Accuracy of sonographic fetal weight estimation: a matter of presentation

Authors

  • N. Melamed,

    Corresponding author
    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
    • Department of Obstetrics and Gynecology, Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva 49100, Israel.
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  • A. Ben-Haroush,

    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
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  • I. Meizner,

    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
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  • R. Mashiach,

    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
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  • Y. Yogev,

    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
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  • J. Pardo

    1. Helen Schneider Hospital for Women, Rabin Medical Center, Petah Tiqva, and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
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Abstract

Objectives

To assess the accuracy of sonographic weight estimation for fetuses in breech presentation, and to determine whether certain sonographic models perform better than others in cases of breech presentation.

Methods

This was a retrospective cohort study of all sonographic weight estimations of fetuses in breech presentation performed within 3 days prior to delivery (n = 165). The accuracy of weight estimation was evaluated using eight sonographic models and was compared with a control group of fetuses in vertex presentation matched to the study group by birth weight and fetal gender (n = 165).

Results

After exclusion of a model based on femur diaphysis length alone, which was found to be highly inaccurate, the systematic error for fetuses in breech presentation was smaller than that observed for fetuses in vertex presentation (mean of all models − 0.14% vs. 2.0%, P = 0.01). The random error was higher in cases of breech presentation (9.4–13.2% vs. 7.5–8.9%, P < 0.05), and was lower for models that are based on three to four biometric indices (9.4–9.5%) compared with models that incorporate one to two biometric indices (10.8–13.6%, P < 0.05). Overall, the higher random error outweighed the decrease in the systematic error, as reflected by the lower fraction of weight estimations within 10% of birth weight among fetuses in breech presentation. Models based on three to four biometric indices were more accurate in detecting the weight thresholds beyond which a trial of vaginal delivery is usually not recommended.

Conclusion

Sonographic weight estimation appears to be less accurate for fetuses in breech presentation, principally because of a larger random error. The use of sonographic models that are based on three to four biometric indices, training aimed at improving measurement in breech fetuses and the development of sonographic models derived from fetuses in breech presentation, may improve the accuracy of weight estimation in these cases. Copyright © 2011 ISUOG. Published by John Wiley & Sons, Ltd.

Introduction

Accurate estimation of fetal weight has an important role in routine antenatal care and in the detection of fetal growth abnormalities1.

For fetuses in the breech presentation, the accuracy of fetal weight estimation gains even further importance as the criteria for a trial of vaginal breech delivery include an estimated fetal weight (EFW) of more than 2000–2500 g and less than 3800–4000 g2–5. These criteria are based on the assumption that the accuracy of weight estimation in cases of breech presentation is similar to that of fetuses in vertex presentation2. However, considering the greater tendency for dolichocephaly and the different orientation of fetal body parts in breech presentation, it may well be that the accuracy of fetal weight estimation and the performance of common sonographic models for weight estimation will differ in cases of breech presentation compared with vertex presentation6, 7.

Surprisingly, data regarding the accuracy of sonographic weight estimation, as well as the optimal sonographic model in cases of breech presentation, are scarce8–10. In fact, in most of the large studies that investigated the accuracy of sonographic fetal weight estimation, cases with non-vertex presentation were excluded6, 7.

The aims of the current study were to assess the accuracy of sonographic fetal weight estimation for fetuses in breech presentation and to compare it with that of fetuses in vertex presentation, and to determine whether certain sonographic models perform better than others in cases of breech presentation.

Methods

Data collection

A retrospective cohort study design was used. Data were collected from a comprehensive database of sonographic examinations at a single tertiary center. Routine sonographic evaluations included fetal presentation and the standard fetal biometry measurements (abdominal circumference (AC), femur diaphysis length (FL), biparietal diameter (BPD) and head circumference (HC)), and the findings were saved directly in the database. Antenatal data, gestational age at delivery, fetal sex and actual birth weights were obtained from the hospital's perinatal database.

