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Estimation of Fetal Weight: Mean Value from Multiple Formulas

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variety of formulas and parameters have been correlated with fetal weight.1–4 Among them, the Shepard formula, which includes BPD and AC,5 and the Hadlock formula using FL and AC6 are widely accepted and

com-monly used for estimation of fetal weight. These parameters are considered to be more accurate and simpler than others.7–9 The results from combining all three parameters (BPD, FL, and AC) for predict-ing fetal weight appear to be controversial in the lit-erature. Hadlock and coworkers10 and Rose and McCallum11found that combining all three of these parameters produced more accurate results than the use of only two parameters, but Woo and Wan12 con-versely found no improvement in predictive accu-racy over that of formulas using two parameters.

Although the Shepard and Hadlock formulas cor-relate well with fetal weight, significant errors in esti-mation still occur and have been attributed to biologic variation (difference of somatic types), pathologic variations (fetal dystrophy, hypertrophy, malformations), subjective operator errors of mea-surement, or any combination of these. Recently, a volume based model was reported to be superior to the biometric based formulas.13

Received May 28, 1999, from the Division of Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, Maine Medical Center, Scarborough, Maine. Revised manuscript accepted for publi-cation September 5, 1999.

Address correspondence and reprint requests to Michael G. Pinette MD, Division of Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, Maine Medical Center, 482 Payne Road, Scarborough, ME 04074.

ABBREVIATIONS

BPD, Biparietal diameter; AC, Abdominal circumference; FL, Femur length; EFW, Estimated fetal weight

 1999 by the American Institute of Ultrasound in Medicine • J Ultrasound Med 18:813–817, 1999 • 0278-4297/99/$3.50

A

Mean Value from Multiple Formulas

Michael G. Pinette, MD, Yuqun Pan, MD, Sheila G. Pinette, RPA-C, Jacquelyn Blackstone, DO,

John Garrett, Angelina Cartin

Mean fetal weight value from multiple formulas was compared to fetal weight from single formulas. Data were collected on 975 fetuses who had estima-tion of fetal weight by ultrasonography within 1 week before birth. Improvement in estimation of fetal weight occurred using either the mean value of multiple formulas or the Hadlock BPD/FL/AC, in

comparison to fetal volume, BPD/AC, or FL/AC. BPD/FL/AC appeared to provide the best estimate of true weight in terms of overall accuracy and in terms of not showing a trend in either overestimat-ing or underestimatoverestimat-ing true weight. KEY WORDS:

Weight, fetal, estimation; Fetus, weight; Formulas, fetal weight estimation.

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This study was designed to test the hypothesis that application of the mean value of multiple formulas for predicting fetal weight may improve the predic-tive accuracy by decreasing the influence of biologic and pathologic variations. The Shepard BPD/AC, Hadlock FL/AC, and BPD/FL/AC models were chosen in the study because they are commonly used. The recently published fetal volume model of Combs and associates13 also was chosen because of its reported superiority. These four models are repre-sentative of the models published in the literature.

SUBJECTS AND METHODS

We analyzed data on 975 fetuses who were born from January 1991 to August 1995 and who had had ultrasonographic examinations for EFW within 1 week before birth. Fetuses with congenital malfor-mations were excluded.

Sonographic evaluation was performed using any of the following machines: ATL-HDI Ultramark 9 or ATL Ultramark 9 (Advanced Technology Labora-tories, Bothell, WA) or Acuson 128 (Acuson, Mountain View, CA).

EFW was based on the Shepard BPD/AC for-mula,5 the Hadlock FL/AC and BPD/FL/AC for-mulas,6the Combs formula using fetal volume,13and the fifth formula using mean EFW from the previous four formulas (multiple mean) (Table 1).

The deviations between EFW and actual birth weight were considered as the estimating error, which was calculated on the basis of the following formula:

Absolute Percentage Error = [(EFW – Birth weight)/Birth weight] ×100

Mean absolute percentage errors were calculated and compared among all the formulas.

Mean differences between EFW and actual birth weight for the formulas were compared. Statistical analysis was performed using a paired t-test pro-vided by the StatView computer program (Abacus Concepts, Inc., Berkeley, CA).

