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Birth weight prediction from remote ultrasonographic examination
Birth weight prediction from remote ultrasonographic examination Joseph A. Spinnato, MD, Robert D. Allen, and Hiram W. Mendenhall, MD
Mobile, Alabama Multiple linear regression by the least squares method was used to remodel five existing static equations to permit birth weight estimates from remote ultrasonographic parameters. By incorporating lapse time (examination-to-delivery interval), the new equations be used to estimate birth weight 0 to 35 days after ultrasonographic examination. For each model, R2 approached 1.0. The generated equations were tested on 167 non model cases. Among the three best equations, 65% to 67% of estimates were within 100 mg/kg birth weight. The mean absolute error ranged from 86 to 91 gm/kg.With a mean lapse time of 16.8 ± 11 days, the accuracy of birth weight estimates equaled or exceeded that reported for existing static formulas. The accuracy of the estimates was maintained across the entire range of lapse times and birth weights observed. In intrapartum situations when ultrasonography is unavailable or technically difficult, birth weight can be estimated from remote ultrasound parameters. (AM J OasTET GVNECOL 1989;161 :742-7.)
can
Key words: Ultrasonography, estimated fetal weight
In a previous report' we described the development of an equation to predict birth weight from ultrasonographic examinations. By incorporating the interval from ultrasonographic examination to delivery (lapse time), the model predicted birth weight based on ultrasonographic measurements taken as early as 35 days before delivery. The rationale for the model was based on the hypothesis that ultrasonographic measurements of fetal dimensions at a point in gestation could be coupled with elapsed time to mathematically predict a birth weight based on observed growth in a population. We extrapolated this concept to five existing formulas by including a lapse-time modifier in the structure of these existing equations. The lapse-time modifier for each equataion was determined individually from model building that analyzed the initial static estimate and the lapse time that occurred versus actual birth weight.
Material and methods This study had two phases. In phase I, model building generated new equations based on five static equa-
From the Department of ObstetriCs and Gynecology, Unzversity of South Alabama Medzeal Center. Presented at the Ninth Annual Meeting of the Soaety of Perinatal Obstetricians, New Orleans, Louisiana, February 2-4, 1989. Reprint requests: Joseph A. Spinnato, MD, Division of MaternalFetal Medicine, Department of Obstetrics and Gynecology, University of Louisvzlie, Louisvzlie, KY 40292. 6/6114093
742
tions. In Phase II, the new equations were tested on cases other than model cases. Phase I-Model development. The records of all patients seen in the Perinatal Unit of the University of South Alabama Medical Center between October 1984 and September 1986 for obstetric ultrasonographic evaluation were reviewed. The patient population was a racially mixed (55% black), low-income clinic population. Patients were included in the study if they met the following criteria: (1) the pregnancy was a singleton gestation; (2) the biparietal diameter, occipitofrontal diameter, femur length, transverse and anteroposterior diameters of the fetal abdomen had been measured by ultrasonography; (3) data on the outcome of the delivery were available; (4) the interval (lapse time) from ultrasonographic ex~mination to delivery was :5':35 days; and (5) birth weight was :55000 grams. All ultrasonographic examinations were performed by one of three experienced ultrasonographers using a linear array real-time scanner (ADR Model 4000) with a 3.5 MHz transducer. As in our previous study,' standard imaging and measurement techniques were used. Model generation and all statistical methods were performed with the Statistical Analysis System (SAS) and the IBM-434 I-II mainframe computer of the University of South Alabama. Multiple linear regression using the least squares method was used to construct the models. Using the five formulas (Table I), the fetal weight estimates determined on the day of ultrasonographic examination (in logarithmic form) and the
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Volume 161 Number 3
Table I. Static equations Author
EquatIOn
1. Hadlock et al: Log (weight) = 1.326 - 0.00326 AC X FL + 0.0107 HC + 0.0438 AC + 0.158 FL 2. Hadlock et al. 6 Log (weight) = 1.5662 - 0.0108 HC + 0.0468 AC + 0.171 FL + 0.00034 HC2 - 0.003685 (AC x FL) 3. Hadlock et al. 6 Log (weight) = 1.5115 + 0.0436 AC + 0.1517 FL - 0.00321 (AC x FL) + 0.0006923 (BPD x HC) 4. Ott et aU Log (weight) = 0.04355 HC + 0.05394 AC - 0.0008582 HC x AC + 1.2594 (FLI AC) 2.0661 5. Shepard et al? Log (weight) = -1.7492 + 0.166 (BPD) + 0.046 (AC) - 2.646 (AC x BPD)11000 AC, Abdominal circumference; FL, femur length; HC, head circumference in centimeters; BPD, biparietal diameter.
lapse time observed were analyzed versus the logarithm of actual birth weight. For each equation the constructed model generated a lapse-time modifier. After model development, the modified equations were tested with the model cases. The mean error (estimated - actual birth weight), mean absolute error (absolute value of estimated - actual birth weight), and the standardized absolute error (absolute error/kilogram birth weight) were determined for each modified equation. The equations were examined for accuracy across the range of birth weights and lapse times observed. To allow comparisons to previous reports, the observed error was converted to percentage error by the formula ([predicted weight - actual weight]/ actual weight X 100) to generate a mean ± SD of percent error. The correlation coefficient (Pearson's r) of estimated versus actual birth weight was determined, and the percent of estimates within 50, 100, and 150 gm/kg of actual birth weight was calculated. One- and two-way analyses of variance were used to test for differences among means. Tukey's studentized range test was used to evaluate differences among group means. The significance level was set at alpha = 0.05. Phase II-Model validation. The modified equations were validated by use of different cases from those used to develop the models. Patients seen in the Perinatal Unit for fetal ultrasonographic evaluation from October 1986 to August 1987 were reviewed for inclusion in the validation phase of the study. The inclusion criteria and ultrasonographic method were unchanged from phase 1. Modified equations developed in phase I were used to generate birth weight estimates that were compared to actual birth weight. Accuracy of the estimates was determined as outlined in phase 1.