Study population

The database was searched for all sonographic fetal weight estimations performed within 3 days prior to delivery between 2002 and 2008. Fetuses in the breech presentation constituted the study group (n = 165), while those in the vertex presentation served as controls. Because group size can affect the random error of weight estimation (see the definitions below), the size of the vertex group was set to be equal to that of the study breech group (n = 165), and was composed of the fetuses in vertex presentation (evaluated within 3 days prior to delivery) that immediately followed each of the fetuses in the breech group in the database, matched by birth weight (within ± 50 g) and fetal gender.

Only liveborn singleton pregnancies were included in the study. The following exclusion criteria were applied: birth weight < 500 g, gestational age < 24 weeks, the presence of fetal malformations or hydrops, pregnancies complicated by gestational or pregestational diabetes, women in active labor or with ruptured membranes and cases in which not all four biometric indices were recorded. In addition, because of the small number of fetuses in transverse or oblique lie (n = 23), these cases were not included in the study.

Definitions

Gestational age at the time of examination was recorded in the database along with the details of the sonographic examination and was calculated from the date of the last menstrual period (LMP). When first-trimester ultrasound results were available, the LMP was corrected based on the crown–rump length (CRL) when the discrepancy between the calculated LMP (based on the Hadlock's CRL reference tables11) and the reported LMP exceeded 7 days, according to the recommendations of the American College of Obstetricians and Gynecologists (ACOG)12. Gestational age at the time of examination was further verified by comparing the interval (in days) between the ultrasound-examination date and the delivery date with the interval between gestational age at the time of examination and gestational age at delivery (the latter was available from the perinatal database). As these intervals are expected to be identical (considering that the gestational age in both cases should have been calculated using the same LMP), cases in which the difference between these intervals was greater than 1 day were excluded.

All sonographic fetal weight estimations were performed in our ultrasound unit. Weight estimations were performed by physicians specialized in ultrasonography or by experienced ultrasound technicians. In the latter case, the examination was reviewed by a specialized physician.

The BPD was measured from the proximal echo of the fetal skull to the proximal edge of the deep border (outer–inner) at the level of the cavum septi pellucidi. The HC was measured as an ellipse around the perimeter of the fetal skull13. The AC was measured in the transverse plane of the fetal abdomen at the level of the umbilical vein in the anterior third and with the stomach bubble in the same plane; measurements were taken around the perimeter14. The FL was measured in a view where the full femoral diaphysis was seen and was taken from one end of the diaphysis to the other, not including the distal femoral epiphysis15. The cephalic index was calculated as the ratio between the BPD and the occipitofrontal diameter (OFD)16.

Birth weight percentiles were determined using the local birth weight curves17.

Sonographic models

In order to evaluate the possible contribution of each of the various biometric indices (i.e. AC, FL, BPD and HC) to the presentation-related differences in the accuracy of sonographic weight estimation, we calculated the EFW using eight common sonographic models that are based on different combinations of fetal biometric indices (Table 1). These specific models were chosen as they are internationally accepted, are widely used and are incorporated in many ultrasound machines. In addition, we chose to use models that were derived from the same population in order to avoid the introduction of differences that are related to the differences in the populations from which the models were generated, thereby isolating the factor of interest (i.e. the combination of biometric indices included in the model).

Table 1. Models used for sonographic fetal weight estimation
ModelReferenceBiometric measuresEquation
  1. Weight is expressed in g and biometric indices in cm, except for Model 1 (Warsof), in which weight is expressed in kg and FL is expressed in mm. AC, abdominal circumference; BPD, biparietal diameter; BW, birth weight; EFW, estimated fetal weight; FL, femur diaphysis length; HC, head circumference.