The fetuses were then divided into four groups on the basis of their actual weights in order to observe any possible effect of weight categories on estimating error. The four groups were birth weights of ≥500 g and ≤999 g (71 fetuses); ≥1000 g and ≤1999 g (184 fetuses); ≥ 2000 g and ≤ 3499 g (464 fetuses); and

≥ 3500 g (244 fetuses). The estimating errors were compared for each of the different fetal weight groups, using all of the five methods.

A sign test for trend was performed.

RESULTS

Gestational age of the 975 fetuses at the time of deliv-ery ranged from 20.3 to 42.0 weeks. Birth weights ranged from 260 g to 5368 g.

All told, the new model using the mean value from multiple formulas and BPD/FL/AC showed statisti-cally significantly improved accuracy with mean absolute percentage errors of 8.5% and 8.6%, respec-tively (Table 2). The Combs volume model had a mean error of 9.5%, the Shepard BPD/FL model showed a mean error of 9.7%, and the Hadlock FL/AC and BPD/FL/AC models resulted in mean errors of 9.1% and 8.7%, respectively. The volume based model, recently reported to have improve-ment in accuracy for EFW,13 and BPD/AC were the least accurate overall.

Table 1: Formulas Shepard BPD/AC (formula 1):

Log 10 birth weight = –1.7492 + 0.166 (BPD) + 0.046 (AC) – 2.646 (AC × BPD) 1000 Hadlock FL/AC (formula 2):

Log 10 birth weight = 1.3598 + 0.051 (AC) + 0.1844 (FL) – 0.0037 (AC ×FL) Hadlock BPD/FL/AC (formula 3):

Log 10 birth weight = 1.4787 + 0.001837 (BPD)2+ 0.0458 (AC) + 0.158 (FL) – 0.003343 (AC ×FL) Combs fetal volume (formula 4):

EFW = (0.23718 ×AC2×FL) + (0.03312 ×HC3) Pinette mean fetal weight:

Birth weight = Formula 1 + Formula 2 + Formula 3 + Formula 4 4

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In terms of the specific weight categories, interest-ing differences were noted.

In the 500–999 g group (Table 3), BPD/FL/AC tended to be most accurate; however, no significant difference occurred between BPD/FL/AC, FL/AC, multiple formulas, and BPD/AC. Volume estimate was significantly less accurate.

In fetuses weighing 1000–1999 g (Table 4), BPD/FL/AC tended to be most accurate; however, no significant difference was found between BPD/FL/AC, multiple formulas, and BPD/AC. BPD/FL/AC, when compared with FL/AC and BPD/AC, was significantly better for EFW. Once again the volume model was significantly less accu-rate.

With fetuses weighing 2000–3499 g (Table 5), vol-ume tended to be the best model of estimation; however, no significant difference occurred when compared to multiple formulas. BPD/FL/AC and FL/AC were significantly less accurate, and BPD/AC was significantly the least accurate model.

In fetuses weighing 3500 g or more (Table 6), mul-tiple formulas were significantly the most accurate predictor of fetal weight. BPD/FL/AC, FL/AC, vol-ume, and BPD/AC were significantly less accurate to the same degree.

The results of the sign test, each patient counting as +1 (if EFW is overestimated) or –1 (if EFW is underestimated), are reported in Table 7. As a whole, volume, FL/AC, and mean weight showed a signifi-cant trend toward overestimation of fetal weight. Likewise, BPD/AC and BPD/FL/AC did not show a trend to overestimate or underestimate fetal weight. BPD/FL/AC appeared to be best with regard to not showing a trend in either overestimat-ing or underestimatoverestimat-ing fetal weight.

In the data set taken as a whole (i.e., all patients), mean differences in grams from actual birth weights were similar, although FL/AC significantly under-estimates and BPD/AC significantly overunder-estimates the actual birth weight (Table 8).

Looking at mean differences in specific weight cat-egories, it became very apparent that significant interesting differences existed between weight cate-gories. When looking at mean differences from birth weight, all formulas underestimate fetal weight in fetuses with birth weights under 1000 g (Table 9). For birth weights of 1000–1999 g (Table 10), the EFW tended to be underestimated, with the FL/AC, mul-tiple formulas, and volume methods reaching statis-tical significance. Most methods, except FL/AC, showed no trend in overestimating or underestimat-ing fetal weight in the 2000–3499 g group (Table 11). All methods except FL/AC tended to significantly overestimate fetal weight in the 3500 g or greater group (Table 12).