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Table II. Descriptive statistics of included cases for both phases of the study*
Vanable
Examination gestational age (wk) Birth gestational age (wk) Lapse time (days) Femur length (mm) Abdominal circumference (mm) Head circumference (mm) Birth weight (gm)
Model development (N = 245)
Validation (N = 167)
35.4 ± 3.2 (25-42) 37.6 ± 2.9 (28-44) 15.7 ± 10.7 (0-35) 68.9 ± 6.7 (46-82) 302.5 ± 32.7 (188-388) 314.4 ± 21.2 (243-356) 2978 ± 680 (1134-4876)
34.7 ± 2.9 (30-42) 37.1 ± 2.8 (30-44) 16.8 ± 11.0 (0-35) 68.0 ± 6.1 (55-82) 302.5 ± 35.0 (207-396) 310.7 ± 19.0 (261-364) 3074 ± 713 1375-4870)
*Data are presented as mean ± SD, with range in parentheses.
Table III. Modified equations 1. Log [birth weight) 0.0043 (LT) 2. Log [birth weight) 0.0043 (LT) 3. Log [birth weight] 0.0043 (LT) 4. Log [birth weight) 0.0034 (LT) 5. Log [birth weight) 0.0047 (LT)
= 1.0009 [Log initial weight)
+
= 1.0009 [Log initial weight)
+
= 1.0 [Log initial weight)
+
= 1.001 [Log initial weight) =
+
0.9994 [Log initial weight) +
Birth weight in grams. LT, Lapse time in days.
Phase I-Model development. From 259 ultrasonographic examinations for which delivery outcome was known, 245 examinations and paired delivery outcomes fulfilled the study criteria. Table II presents the descriptive statistics of these cases. A model to predict birth weight from remote ultrasonographic examination was generated for each of the five equations. For each model, R2 approached 1.0. In each, the intercept did not differ significantly from zero and was deleted from the modified equation (Table III). The coefficients for each model's parameters are described in Table IV. Both lapse time and the logarithm of the initial fetal weight estimate contributed significantly to the birth weight predictions, p s 0.000 I. The modified equations were tested on the model cases. Modified equations 1, 2, and 3 performed quite similarly. Remarkably accurate birth weight estimates were noted. For each estimate, the mean error was very small and did not differ statistically from zero. The percent mean error was < 1%. The mean absolute error per kilogram actual birth weight was less than 100 gm/kg. There was no significant difference in the ac-
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Spinnato, Allen, and Mendenhall
September 1989 Am J Obstet Gynecol
Table IV. Description of models Model
LT coefficient
SE
Zero coefficient
SE
R2
0.00428326 0.00429440 0.00434518 0.00344469 0.00473645
0.0003 0.0003 0.0003 0.0004 0.0004
1.00086433 1.00293973 1.00002378 1.00112376 0.99972076
0.0016 0.0016 0.0016 0.0022 0.0025
0.9998 0.9998 0.9998 0.9996 0.9995
I
1 2 3 4 5
LT coefficient, Lapse-time coefficient; SE, standard error of the estimate; Zero coefficient, coefficient of the log of the original
static estimate.
Table V. Validation phase-Overall performance of the new equations in descending order of accuracy* Error (gm) (mean ± SD)
Equation
-112 -112 -118 -187 -154
1 2 3 4 5
± ± ± ± ±
314 315 319 426 468
% Error
(mean ± SD) -3.6 -3.6 -3.8 -5.4 -4.6
± ± ± ± ±
10.7 10.8 10.8 15.2 16.1
Absolute error (gm)
(mean ± SD)
Maximum absolute error (gm)
Standardized absolute error (gmt kg) birth weight
rt
± ± ± ± ±
1175 1197 1288 1090 1296
90.0 90.2 91.3 132.7 138.5
0.91 0.91 0.91 0.84 0.82
267 268 272 389 410
198 199 202 254 273
*Lapse time mean = 16.8 ± 11 days, range 0 to 35 days. Error estimates expressed as negative numbers indicate underestimation of actual birth weight; positive numbers indicate overestimation. tPearson's correlation coefficient for estimated versus actual birth weight.
Table VI. Validation phase-Accuracy of birth weight estimates within segments of lapse time Lapse time (days) s7 (n
= 48)
Absolute error* Standardized absolute errort 8-14 (n
= 22)
Absolute error* Standardized absolute errort 15-21 (n
= 30)
22-28 (n
= 35)
29-35 (n
= 32)
Absolute error* Standardized absolute errort Absolute error* Standardized absolute errort Absolute error* Standardized absolute errort
Equation 2
Equation 3
Equation 4
EquatIOn
280 ± 202 100.0
280 ± 204 100.0
288 ± 206 102.3
371 ± 257 135.7
455 ± 313 162.0
209 ± 174 66.3
213 :±: 174 67.3
226 ± 169 71.6
382 ± 201 123.0
424 ± 220 136.9
328 ± 254 102.7
329 :±: 255 102.9
337 ± 268 105.3
420 ± 230 141.5
451 ± 311 146.0
230 ± 166 79.7
230 ± 167 80.0
229 ± 170 79.3
388 ± 242 133.5
337 ± 223 117.7
273 ± 169 90.8
273 ± 170 90.8
267 ± 171 88.6
394 ± 318 125.5
373 ± 243 120.3
Equation 1
5
*In grams, mean ± SD. t Absolute error per kilogram actual birth weight in grams per kilogram.
curacy of estimates with increasing lapse time. In contrast, although the mean error for modified equations 4 and 5 did not differ statistically from zero, the percent mean error was between 1% and 2%, and the mean absolute error per kilogram actual birth weight exceeded 100 gm/kg for both. The accuracy of estimates was not stable over the range oflapse times for modified equation 4 nor over the range of birth weights for either modified equations 4 or 5.