1Warsof et al. (1986)21FLLn BW = 4.6914 + 0.00151(FL)2− 0.0000119(FL)3
2Hadlock et al. (1984)20ACLn BW = 2.695 + 0.253(AC) − 0.00275(AC)2
3Hadlock et al. (1985)19AC and FLLog10 EFW = 1.304 + 0.05281(AC) + 0.1938(FL) − 0.004(AC)(FL)
4Hadlock et al. (1984)20AC and BPDLog10 EFW = 1.1134 + 0.05845(AC) − 0.000604(AC)2− 0.007365(BPD)2 + 0.000595(BPD)(AC) + 0.1694(BPD)
5Hadlock et al. (1984)20AC and HCLog10 EFW = 1.182 + 0.0273(HC) + 0.07057(AC) − 0.00063(AC)2− 0.0002184(HC)(AC)
6Hadlock et al. (1985)19AC, FL and BPDLog10 EFW = 1.335 − 0.0034(AC)(FL) + 0.0316(BPD) + 0.0457(AC) + 0.1623(FL)
7Hadlock et al. (1985)19AC, FL and HCLog10 EFW = 1.326 − 0.00326(AC)(FL) + 0.0107(HC) + 0.0438(AC) + 0.158(FL)
8Hadlock et al. (1985)19AC, FL, BPD and HCLog10 EFW = 1.3596 + 0.0064(HC) + 0.0424(AC) + 0.174(FL) + 0.00061(BPD)(AC) − 0.00386(AC)(FL)

Measures of accuracy

The accuracy of each of the eight models for fetuses in the breech and vertex presentations was evaluated using the following measures of accuracy: (a) systematic error (mean of (EFW − BW)/BW × 100), which reflects the systematic deviation of a model from the actual birth weight, expressed as a percentage of the actual birth weight; (b) random error (SD of the systematic error × 100)—a measure of precision (rather than accuracy) that reflects the random (or non-systematic) component of the prediction error; and (c) the fraction of estimates within 10% of the actual birth weight.

In addition, in order to evaluate the accuracy of weight estimation for fetuses in the breech presentation from a more practical perspective, we analyzed the predictive accuracy of the eight models for the detection of the weight thresholds beyond which a trial of vaginal delivery is usually not recommended5. For the purpose of the current study, the thresholds of < 2500 and > 3800 g were chosen, and the predictive accuracy for the detection of these thresholds was determined using the following measures: (a) sensitivity, (b) specificity, (c) positive predictive value (PPV), (d) negative predictive value (NPV), (e) overall accuracy (defined as (true negative and true positive cases)/(all cases)), and (f) area under the receiver–operating characteristics (ROC) curve (AUC).

Statistical analysis

Data analysis was performed using the SPSS v.15.0 software (SPSS Inc., Chicago, IL, USA). The one-sample t-test was used to assess whether the systematic errors were significantly different from zero. Comparison of the measures of accuracy between fetuses in the vertex and breech presentations was performed using an independent-samples Student's t-test for the systematic error, Levene's test (equality of variance) for the random error and the chi-square test for the fraction of estimations within 10% of the actual birth weight.

In order to determine whether certain models perform better than others for fetuses in breech presentation, the accuracy of the different models for fetuses in breech presentation was compared using a paired-samples Student's t-test for the systematic error, Pitman's t-test for the random error, the chi-square test for the fraction of estimations within 10% of the actual birth weight and the extended McNemar's test for the sensitivity and specificity measures18.

Comparison of the characteristics of the women in the vertex and breech groups was performed using the independent-samples Student's t-test and the chi-square test for continuous and categorical variables, respectively.

A P < 0.05 was considered significant. Bonferroni corrections were used as necessary to maintain an overall type I error rate of 0.05 when multiple comparisons were performed.

The study was approved by the local Institutional Review Board.

Results

Characteristics of the study and control groups

Of the total 3174 fetal weight estimations that met the inclusion criteria, 165 (3.2%) involved fetuses in breech presentation, to which a control group of 165 fetuses in vertex presentation was matched by birth weight and fetal gender. The demographic and obstetric characteristics of the women in the breech and vertex groups are presented in Table 2. The two groups differed only with regard to the cephalic index, which was lower (i.e. a higher rate of dolichocephaly) in the breech group (Table 2).