DISCUSSION

Many different formulas have been published in the literature for EFW, and various studies have been done to evaluate the accuracy of these formulas.14–16 The meta-analysis performed by Medchill and coworkers14 in 1991 with 20 published formulas for low birth weight fetuses, found no significant differ-ence in accuracy. Combs and colleagues’ model Table 2: Mean Absolute Percentage Errors: All

Patients % SD P Value Multiple 8.5 7.4  -NS BPD/FL/AC 8.6 7.5   -P = 0.005* FL/AC 9.0 7.9   -P = 0.0121* Volume 9.5 8.4   -NS BPD/AC 9.7 8.3  *Statistically significant.

Table 3: Mean Absolute Percent Error: 500–999g

% SD P Value BPD/FL/AC 11.4 8.5  -NS  FL/AC 11.8 9.0   -NS  Multiple 12.0 8.8   -NS  BPD/AC 12.7 9.7   -P = 0.004* Volume 16.2 11.1  *Statistically significant. -NS 

Table 4: Mean Absolute Percentage Error: 1000–1999g

% SD P Value BPD/FL/AC 8.9 8.1  -NS  Multiple 9.4 8.5   -NS  FL/AC 9.8 9.1   -NS BPD/AC 10.4 9.3   -P = 0.002* Volume 12.5 10.3  *Statistically significant. -P = 0.002*

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using fetal volume, which was reported recently as being accurate in a wide range of fetal weight,13was not investigated previously.

Theoretically, an average of values predicted by different methods should yield the most accurate estimation of fetal weight by balancing each mula’s limitation. The mean value of multiple for-mulas (Shepard BPD/AC, Hadlock FL/AC and BPD/FL/AC, and Combs fetal volume) in this study

appeared statistically superior to the BPD/AC, FL/AC, and fetal volume. However, altogether the multiple formulas were no better than BPD/FL/AC alone in predicting EFW.

Table 5: Mean Absolute Percentage Error: 2000–3499g

% SD P Value Volume 7.7 6.8  -NS Multiple 8.0 6.9   -P = 0.01* BPD/FL/AC 8.2 7.2   -NS FL/AC 8.3 7.4   -P = 0.008* BPD/AC 9.4 8.2  *Statistically significant.

Table 6: Mean Absolute Percentage Error: ≥3500g

% SD P Value Multiple 6.7 7.8  -P = 0.01* BPD/FL/AC 6.9 8.0   -NS FL/AC 7.1 8.5   -NS Volume 6.9 8.5   -NS BPD/AC 7.1 8.6  *Statistically significant.

Table 7: Sign Test

Volume BPD/AC FL/AC BPD/AC/FL Mean

+ 539 474 554 482 518

– 435 500 419 493 455

Difference +104 –26 +125 –11 +63

n 974 974 973 975 973

P <0.001 0.13 <0.001 0.26 <0.001

Table 8: Mean Difference from Actual Birth Weight: All Patients Grams P Value Multiple +8.1 NS  -NS Volume +15 NS   -NS BPD/FL/AC +17.6 NS   -P = 0.0001* FL/AC –27.7 0.008*   -P = 0.0001* BPD/AC +27.7 0.0112*  *Statistically significant.

Table 12: Mean Difference from Actual Birth Weight:

≥3500g Grams P Value FL/AC +26.0 NS  -NS BPD/FL/AC +99.4 0.0002*  -NS BPD/AC +112.8 0.0001*   -NS Multiple +114.2 0.0001*   -P = 0.0002* Volume +22.9 0.001*  *Statistically significant.

Table 11: Mean Difference from Actual Birth Weight: 2000–3499g Grams P Value BPD/FL/AC +2.9 NS  -P = 0.001* Multiple –9.7 NS   -P = 0.001* BPD/AC +15.9 NS   -P = 0.0003* Volume –18.6 NS   -P = 0.0008* FL/AC –44.0 0.003*  *Statistically significant.