Phase II-Model validation. One hundred sixtyseven cases fulfilled the study criteria for the validation phase. The descriptive statistics are presented in Table
II. Table V shows the overall accuracy of the modified equations. Modified equations 1,2, and 3 again proved superior to 4 and 5. The accuracy of individual estimates, as best expressed by absolute error and standardized absolute error, was larger for the modified
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745
Table VII. Validation phase-Accuracy of equations within birth weight segments Weight group (gm) 1000-2000 (n
=
12)
Absolute error* Standardized absolute errort 2000-3000 (n
= 69)
Absolute error* Standardized absolute errort 3000-3500 (n
=
34)
=
38)
=
14)
Absolute error* Standardized absolute errort 3500-4000 (n
Absolute error* Standardized absolute errort 4000-5000 (n
Absolute error* Standardized absolute errort
Equation 1
Equation
Equation 3
2
Equation 4
Equation
5
195 ± 152 117.3 (3.7)
193 ± 155 116.4 (3.8)
191 ± 149 115.8 (4.1)
370 ± 185 228.5 (17.6)
355 ± 185 218.8 (11.7)
251 ± 184 96.9 (-4.8)
252 ± 184 97.1 (-4.9)
250 ± 184 96.6 (-5.2)
339 ± 222 127.6 (-7.4)
332 :t 221 128.6 (- 5.3)
273 ± 194 85.7 (-5.3)
273 ± 195 85.8 (-5.4)
280 ± 192 87.9 (-6.2)
504 ± 246 158.7 (-10.6)
492 ± 238 154.7 (-12.7)
314 ± 238 83.5 (-2.8)
314 ± 243 83.4 (-2.7)
328 ± 260 87.3 (-2.6)
435 ± 307 116.3 (- 6.8)
526 :t 335 140.4 ( - 3.2)
272 ± 183 61.5(-1.7)
281 ± 174 63.7 (-1.4)
281 ± 157 64.0 (-1.0)
250 ± 197 56.8 (0.7)
326 ± 321 74.6 (0.6)
*In grams, mean ± SD. t Absolute error per kilogram actual birth weight in grams per kilogram. Percent mean error in parentheses.
Table VIII. Validation phase-Comparisons of new equations to their static counterpart for cases delivering within 1 week of ultrasonographic examination*
Error (gm) (mean ± SD)
Equation
2 3 4 5
Original Modified Original Modified Original Modified Original Modified Original Modified
-252 -140 -297 -141 -238 -144 -163 -61 -246 -163
± ± ± ± ± ± ± ± ± ±
316 318 318 319 324 326 446 450 530 532
% Error (mean ± SD)
Absolute error (gm)
(mean ± SD)
-7.6:t 12 -4.1 :t 12
333 :t 226 280 :t 202
-9.1 ± -4.1 ± -7.2 ± -4.2 ± -2.8:t -0.6:t -6.6:t -3.9:t
362 280 331 288 382 371 470 455
12 12 12 12 17 17 19 20
± ± :t :t ± ± ± :t
240 204 225 206 277 257 342 313
Maximum absolute error (gm)
Standardized absolute error (gm / kg) birth weight
957 883 990 886 940 878 948 882 1338 1199
110.4 100.0 120.0 100.0 109.7 102.3 126.6 135.7 155.8 162.0
*n = 48, mean birth weight 3017 gm, mean lapse time 3.1 :t 1.8 days. Error estimates expressed as negative numbers indicate underestimation of actual birth weight; positive numbers indicate overestimation.
equations 4 and 5 when compared with equations 1,2, and 3. The ability of the modified equations to maintain accuracy over the range of lapse times observed is presented in Table VI. For each modified equation, analysis of variance for differences among lapse time group segments failed to demonstrate differences for mean error, mean absolute error, or mean absolute error per kilogram birth weight (p > 0.05). In other words, increasing lapse time caused no deterioration in the accuracy of estimates. Table VII shows the data on the accuracy of estimates across the range of birth weights encountered. Equations 1, 2, and 3 were consistently accurate across the range of birth weight groups, with no significant differences noted for mean absolute error or mean ab-
solute error per kilogram birth weight (analysis of variance p > 0.05). A trend toward overestimating the weight of small infants as expressed by percent mean error was seen with equation 1 (p = 0.09) and equation 2 (p = 0.07) and was significant for equation 3 (p = 0.02). The estimates of equations 4 and 5 were not stable across weight groups for each measure of accuracy considered (p < 0.005). In Table VIII, the estimates from the original static equations are compared with the estimates from the modified equations for patients delivering within 1 week of examination. The new equations, which adjusted for a mean lapse time of 3.1 ± 1.8 days, were associated with a notable reduction in mean error, percent mean error, mean absolute error, and maximum observed error. For each equation the modification less-
746
Spinnato, Allen, and Mendenhall
September 1989 Am J Obstet Gynecol
Table IX. Validation phase- Percent of birth weight estimates noted within 50, 100, and 150 gm per kilogram actual birth weight (n = 167) Estimates (%) withm Eqootzon
50 gmlkg
JOO gmlkg
150 gmlkg
1 2 3 4 5
32.3 31.1 29.9 20.4 19.2
64.7 65.9 65.9 43.1 39.5
83.8 83.8 82.0 59.9 6Ll
ened the overall tendency to underestimate birth weight. The relative accuracy of each modified equation is shown in Table IX as the percent of each equation'S estimates that fall within ranges of absolute error per kilogram birth weight. The performance of equations 1, 2, and 3 were virtually identical to each other; 65% to 67% of the estimates fell within 100 gm/kg actual birth weight. The estimates of equations 4 and 5 were considerably less accurate.