Table 2. Demographic and obstetric characteristics of the study population
CharacteristicVertex (n = 165)Breech (n = 165)P*
  • Data are presented as mean ± SD or n (%).

  • *

    Independent-samples Student's t-test and chi-square test used for continuous and categorical variables, respectively. GA, gestational age.

Maternal age (years)29.6 ± 5.130.2 ± 5.30.3
Nulliparous86 (52.1)77 (46.7)0.3
GA at delivery (weeks)36.5 ± 3.436.2 ± 3.10.3
Delivery at:   
 < 37 weeks65 (39.4)70 (42.4)0.6
 < 34 weeks15 (9.1)20 (12.1)0.4
 < 30 weeks9 (5.5)10 (6.1)0.8
Male fetus84 (50.9)84 (50.9)1.0
Time from fetal weight estimation to delivery (days)1.2 ± 1.01.1 ± 1.10.4
Fetal weight estimated:   
 On day of delivery42 (25.5)48 (29.1)0.5
 1 day prior to delivery66 (40.0)62 (37.6)0.7
 2 days prior to delivery35 (21.2)28 (17.0)0.3
 3 days prior to delivery22 (13.3)27 (16.3)0.4
Birth weight (g)2539 ± 7422537 ± 7460.9
 < 2500 g73 (44.2)75 (45.5)0.8
 > 3800 g8 (4.8)7 (4.2)0.8
Birth weight percentile42.1 ± 28.039.3 ± 27.50.4
 < 10th centile15 (9.1)18 (10.9)0.6
 > 90th centile13 (7.9)14 (8.5)0.8
Cephalic index81.3 ± 3.476.1 ± 4.1< 0.001
 < 701 (0.6)13 (7.9)0.001
 < 756 (3.6)60 (37.0)< 0.001

Systematic error

Overall, after exclusion of the model that is based on FL as a single measure (Model 1), which was found to be highly inaccurate, the systematic error for fetuses in breech presentation was smaller than that observed for fetuses in vertex presentation (mean of all models: − 0.14% vs. 2.0%; P = 0.01; Table 3). Furthermore, the systematic error for fetuses in breech presentation was non-significant (i.e. not significantly different from zero) for all models tested (except for Model 1), while in the vertex group only two models (AC-HC and AC-FL-HC) were associated with such a non-significant systematic error (Table 3).

Table 3. Comparison of the accuracy of fetal weight estimations for fetuses in breech vs. vertex presentation
 Systematic error (%, mean (95% CI))Random error (%, mean (95% CI))EFW within 10% of birth weight (% (95% CI))
ModelVertexBreechP*VertexBreechPVertexBreechP
  • *, **

    Comparison of absolute value of systematic error (independent-samples Student's t-test). P < 0.001 for the comparison of the signed values of the systematic error for Models 7 and 8.

  • Comparison of random error between vertex and breech groups (Levene's test).

  • Comparison of fraction within 10% of birth weight between vertex and breech groups (chi-square test).

  • §

    Systematic error significantly higher compared with Models 3–8 for fetuses in the breech group (P < 0.001, paired-samples Student's t-test).

  • Fraction within 10% of birth weight significantly lower compared with Models 3–5 (P < 0.05) and Models 6–8 (P < 0.001) for fetuses in the breech group (chi-square test).

  • **

    Systematic error not significantly different from zero (one-sample t-test).

  • g

    Random error significantly lower compared with Models 1 and 2 (P < 0.01) for fetuses in the breech group (Pitman's t-test).

  • h

    Random error significantly lower compared with Models 3–5 (P < 0.01) and Models 1 and 2 (P < 0.001) for fetuses in the breech group (Pitman's t-test). AC, abdominal circumference; BPD, biparietal diameter; EFW, estimated fetal weight; FL, femur diaphysis length; HC, head circumference.

