecology, Obstetrics and Neonatology, University of Medical Science of Bari, Policlinico di Bari, Piazza Giulio Cesare 11, 70100 Bari, Italy; e-mail:

Financial Disclosure The authors have no potential conflicts to disclose.

Ultrasonographic assessment of fetal growth to estimate fetal weight is widely used in obstetrics because birth weight represents the most important risk indicator for neonatal and infant mortality and morbidity.1 An accurate estimation of fetal weight is valuable information for planning the mode of delivery and management of labor. Several formulas that have been proposed over the past 30 years use different combinations of standardized fetal biometric parameters, such as biparietal diameter (BPD), head circumference, abdominal circumference, and femur length.2 A few attempts to improve accuracy have been published that combine the above mentioned parameters and nonstandard ultrasonographic measurements (subcutaneous tissue, cheek-to-cheek diameter),3,4 maternal or fetal data such as parental characteristics, fetal gender, gestational age, or fundal height, but these have yielded few improvements.5 The introduction of three-dimensional (3D) ultrasonography has led some authors to propose new formulas that incorporated volumetric data of fetal limbs.6–8 The application of these techniques was generally limited by the excessive time required for making volume measurements (scan and data processing)7 and by the need for access to a 3D machine with specific software. Therefore, such complex formulas (integrated formulas and volumetric assessment) seem poorly suited for everyday clinical practice.

Formulas based on two-dimensional (2D) ultrasonography are certainly the most widely used for the estimation of birth weight, although they are inaccurate at the extremes of fetal weight.9 Besides, improvements in ultrasound technology in the past 10 years have not improved the accuracy of estimating fetal weight.10 This prospective cross-sectional study was to verify the accuracy of various 2D ultrasonographic formulas to predict actual birth weights.

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This was a single-center study based on the prospective recruitment of 589 women with singleton pregnancies likely to give birth within 48 hours. This study was carried out at the University Hospital of Bari with the approval of the local ethics review board. Patients were consecutively selected among those admitted to hospital for initial spontaneous labor, induction of labor (postterm pregnancies, prelabor rupture of the membranes), elective cesarean delivery (maternal request or previous cesarean delivery), or those patients with high-risk pregnancy (diabetes, hypertension, intrauterine growth restriction) who were about to undergo induction of labor or caesarean delivery for fetal or maternal indications. Because the population referred to our ultrasound department is 99% white, we excluded from the study all the other racial and ethnic groups.

Standard biometric parameters (BPD, head circumference, abdominal circumference, and femur length) and additional fetal measurements (head and abdominal areas and abdominal transverse diameter) were taken ultrasonographically by four consultants (first four authors) with extensive experience in obstetric ultrasonography using a 3.5–6 MHz or 3.5–5 MHz convex transducer on Acuson 128/XP (Mountain View, CA) or Aloka ProSound alpha5 (Tokyo, Japan) machines. Only those women who succeeded in delivering within 48 hours after ultrasonography were considered for the analysis. Intra- and interobserver variability were not evaluated because this was beyond the aim of this study. Neonatal birth weights were recorded at delivery.

Thirty-five formulas for the estimated birth weight based on 2D measurements were assessed in this study (Table 1).9,11–31 All formulas targeted to selected groups of fetuses (preterm fetuses, expected low birth weight infants) were not considered in this study because they have the disadvantage of requiring an antenatal subjective evaluation (choosing one or the other formula).

The accuracy of all formulas has been evaluated by using the percentage error method because this is more intuitive for clinicians. This was calculated as the absolute value of the “potential error” of the estimated weight using the following formula expressed in percentage terms (where ABW is actual birth weight and EBW is estimated birth weight): ABW–EBW÷EBW. This method was previously proposed by Edwards et al32 and adopted by Anderson et al,10 who highlighted that ultrasonographic estimation represents the actual relevant information to clinicians for decision making (clinical management), and thus, estimated birth weight, not actual birth weight, was used as the denominator. The absolute value was preferred to the signed mean percentage differences because all formulas tend to over- and underestimate birth weights at the extremes, as demonstrated by Kurmanavicius and coworkers.9 This method provides information about the size of the error (overestimations would compensate for underestimations, making the signed mean error close to zero). All algorithms that showed an overall mean absolute percentage error greater than 10% were not considered for subsequent analyses to ensure homogeneous data.

The general tendency of each formula to over- or underestimate birth weights was assessed by using the Bland-Altman method33 and reported as signed biases (negative values indicate that there was an overall tendency of that algorithm to overestimations). This method assesses the agreement between two measurements (estimated birth weight and actual birth weight), not the strength of a relationship as the correlation coefficient does. The bias (mean difference between the paired measurements) and 95% limits of agreement (the two values within which 95% of the differences between paired measurements will lie) were calculated for all algorithms. To run the limits of agreement analysis (Bland-Altman), a logarithmic transformation of weights was necessary because of the variability in the difference between estimated birth weight and actual birth weight as birth weight increased. The performance of all algorithms was calculated as the ability to successfully predict the actual birth weight within 10% and 15% of absolute error.