Comment The remodeling of existing static equations to predict birth weight from remote ultrasonographic data was successfully accomplished. The accuracy of each equation's conversion was directly related to the accuracy of its original static estimate. The relative inaccuracy of the modified equations 4 and 5 is heralded by the less accurate predictions made by the parent static formulas (Table VIII). The accuracy of birth weight predictions of the modified equations 1,2, and 3 is remarkable and compares favorably to other studies of static formulas. Shepard, et aU reported that 54.8% and 50.7% of the estimates from equations 1 and 2, respectively, were within 100 gm/kg birth weight. Wars of et a1,3 reported four equations with percent of estimates within 100 gm/kg that ranged from 52% to 57%. Weiner et a1. 4 evaluated the use of eight formulas with preterm infants; the percent of estimates within 100 gm/kg ranged from 19% to 63%. In each of these studies the estimates were made within 48 to 72 hours of delivery. In this study 65% to 67% of the estimates were within 100 mg/kg birth weight. Warsof et a1. 3 reported the mean absolute error per kilogram birth weight to range from 104 to 125 gm/kg among four equations tested. The modified equations 1, 2, and 3 had mean absolute errors that ranged from 86 to 91 gm/kg. Equations 1 and 2 (from Hadlock et a1.') may offer advantages over our previously reported equation! as a result of improved accuracy across birth weight ranges. Hadlock et a1.'·6 reported 19 static formulas in which
the standard deviation of percent mean error ranged from ± 7.3% to 12.9%. Ott et a1.' observed a range from 13% to 18% for the same statistic among eight formulas. The same authors noted a range from ± 8.7% to 11.1 % among six other formulas." In this study, the standard deviation of percent error ranged from ± 10.1 % to 10.8% for the three modified formulas derived from Hadlock et a1. Shephard et aU reported the mean absolute error to be ± 343.4 and ± 349 gm for their equations 1 and 2 for all estimates, and a maximum absolute error observed of 1266 and 1099 gm, respectively, for each equation. The mean absolute error for the modified formulas 1 through 3 was <280 gm, and the maximum absolute error ranged from 962 to 1288 gm (Table V). The results of this study validate the concept of incorporating a lapse-time factor in equations to predict birth weight from remote ultrasonographic data. Weight estimates were improved even when birth occurred within 1 week of ultrasonographic examination. The accuracy of the estimates was maintained across the full range of lapse times observed. When lapse time exceeded 35 days, unacceptable deterioration of accuracy is noted (our unpublished observations). The use of these equations when lapse time exceeds 35 days is discouraged. Although the number of modified equations is limited, this concept probably could be used to remodel virtually any static formula. These modified equations predict growth subsequent to ultrasonographic examination on the basis of the mean growth observed in our population. Although no attempt was made to exclude growth-retarded or macrosomic infants during model development, the use of the modified equations for pregnancies at risk for excess or subnormal fetal growth may result in significant overestimation or underestimation. Furthermore, these equations have been tested only as birth weight predictors, and their accuracy remote from delivery for interval weight estimations is not suggested, implied, or tested. Rates of fetal growth remote from delivery may differ from that in the 35 days before delivery. The clinical use of the modified equations is straightforward. The weight estimate determined by the static parent formula is coupled with the lapse time that has occurred, and a birth weight estimate is determined by the modified form of that equation. The results achieved in this study and the parameter coefficients determined may be specific to our population. Full validation of the modified equations requires testing outside our population. Although the concept of lapse-time factoring may be confirmed by others, the coefficients for the equations' parameters may differ in other populations. We thank A. L. Bower, RN, RDMS, P. D. Driskell, RN, P. Z. Walters, RN, and Maggie Steptoe, MS, for
Birth weight prediction
Volume 161 Number 3
technical assistance, and P. C. Wagner, BSN, RNC, for help with data collection. REFERENCES 1. Spin nato JA, Allen RD, Mendenhall HW. Birth weight prediction from remote ultrasound examination. Obstet GynecoI1988;71:893-8. 2. Shepard M], Richards VA, Berkowitz RL, WarsofSL, Hobbins ]C. An evaluation of two equations for predicting fetal weight by ultrasound. AM] OBSTET GYNECOL 1982;142:4754. 3. Warsof SL, Wolf P, Couleban], Queenan ]T. Comparison of fetal weight estimation formulas with and without head measurements. Obstet Gynecol 1986;67:569-73.
4. Weiner CP, Sabbagha RE, Vias rub N, Socol ML. Ultrasound fetal weight prediction: role of He and FL. Obstet GynecoI1985;65:812-7. 5. Hadlock FP, Harrist RB, Sharman RS, Deter RL, Park SK. Estimation of fetal weight with the use of head, body, and femur measurements-a prospective study. AM] OBSTET GYNECOL 1987;151:333-7. 6. Hadlock FP, Harrist RB, Carpenter R], Deter RL, Park SK. Sonographic estimation of fetal weight. Radiology 1984; 150:535-40. 7. Ott W], Doyle S, Flamm S. Accurate ultrasonic estimation of fetal weight. Am] Perinatol 1985;2: 178-82. 8. Ott W], Doyle S, Flamm S, Wittman J. Accurate ultrasonic estimation of fetal weight. Am] Perinatol 1986;3:307-10.
Dating the early pregnancy by sequential appearance of embryonic structures Wendy B. Warren, MD, Han Timor-Tritsch, MD, David B. Peisner, MD, Sashi Raju, and Mortimer G. Rosen, MD New York, New York A total of 97 transvaginal scans were performed from 4 to 12 weeks' gestation in normal and accurately dated gestations. The sequential appearance of six structures were examined: (1) the gestational sac only was present during week 4; (2) the yolk sac appeared in week 5; (3) the fetal pole with detectable heart motion was first seen in week 6; (4) the single unpartitioned ventricle in the brain marked week 7; (5) the falx cerebri appeared during week 9; and (6) the appearance and the disappearance of the physiologic midgut herniation were seen in week 8 and week 11, respectively. Inasmuch as the time in gestation at which these structures appear characterizes the gestational age more than any measurement at this age, we propose a practical method to determine the correct gestational age in early first-trimester pregnancy. (AM J OBSTET GYNECOl 1989;161 :747-53.)