1 (FL)2.26.4§0.00413.113.60.961.151.90.02
 (0.1–4.3)(4.4–8.4) (12.1–14.2)(12.5–14.7) (57.1–65.1)(48.0–55.8) 
2 (AC)2.71.5**§0.38.913.20.00173.964.80.01
 (0.8–4.6)(−0.3 to 3.3) (7.7–10.1)(12.2–14.2) (69.8–78.0)(61.0–68.6) 
3 (AC-FL)2.8− 0.3**0.018.110.8 0.00775.568.10.02
 (1.0–4.6)(−2.4 to 1.8) (7.2–9.0)(9.1–10.5) (71.3–79.7)(64.2–72.0) 
4 (AC-BPD)3.30.4**0.0088.211.1 0.0276.668.30.02
 (1.6–5.0)(−1.5 to 2.3) (7.5–8.9)(10.3–11.9) (72.8–80.4)(64.3–72.3) 
5 (AC-HC)− 0.3**− 0.1**0.88.611.3 < 0.00179.272.10.03
 (−2.1 to 1.5)(−2.1 to 1.9) (8.0–9.2)(10.5–12.1) (75.3–83.1)(68.1–76.1) 
6 (AC-FL-BPD)2.9− 0.6**0.017.59.40.0378.377.60.8
 (0.9–4.9)(−2.4 to 1.2) (6.8–8.2)(8.4–10.4) (74.6–82.0)(73.7–81.5) 
7 (AC-FL-HC)0.9**− 1.0**0.9*7.79.50.0481.277.00.2
 (−1.0 to 2.8)(−2.7 to 0.7) (6.6–8.8)(8.6–10.4) (77.2–85.2)(73.2–80.8) 
8 (AC-FL-BPD-HC)1.7− 0.9**0.4*7.69.40.0580.777.60.3
 (0.1–3.3)(−2.8 to 1.0) (6.8–8.4)(8.7–10.1) (76.8–84.6)(73.9–81.3) 

The relationship between fetal presentation and the systematic error varied with the model used. For models that incorporated only BPD as the head measure (i.e. Model 4 (AC-BPD) and Model 6 (AC-FL-BPD)), breech presentation was associated with a systematic error that was significantly lower than that of fetuses in vertex presentation (Table 3). The use of models that incorporate HC as the head measure eliminated these presentation-related differences (i.e. Model 5 (AC-HC), Model 7 (AC-FL-HC) and Model 8 (AC-FL-BPD-HC)) (Table 3).

For fetuses in the breech presentation, the systematic error was similar for all models tested, except for Models 1 (FL) and 2 (AC), which were associated with a systematic error that was significantly higher than that of the other six models (P < 0.005).

Random error

The random error was significantly higher in cases of breech presentation compared with cases of vertex presentation, regardless of the model used (excluding Model 1) (Table 3).

For fetuses in breech presentation, the random error was related to the number of biometric indices incorporated in the models: it was significantly lower for models that are based on three or four biometric indices (Models 6–8; 9.4–9.5%) compared with models that are based on a single biometric index (Models 1 and 2; 13.2–13.6%; P < 0.001) or two biometric indices (Models 3–5; 10.8–11.3%; P < 0.01) (Table 3).

Fraction of estimations within 10% of birth weight

Overall, the fraction of weight estimations within 10% of actual birth weight in cases of breech presentation ranged widely, from 51.9 to 77.6%. Similarly to the random error, this fraction increased with the number of biometric indices incorporated into the model: it was significantly lower for models that are based on a single biometric index (Models 1 and 2; 51.9–64.8%) compared with models that include two biometric indices (Models 3–5; 68.1–72.1%; P < 0.05), or three or four indices (Models 6–8; 77.0–77.6%; P < 0.001) (Table 3).

Compared with fetuses in vertex presentation, the fraction of weight estimations within 10% of the actual birth weight was lower in cases of breech presentation, and these differences were statistically significant for models that are based on only one or two biometric indices (Models 1–5; Table 3).

Detection of weight thresholds for vaginal delivery

To assess the accuracy of sonographic weight estimation in cases of breech presentation from a more practical perspective, we analyzed the accuracy of the different models in the detection of the lower or the upper weight thresholds (2500 and 3800 g, respectively) beyond which a trial of vaginal delivery is usually not recommended (Table 4).