Subsequently, a categorization of all algorithms was carried out according to the type of fetal biometric information that they incorporate (H, head; A, abdomen; F, femur), producing an arrangement into five groups as reported in Table 1. All these groups were analyzed as reported above for single algorithms (mean absolute percentage error calculation and predictions within ±10% and ±15% of error).

Because the precision of each formula can vary across the range of birth weights, the consistency of error throughout the weight range was assessed in six birth weight groups subdivided by 500-g intervals. The differences in proportions of birth weights that were predicted accurately within 10% of absolute error were assessed using two methods: 1) graphically, to show the accuracy of all groups within each weight interval, and 2) statistically, using χ2 analyses to quantify the difference of the best-performing group of algorithms for each class of birth weight. Furthermore, signed mean errors expressed in grams were plotted according to algorithm categorization for all subgroups of actual birth weight. Bartlett’s test34 was used to evaluate differences in standard deviations.

A study population of four hundred cases (patients who succeed in delivering within 48 hours) was considered sufficient to draw information after stratification for actual birth weight (six classes, as reported above). The proportion of accurate predictions (within 10% of mean absolute error) was reported to range between 55% and 78% using different algorithms,35 so a study population of 52 cases per group was required to obtain a power of 0.8 and an alpha of 0.05. Assuming that our study population had a Gaussian distribution with a mean birth weight of 3,000 g, about 68% of values would have been within one standard deviation of the mean, with the need for 411 cases to ensure sufficient numbers in the tails of the distribution (less than 2,000 g and more than 4,000 g). According to findings of a previous study of ours (which is under revision for publication at present), about 70% of all women deemed likely to delivery within 48 hours actually succeed in that. Therefore, 580 women were required to obtain 406 cases. Over an 18-month period, a total of 589 pregnant women consented to participate in this study, which was approved by the University Hospital of Bari Ethics Review Board. Data were analyzed with the GraphPad Prism 4.00 for Windows (GraphPad Software, San Diego, CA), with significance set at P<.05.

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Delivery within 48 hours was observed in 441 cases (74.9%) that were included in the analysis (Table 2). The birth weights ranged from 740 g to 4550 g, with 58.3% of cases (257 of 441) within the 3,000–4,000 g interval.

Mean absolute percentage errors of all 35 algorithms were shown in Figure 1. Six of 35 formulas failed to provide accurate estimates of birth weight (that was defined as 10% or less of mean absolute error) and were excluded form subsequent analyses. The percentage of birth weight predictions within ±10% and ±15% of actual birth weight of the studied 29 formulas were, on average, 69.2% and 86.5%, respectively (Fig. 2).

Table 3 shows the agreement between the estimated birth weight and the actual birth weight assessed by the limits of agreement method. Seven algorithms tended to overestimate birth weight (negative values). Twenty-formulas had a bias 0.50 or less and low variability (mean standard deviation of the difference between estimated and actual weight of 1.2).

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).

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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.

Kurmanavicius and coworkers9 assessed the accuracy of estimated birth weight in different birth weight intervals using five formulas on retrospective data. Moreover, ultrasound examinations were performed within 1 week before delivery by more than 90 ultrasonographers without details on their experience. Dudley2 carried out a systematic review of a number of studies on the ultrasound-estimated fetal weight. Comparison of the performance of the algorithms was made by using the signed mean error method, which as reported above, fails to provide the actual size of the error because overestimations compensate underestimations. This makes the evaluation subject to the study population (birth weight range), and the cross-assessment of algorithms are less consistent between studies. Only two studies assessed formulas clustered on the basis of the parameters they incorporate. Mirghani and coworkers40 reported a neat prospective study on term fetuses comparing eight formulas. The weak point of that study was that three out of five classes of algorithms (namely, abdominal circumference only, femur length only, and abdominal circumference-femur length) included only one formula each, thus allowing the evaluation of the formula considered instead of a “class of formulas.” Nahum and coworkers35 investigated retrospectively the accuracy of 25 formulas on 82 term fetuses. The ultrasound examination was performed within 3 weeks of delivery, with subsequent adjustment for 1) ethnic group, 2) maternal hypertension, 3) cigarette smoking, 4) fetal gender, and 5) days elapsed between the scan and the delivery. Furthermore, no information was provided about the experience of ultrasonographers in both studies.

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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Figure. No caption available.

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© 2008 by The American College of Obstetricians and Gynecologists. Published by Wolters Kluwer Health, Inc. All rights reserved.