Key words: Transvaginal ultrasonography, embryologic development, pregnancy, first trimester Pregnancy dating is an important consideration in several diagnostic and therapeutic processes in perinataology. The later in pregnancy the "dating" process is performed, the larger the confidence limits become. l Measurement of the crown-rump length by ultrasonography is considered to be the most accurate method to establish gestational age in the first trimester. However, crown-rump length is measurable by abdominal
From the Department of Obstetrics and Gynecology, and the DivisIOn of Ultrasound, Columbia University College of Physicians and Surgeons. Presented at the Ninth Annual Meeting of the Society of Perinatal Obstetricians, New Orleans, Louisiana, February 2-4, 1989. Reprint requests: [Ian E. Timor, MD, Department of Obstetrics and Gynecology, Columbia Presbyterian Medical Center, 622 W. 168th St., Room 1212, New York, NY 10032. 616114092
ultrasonography only after 6Y2 weeks' gestation!-5 The accuracy of early first-trimester crown-rump length measurements by abdominal ultrasonography has been estimated to be ± 5 days at best. 6 Attempts have been made to date the very early gestation by measuring the size of the gestational sac. 1. 7 However this was not widely accepted as a useful clinical tool because the confidence limits of these measurements are ± 12 days and the size of the sac varies because of variable influences of the bladder and scanning plane. l In earlier publications we described the ability of a 6.5 MHz transvaginal transducer probe to image embryonic and extraembryonic structures in the first trimester. 8 In early anatomic studies of human embryos, the structures of developing embryos have been used as a method to determine their postconceptional age. 9 • lO We hypothesize that the sequential appearance
747
Mobile, Alabama Multiple linear regression by the least squares method was used to remodel five existing static equations to permit birth weight estimates from remote ultrasonographic parameters. By incorporating lapse time (examination-to-delivery interval), the new equations be used to estimate birth weight 0 to 35 days after ultrasonographic examination. For each model, R2 approached 1.0. The generated equations were tested on 167 non model cases. Among the three best equations, 65% to 67% of estimates were within 100 mg/kg birth weight. The mean absolute error ranged from 86 to 91 gm/kg.With a mean lapse time of 16.8 ± 11 days, the accuracy of birth weight estimates equaled or exceeded that reported for existing static formulas. The accuracy of the estimates was maintained across the entire range of lapse times and birth weights observed. In intrapartum situations when ultrasonography is unavailable or technically difficult, birth weight can be estimated from remote ultrasound parameters. (AM J OasTET GVNECOL 1989;161 :742-7.)
can
Key words: Ultrasonography, estimated fetal weight
In a previous report' we described the development of an equation to predict birth weight from ultrasonographic examinations. By incorporating the interval from ultrasonographic examination to delivery (lapse time), the model predicted birth weight based on ultrasonographic measurements taken as early as 35 days before delivery. The rationale for the model was based on the hypothesis that ultrasonographic measurements of fetal dimensions at a point in gestation could be coupled with elapsed time to mathematically predict a birth weight based on observed growth in a population. We extrapolated this concept to five existing formulas by including a lapse-time modifier in the structure of these existing equations. The lapse-time modifier for each equataion was determined individually from model building that analyzed the initial static estimate and the lapse time that occurred versus actual birth weight.
Material and methods This study had two phases. In phase I, model building generated new equations based on five static equa-
From the Department of ObstetriCs and Gynecology, Unzversity of South Alabama Medzeal Center. Presented at the Ninth Annual Meeting of the Soaety of Perinatal Obstetricians, New Orleans, Louisiana, February 2-4, 1989. Reprint requests: Joseph A. Spinnato, MD, Division of MaternalFetal Medicine, Department of Obstetrics and Gynecology, University of Louisvzlie, Louisvzlie, KY 40292. 6/6114093
742
tions. In Phase II, the new equations were tested on cases other than model cases. Phase I-Model development. The records of all patients seen in the Perinatal Unit of the University of South Alabama Medical Center between October 1984 and September 1986 for obstetric ultrasonographic evaluation were reviewed. The patient population was a racially mixed (55% black), low-income clinic population. Patients were included in the study if they met the following criteria: (1) the pregnancy was a singleton gestation; (2) the biparietal diameter, occipitofrontal diameter, femur length, transverse and anteroposterior diameters of the fetal abdomen had been measured by ultrasonography; (3) data on the outcome of the delivery were available; (4) the interval (lapse time) from ultrasonographic ex~mination to delivery was :5':35 days; and (5) birth weight was :55000 grams. All ultrasonographic examinations were performed by one of three experienced ultrasonographers using a linear array real-time scanner (ADR Model 4000) with a 3.5 MHz transducer. As in our previous study,' standard imaging and measurement techniques were used. Model generation and all statistical methods were performed with the Statistical Analysis System (SAS) and the IBM-434 I-II mainframe computer of the University of South Alabama. Multiple linear regression using the least squares method was used to construct the models. Using the five formulas (Table I), the fetal weight estimates determined on the day of ultrasonographic examination (in logarithmic form) and the
Birth weight prediction
Volume 161 Number 3
Table I. Static equations Author
EquatIOn
1. Hadlock et al: Log (weight) = 1.326 - 0.00326 AC X FL + 0.0107 HC + 0.0438 AC + 0.158 FL 2. Hadlock et al. 6 Log (weight) = 1.5662 - 0.0108 HC + 0.0468 AC + 0.171 FL + 0.00034 HC2 - 0.003685 (AC x FL) 3. Hadlock et al. 6 Log (weight) = 1.5115 + 0.0436 AC + 0.1517 FL - 0.00321 (AC x FL) + 0.0006923 (BPD x HC) 4. Ott et aU Log (weight) = 0.04355 HC + 0.05394 AC - 0.0008582 HC x AC + 1.2594 (FLI AC) 2.0661 5. Shepard et al? Log (weight) = -1.7492 + 0.166 (BPD) + 0.046 (AC) - 2.646 (AC x BPD)11000 AC, Abdominal circumference; FL, femur length; HC, head circumference in centimeters; BPD, biparietal diameter.