Table 4. Accuracy of the different models in the detection of a birth weight below 2500 g or above 3800 g for fetuses in breech presentation
 Detection of birth weight < 2500 gDetection of birth weight > 3800 g
ModelAUCSens. (%)Spec. (%)PPV (%)NPV (%)Overall accuracy (%)AUCSens. (%)Spec. (%)PPV (%)NPV (%)Overall accuracy (%)
  • *

    P < 0.005 compared with Models 1 and 2 and P < 0.05 compared with Models 3 and 4 (extended McNemar's test). AC, abdominal circumference; AUC, area under the receiver–operating characteristics curve; BPD, biparietal diameter; FL, femur diaphysis length; HC, head circumference; NPV, negative predictive value; PPV, positive predictive value; Sens., sensitivity; Spec., specificity.

1 (FL)0.92568.074.468.973.671.50.93141.785.017.994.981.8
2 (AC)0.93976.078.975.079.877.60.94750.086.923.195.784.2
3 (AC-FL)0.95584.082.279.786.083.00.96375.089.536.097.988.5
4 (AC-BPD)0.96281.384.481.384.481.30.95966.790.234.897.286.3
5 (AC-HC)0.96486.786.784.488.686.70.96783.391.543.598.690.9
6 (AC-FL-BPD)0.97090.788.987.292.089.7*0.97283.392.245.598.691.5*
7 (AC-FL-HC)0.97494.792.291.095.493.3*0.97791.794.155.099.393.9*
8 (AC-FL-BPD-HC)0.97193.390.088.694.291.5*0.97391.792.850.099.392.7*

There was a considerable variation in the sensitivity and specificity of the different models in the detection of birth weight < 2500 or > 3800 g (Table 4). Overall, models that are based on a single biometric index (Models 1 and 2) were the least accurate (sensitivity 68.0–76.0%, specificity 74.4–78.9%, for birth weight < 2500 g) while models that are based on three or four biometric indices (Models 6–8, sensitivity 90.7–94.7%, specificity 88.9–92.2%, for birth weight < 2500 g) were associated with a significantly greater predictive accuracy compared with Models 1 (FL) and 2 (AC) (P < 0.005 for each of the three Models 6–8) and Models 3 (AC-FL) and 4 (AC-BPD) (P < 0.05 for each of the three Models 6–8) (Table 4). The same pattern was also observed with regard to the AUC measure (Table 4).

Discussion

In the present study we sought to assess the accuracy of sonographic fetal weight estimation for fetuses in breech presentation and to determine whether certain sonographic models perform better than others in cases of breech presentation. Our study has several key findings. First, sonographic fetal weight estimation for fetuses in breech presentation is associated with a smaller systematic error but a larger random error compared with fetuses in vertex presentation. Second, the smaller systematic error appears to be related to the lower cephalic index in cases of breech presentation because these presentation-related differences are eliminated when models that incorporate HC as the head measure are employed. Third, the random error decreases with the number of biometric indices incorporated into the model. Fourth, the larger random error appears to outweigh the decrease in systematic error in cases of breech presentation, as reflected by the lower fraction of weight estimations within 10% of birth weight among fetuses in breech presentation compared with vertex presentation. Finally, for fetuses in breech presentation, models that are based on three to four biometric indices are more accurate in detecting the weight thresholds beyond which a trial of vaginal delivery is usually not recommended.