Table 10: Mean Difference from Actual Birth Weight: 1000–1999g Grams P Value BPD/FL/AC –23.6 NS  -NS BPD/AC –29.6 NS   -NS FL/AC –47.2 0.0013*   -P = 0.03* Multiple –59.0 0.0001*   -P = 0.0001* Volume –135.3 0.0001*  *Statistically significant.

Table 9: Mean Difference from Actual Birth Weight: 500–999g Grams P Value BPD/AC –31.1 0.02*  -P = 0.02* BPD/FL/AC –49.1 0.0001*  -NS FL/AC –52.1 0.0001*   -NS Multiple –58.0 0.0001*   -P = 0.0001* Volume –99.8 0.0001*  *Statistically significant.

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All formulas tested appeared to significantly underestimate fetal weight in the 500–999 g group on the average of 30 to 100 g. If viability is being judged on the basis of weight, this factor should be taken into account.

In terms of predicting the weight of fetuses over 3500 g, the EFW formulas tested appeared to signifi-cantly overestimate fetal weight by 100 to 200 g on average, except for FL/AC. This difference may not be clinically significant since it is relatively small.

In general, in terms of trends as well as accuracy of true weight, the BPD/FL/AC appeared to be the best estimate of fetal weight.

REFERENCES

1. Ianniruberto A, Gibbons, JM: Prediction of fetal weight by ultrasonic B-scan cephalometry: An improved technique with disappointing results. Obstet Gynecol 37:689, 1971 2. Thompson HE, Makowski EL: Birth weight of fetal

gesta-tional age. Obstet Gynecol 37:44, 1971

3. Suzuki K, Minei LJ, Schnitzer LE, et al: Ultrasonography measurement of fetal heart volume for estimation of birth weight. Obstet Gynecol 43:867, 1974

4. Campbell S, Wilkin D: Ultrasonic measurement of fetal abdominal circumference in estimation of fetal weight. Br J Obstet Gynecol 82:689, 1975

5. Shepard MJ, Richards VA, Berkowitz RL, et al: An evalu-ation of two equevalu-ations for predicting fetal weight by ultrasound. Am J Obstet Gynecol 142:47, 1982

6. Hadlock FP, Harrist RB, Carpenter RJ, et al: Sonographic estimation of fetal weight: The value of femur length in addition to head and abdominal measurements. Radiology 150:535, 1984

7. Sampson MB, Thomason JL, Kelly SL, et al: Prediction of intrauterine fetal weight using real-time ultrasound. Am J Obstet Gynecol 142:554, 1982

8. Timor-Tritsch JE, Itskovitz J, Brandes JM: Estimation of fetal weight by real-time sonography. Obstet Gynecol 57:653, 1981

9. Ott WJ: Clinical application of fetal weight determination by real-time ultrasound measurements. Obstet Gynecol 57:758, 1981

10. Hadlock FP, Harrist RB, Sharman RS: Estimation of fetal weight with the use of head, body and femur measure-ments: A prospective study. Am J Obstet Gynecol 153:333, 1985

11. Rose BI, McCallum WD: A simplified method for esti-mating fetal weight using ultrasound measurements. Obstet Gynecol 69:671, 1987

12. Woo JSK, Wan MCW: An evaluation of fetal weight pre-diction using a simple equation containing the fetal femur length. J Ultrasound Med 5:453, 1986

13. Combs AC, Jaekle RK, Rosenn B, et al: Sonographic esti-mation of fetal weight based on a model of fetal volume. Obstet Gynecol 82:365, 1993

14. Medchill MT, Peterson CM, Kreinick C, et al: Prediction of estimated fetal weight in extremely low birth weight neonates (500–1000 g). Obstet Gynecol 78:286, 1991 15. Pielet B, Sabbagha RE, MacGregor SN, et al: Ultrasonic

prediction of birth weight in preterm fetuses: Which for-mula is best? Am J Obstet Gynecol 157:1411, 1987 16. Robson SC, Gallivan S, Walkinshaw SA, et al: Ultrasonic

estimation of fetal weight: Use of targeted formulas in small for gestational age fetuses. Obstet Gynecol 82:359, 1993

17. Warsof S, Gohari P, Berkowitz R, et al: The estimation of fetal weight by computer-assisted analysis. Am J Obstet Gynecol 128:881, 1977

References

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