lapse time observed were analyzed versus the logarithm of actual birth weight. For each equation the constructed model generated a lapse-time modifier. After model development, the modified equations were tested with the model cases. The mean error (estimated - actual birth weight), mean absolute error (absolute value of estimated - actual birth weight), and the standardized absolute error (absolute error/kilogram birth weight) were determined for each modified equation. The equations were examined for accuracy across the range of birth weights and lapse times observed. To allow comparisons to previous reports, the observed error was converted to percentage error by the formula ([predicted weight - actual weight]/ actual weight X 100) to generate a mean ± SD of percent error. The correlation coefficient (Pearson's r) of estimated versus actual birth weight was determined, and the percent of estimates within 50, 100, and 150 gm/kg of actual birth weight was calculated. One- and two-way analyses of variance were used to test for differences among means. Tukey's studentized range test was used to evaluate differences among group means. The significance level was set at alpha = 0.05. Phase II-Model validation. The modified equations were validated by use of different cases from those used to develop the models. Patients seen in the Perinatal Unit for fetal ultrasonographic evaluation from October 1986 to August 1987 were reviewed for inclusion in the validation phase of the study. The inclusion criteria and ultrasonographic method were unchanged from phase 1. Modified equations developed in phase I were used to generate birth weight estimates that were compared to actual birth weight. Accuracy of the estimates was determined as outlined in phase 1.
743
Table II. Descriptive statistics of included cases for both phases of the study*
Vanable
Examination gestational age (wk) Birth gestational age (wk) Lapse time (days) Femur length (mm) Abdominal circumference (mm) Head circumference (mm) Birth weight (gm)
Model development (N = 245)
Validation (N = 167)
35.4 ± 3.2 (25-42) 37.6 ± 2.9 (28-44) 15.7 ± 10.7 (0-35) 68.9 ± 6.7 (46-82) 302.5 ± 32.7 (188-388) 314.4 ± 21.2 (243-356) 2978 ± 680 (1134-4876)
34.7 ± 2.9 (30-42) 37.1 ± 2.8 (30-44) 16.8 ± 11.0 (0-35) 68.0 ± 6.1 (55-82) 302.5 ± 35.0 (207-396) 310.7 ± 19.0 (261-364) 3074 ± 713 1375-4870)
*Data are presented as mean ± SD, with range in parentheses.
Table III. Modified equations 1. Log [birth weight) 0.0043 (LT) 2. Log [birth weight) 0.0043 (LT) 3. Log [birth weight] 0.0043 (LT) 4. Log [birth weight) 0.0034 (LT) 5. Log [birth weight) 0.0047 (LT)
= 1.0009 [Log initial weight)
+
= 1.0009 [Log initial weight)
+
= 1.0 [Log initial weight)
+
= 1.001 [Log initial weight) =
+
0.9994 [Log initial weight) +
Birth weight in grams. LT, Lapse time in days.
Phase I-Model development. From 259 ultrasonographic examinations for which delivery outcome was known, 245 examinations and paired delivery outcomes fulfilled the study criteria. Table II presents the descriptive statistics of these cases. A model to predict birth weight from remote ultrasonographic examination was generated for each of the five equations. For each model, R2 approached 1.0. In each, the intercept did not differ significantly from zero and was deleted from the modified equation (Table III). The coefficients for each model's parameters are described in Table IV. Both lapse time and the logarithm of the initial fetal weight estimate contributed significantly to the birth weight predictions, p s 0.000 I. The modified equations were tested on the model cases. Modified equations 1, 2, and 3 performed quite similarly. Remarkably accurate birth weight estimates were noted. For each estimate, the mean error was very small and did not differ statistically from zero. The percent mean error was < 1%. The mean absolute error per kilogram actual birth weight was less than 100 gm/kg. There was no significant difference in the ac-
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September 1989 Am J Obstet Gynecol
Table IV. Description of models Model
LT coefficient
SE
Zero coefficient
SE
R2
0.00428326 0.00429440 0.00434518 0.00344469 0.00473645
0.0003 0.0003 0.0003 0.0004 0.0004
1.00086433 1.00293973 1.00002378 1.00112376 0.99972076
0.0016 0.0016 0.0016 0.0022 0.0025
0.9998 0.9998 0.9998 0.9996 0.9995
I
1 2 3 4 5
LT coefficient, Lapse-time coefficient; SE, standard error of the estimate; Zero coefficient, coefficient of the log of the original
static estimate.
Table V. Validation phase-Overall performance of the new equations in descending order of accuracy* Error (gm) (mean ± SD)
Equation
-112 -112 -118 -187 -154
1 2 3 4 5
± ± ± ± ±
314 315 319 426 468
% Error
(mean ± SD) -3.6 -3.6 -3.8 -5.4 -4.6
± ± ± ± ±
10.7 10.8 10.8 15.2 16.1
Absolute error (gm)
(mean ± SD)
Maximum absolute error (gm)
Standardized absolute error (gmt kg) birth weight
rt
± ± ± ± ±
1175 1197 1288 1090 1296
90.0 90.2 91.3 132.7 138.5
0.91 0.91 0.91 0.84 0.82
267 268 272 389 410
198 199 202 254 273
*Lapse time mean = 16.8 ± 11 days, range 0 to 35 days. Error estimates expressed as negative numbers indicate underestimation of actual birth weight; positive numbers indicate overestimation. tPearson's correlation coefficient for estimated versus actual birth weight.