Interestingly, we were able to find only one previous study that directly evaluated the accuracy of sonographic weight estimation in cases of breech presentation8. The authors found that the mean absolute percentage error (MAPE) for fetuses in breech presentation was significantly higher than that for fetuses in vertex presentation. The systematic and random errors, which are the only two fundamental types of prediction error, were not evaluated in that study, so a direct comparison with our findings regarding these two types of error cannot be made. However, the finding that the MAPE, which integrates both the systematic and random errors, was higher among breech fetuses, is in concordance with our findings regarding the lower fraction of estimates within 10% of birth weight in the breech group. In contrast to our findings, the authors reported that all of the seven sonographic models they evaluated were associated with a similar degree of accuracy for fetuses in the breech presentation. Possible explanations for this apparent discrepancy include the smaller sample size (n = 104) and the lack of difference in the rate of dolichocephaly between the breech and vertex groups in their study8.

A more recent study9 that evaluated the effect of nine different factors on the accuracy of fetal weight estimation found that, in contrast to our results, fetal presentation did not affect the accuracy of weight estimation. However, several factors limit the interpretation of the results of that study, including the lack of background information regarding the vertex and non-vertex groups (i.e. demographic and obstetric characteristics, and the cephalic index), the fact that the non-vertex group was not limited to fetuses in breech presentation but also included fetuses in transverse and oblique lie, the lack of matching of the two groups by factors such as birth weight and fetal gender, and the use of only a single measure to estimate accuracy (MAPE)9.

The presentation-related differences in the accuracy of fetal weight estimation observed in the current study can be related to one or more of the following factors. First, presentation-related differences in the relative size or shape of the various biometric indices (e.g. a smaller BPD owing to a higher rate of dolichocephaly among breech fetuses). Second, presentation-related differences in the accuracy of the sonographic measurement of the various biometric indices (e.g. differences in the measurement error of FL owing to the different intrauterine orientation of the femur in cases of breech presentation, or difficulty in gaining the optimal cross-section for the measurement of AC). Third, presentation-related differences in the correlation between the various biometric indices and fetal weight (e.g. owing to an association between non-vertex presentation and fetal growth).

Thus, for example, the smaller systematic error observed for breech fetuses may be explained by the higher rate of dolichocephaly among breech fetuses, which leads to a lower weight estimation (and thus a smaller, or more negative, systematic error) when models that are based on BPD are employed. This explanation is supported by the observation that these presentation-related differences in the systematic error were eliminated when models that incorporate HC (rather than BPD) as the head measure were employed.

The presentation-related differences in the systematic error of models that do not include head measurements suggest that other biometric indices also contribute to these presentation-related differences. Thus, the significant presentation-related differences in the systematic error observed with the FL (Model 1) and the AC-FL (Model 3) models suggest that the FL also contributes to these presentation-related differences in the systematic error. Whether this effect of FL on the systematic error is caused by presentation-related differences in the femur shape or length, or by presentation-related differences in the sonographic measurement error of FL, requires further investigation.

We speculate that the larger random error observed for breech fetuses may be related to the different intrauterine orientation of the various fetal body parts in cases of breech presentation, which leads to a higher measurement error of the various indices (e.g. FL and AC), possibly because of the lower degree of operator experience in measuring these indices in breech presentation. It remains to be studied whether specific training aimed at improving the measurement technique of these indices for fetuses in breech presentation can decrease this presentation-related random error. The convergence to mean principle may explain the decrease in the random error as the number of biometric indices incorporated into the model increases.

The lower fraction of weight estimations within 10% of the birth weight suggests that the increased random error outweighs the lower systematic error observed for fetuses in the breech presentation. This is further supported by the fact that both the random error and the fraction of estimates within 10% of birth weight follow a similar pattern with regard to the different models.

In conclusion, the accuracy of sonographic weight estimation for fetuses in breech presentation appears to be lower than that for fetuses in vertex presentation, principally because of a larger random error. The use of sonographic models that are based on three or four biometric indices, training aimed at improving the measurement technique of the biometric indices for fetuses in breech presentation and the development of sonographic models derived from fetuses in breech presentation, may all lead to a greater accuracy of fetal weight estimation for fetuses in breech presentation. The limited predictive accuracy of the weight thresholds that preclude a trial of vaginal delivery for fetuses in breech presentation should be taken into consideration when discussing the mode of delivery with women having a fetus in the breech presentation.

Ancillary