Table VI. Validation phase-Accuracy of birth weight estimates within segments of lapse time Lapse time (days) s7 (n
= 48)
Absolute error* Standardized absolute errort 8-14 (n
= 22)
Absolute error* Standardized absolute errort 15-21 (n
= 30)
22-28 (n
= 35)
29-35 (n
= 32)
Absolute error* Standardized absolute errort Absolute error* Standardized absolute errort Absolute error* Standardized absolute errort
Equation 2
Equation 3
Equation 4
EquatIOn
280 ± 202 100.0
280 ± 204 100.0
288 ± 206 102.3
371 ± 257 135.7
455 ± 313 162.0
209 ± 174 66.3
213 :±: 174 67.3
226 ± 169 71.6
382 ± 201 123.0
424 ± 220 136.9
328 ± 254 102.7
329 :±: 255 102.9
337 ± 268 105.3
420 ± 230 141.5
451 ± 311 146.0
230 ± 166 79.7
230 ± 167 80.0
229 ± 170 79.3
388 ± 242 133.5
337 ± 223 117.7
273 ± 169 90.8
273 ± 170 90.8
267 ± 171 88.6
394 ± 318 125.5
373 ± 243 120.3
Equation 1
5
*In grams, mean ± SD. t Absolute error per kilogram actual birth weight in grams per kilogram.
curacy of estimates with increasing lapse time. In contrast, although the mean error for modified equations 4 and 5 did not differ statistically from zero, the percent mean error was between 1% and 2%, and the mean absolute error per kilogram actual birth weight exceeded 100 gm/kg for both. The accuracy of estimates was not stable over the range oflapse times for modified equation 4 nor over the range of birth weights for either modified equations 4 or 5.
Phase II-Model validation. One hundred sixtyseven cases fulfilled the study criteria for the validation phase. The descriptive statistics are presented in Table
II. Table V shows the overall accuracy of the modified equations. Modified equations 1,2, and 3 again proved superior to 4 and 5. The accuracy of individual estimates, as best expressed by absolute error and standardized absolute error, was larger for the modified
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745
Table VII. Validation phase-Accuracy of equations within birth weight segments Weight group (gm) 1000-2000 (n
=
12)
Absolute error* Standardized absolute errort 2000-3000 (n
= 69)
Absolute error* Standardized absolute errort 3000-3500 (n
=
34)
=
38)
=
14)
Absolute error* Standardized absolute errort 3500-4000 (n
Absolute error* Standardized absolute errort 4000-5000 (n
Absolute error* Standardized absolute errort
Equation 1
Equation
Equation 3
2
Equation 4
Equation
5
195 ± 152 117.3 (3.7)
193 ± 155 116.4 (3.8)
191 ± 149 115.8 (4.1)
370 ± 185 228.5 (17.6)
355 ± 185 218.8 (11.7)
251 ± 184 96.9 (-4.8)
252 ± 184 97.1 (-4.9)
250 ± 184 96.6 (-5.2)
339 ± 222 127.6 (-7.4)
332 :t 221 128.6 (- 5.3)
273 ± 194 85.7 (-5.3)
273 ± 195 85.8 (-5.4)
280 ± 192 87.9 (-6.2)
504 ± 246 158.7 (-10.6)
492 ± 238 154.7 (-12.7)
314 ± 238 83.5 (-2.8)
314 ± 243 83.4 (-2.7)
328 ± 260 87.3 (-2.6)
435 ± 307 116.3 (- 6.8)
526 :t 335 140.4 ( - 3.2)
272 ± 183 61.5(-1.7)
281 ± 174 63.7 (-1.4)
281 ± 157 64.0 (-1.0)
250 ± 197 56.8 (0.7)
326 ± 321 74.6 (0.6)
*In grams, mean ± SD. t Absolute error per kilogram actual birth weight in grams per kilogram. Percent mean error in parentheses.
Table VIII. Validation phase-Comparisons of new equations to their static counterpart for cases delivering within 1 week of ultrasonographic examination*
Error (gm) (mean ± SD)
Equation
2 3 4 5
Original Modified Original Modified Original Modified Original Modified Original Modified
-252 -140 -297 -141 -238 -144 -163 -61 -246 -163
± ± ± ± ± ± ± ± ± ±
316 318 318 319 324 326 446 450 530 532
% Error (mean ± SD)
Absolute error (gm)
(mean ± SD)
-7.6:t 12 -4.1 :t 12
333 :t 226 280 :t 202
-9.1 ± -4.1 ± -7.2 ± -4.2 ± -2.8:t -0.6:t -6.6:t -3.9:t
362 280 331 288 382 371 470 455
12 12 12 12 17 17 19 20
± ± :t :t ± ± ± :t
240 204 225 206 277 257 342 313
Maximum absolute error (gm)
Standardized absolute error (gm / kg) birth weight
957 883 990 886 940 878 948 882 1338 1199
110.4 100.0 120.0 100.0 109.7 102.3 126.6 135.7 155.8 162.0
*n = 48, mean birth weight 3017 gm, mean lapse time 3.1 :t 1.8 days. Error estimates expressed as negative numbers indicate underestimation of actual birth weight; positive numbers indicate overestimation.
equations 4 and 5 when compared with equations 1,2, and 3. The ability of the modified equations to maintain accuracy over the range of lapse times observed is presented in Table VI. For each modified equation, analysis of variance for differences among lapse time group segments failed to demonstrate differences for mean error, mean absolute error, or mean absolute error per kilogram birth weight (p > 0.05). In other words, increasing lapse time caused no deterioration in the accuracy of estimates. Table VII shows the data on the accuracy of estimates across the range of birth weights encountered. Equations 1, 2, and 3 were consistently accurate across the range of birth weight groups, with no significant differences noted for mean absolute error or mean ab-
solute error per kilogram birth weight (analysis of variance p > 0.05). A trend toward overestimating the weight of small infants as expressed by percent mean error was seen with equation 1 (p = 0.09) and equation 2 (p = 0.07) and was significant for equation 3 (p = 0.02). The estimates of equations 4 and 5 were not stable across weight groups for each measure of accuracy considered (p < 0.005). In Table VIII, the estimates from the original static equations are compared with the estimates from the modified equations for patients delivering within 1 week of examination. The new equations, which adjusted for a mean lapse time of 3.1 ± 1.8 days, were associated with a notable reduction in mean error, percent mean error, mean absolute error, and maximum observed error. For each equation the modification less-
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Spinnato, Allen, and Mendenhall
September 1989 Am J Obstet Gynecol
Table IX. Validation phase- Percent of birth weight estimates noted within 50, 100, and 150 gm per kilogram actual birth weight (n = 167) Estimates (%) withm Eqootzon
50 gmlkg
JOO gmlkg
150 gmlkg
1 2 3 4 5
32.3 31.1 29.9 20.4 19.2
64.7 65.9 65.9 43.1 39.5
83.8 83.8 82.0 59.9 6Ll
ened the overall tendency to underestimate birth weight. The relative accuracy of each modified equation is shown in Table IX as the percent of each equation'S estimates that fall within ranges of absolute error per kilogram birth weight. The performance of equations 1, 2, and 3 were virtually identical to each other; 65% to 67% of the estimates fell within 100 gm/kg actual birth weight. The estimates of equations 4 and 5 were considerably less accurate.
Comment The remodeling of existing static equations to predict birth weight from remote ultrasonographic data was successfully accomplished. The accuracy of each equation's conversion was directly related to the accuracy of its original static estimate. The relative inaccuracy of the modified equations 4 and 5 is heralded by the less accurate predictions made by the parent static formulas (Table VIII). The accuracy of birth weight predictions of the modified equations 1,2, and 3 is remarkable and compares favorably to other studies of static formulas. Shepard, et aU reported that 54.8% and 50.7% of the estimates from equations 1 and 2, respectively, were within 100 gm/kg birth weight. Wars of et a1,3 reported four equations with percent of estimates within 100 gm/kg that ranged from 52% to 57%. Weiner et a1. 4 evaluated the use of eight formulas with preterm infants; the percent of estimates within 100 gm/kg ranged from 19% to 63%. In each of these studies the estimates were made within 48 to 72 hours of delivery. In this study 65% to 67% of the estimates were within 100 mg/kg birth weight. Warsof et a1. 3 reported the mean absolute error per kilogram birth weight to range from 104 to 125 gm/kg among four equations tested. The modified equations 1, 2, and 3 had mean absolute errors that ranged from 86 to 91 gm/kg. Equations 1 and 2 (from Hadlock et a1.') may offer advantages over our previously reported equation! as a result of improved accuracy across birth weight ranges. Hadlock et a1.'·6 reported 19 static formulas in which
the standard deviation of percent mean error ranged from ± 7.3% to 12.9%. Ott et a1.' observed a range from 13% to 18% for the same statistic among eight formulas. The same authors noted a range from ± 8.7% to 11.1 % among six other formulas." In this study, the standard deviation of percent error ranged from ± 10.1 % to 10.8% for the three modified formulas derived from Hadlock et a1. Shephard et aU reported the mean absolute error to be ± 343.4 and ± 349 gm for their equations 1 and 2 for all estimates, and a maximum absolute error observed of 1266 and 1099 gm, respectively, for each equation. The mean absolute error for the modified formulas 1 through 3 was <280 gm, and the maximum absolute error ranged from 962 to 1288 gm (Table V). The results of this study validate the concept of incorporating a lapse-time factor in equations to predict birth weight from remote ultrasonographic data. Weight estimates were improved even when birth occurred within 1 week of ultrasonographic examination. The accuracy of the estimates was maintained across the full range of lapse times observed. When lapse time exceeded 35 days, unacceptable deterioration of accuracy is noted (our unpublished observations). The use of these equations when lapse time exceeds 35 days is discouraged. Although the number of modified equations is limited, this concept probably could be used to remodel virtually any static formula. These modified equations predict growth subsequent to ultrasonographic examination on the basis of the mean growth observed in our population. Although no attempt was made to exclude growth-retarded or macrosomic infants during model development, the use of the modified equations for pregnancies at risk for excess or subnormal fetal growth may result in significant overestimation or underestimation. Furthermore, these equations have been tested only as birth weight predictors, and their accuracy remote from delivery for interval weight estimations is not suggested, implied, or tested. Rates of fetal growth remote from delivery may differ from that in the 35 days before delivery. The clinical use of the modified equations is straightforward. The weight estimate determined by the static parent formula is coupled with the lapse time that has occurred, and a birth weight estimate is determined by the modified form of that equation. The results achieved in this study and the parameter coefficients determined may be specific to our population. Full validation of the modified equations requires testing outside our population. Although the concept of lapse-time factoring may be confirmed by others, the coefficients for the equations' parameters may differ in other populations. We thank A. L. Bower, RN, RDMS, P. D. Driskell, RN, P. Z. Walters, RN, and Maggie Steptoe, MS, for
Birth weight prediction
Volume 161 Number 3
technical assistance, and P. C. Wagner, BSN, RNC, for help with data collection. REFERENCES 1. Spin nato JA, Allen RD, Mendenhall HW. Birth weight prediction from remote ultrasound examination. Obstet GynecoI1988;71:893-8. 2. Shepard M], Richards VA, Berkowitz RL, WarsofSL, Hobbins ]C. An evaluation of two equations for predicting fetal weight by ultrasound. AM] OBSTET GYNECOL 1982;142:4754. 3. Warsof SL, Wolf P, Couleban], Queenan ]T. Comparison of fetal weight estimation formulas with and without head measurements. Obstet Gynecol 1986;67:569-73.
4. Weiner CP, Sabbagha RE, Vias rub N, Socol ML. Ultrasound fetal weight prediction: role of He and FL. Obstet GynecoI1985;65:812-7. 5. Hadlock FP, Harrist RB, Sharman RS, Deter RL, Park SK. Estimation of fetal weight with the use of head, body, and femur measurements-a prospective study. AM] OBSTET GYNECOL 1987;151:333-7. 6. Hadlock FP, Harrist RB, Carpenter R], Deter RL, Park SK. Sonographic estimation of fetal weight. Radiology 1984; 150:535-40. 7. Ott W], Doyle S, Flamm S. Accurate ultrasonic estimation of fetal weight. Am] Perinatol 1985;2: 178-82. 8. Ott W], Doyle S, Flamm S, Wittman J. Accurate ultrasonic estimation of fetal weight. Am] Perinatol 1986;3:307-10.
Dating the early pregnancy by sequential appearance of embryonic structures Wendy B. Warren, MD, Han Timor-Tritsch, MD, David B. Peisner, MD, Sashi Raju, and Mortimer G. Rosen, MD New York, New York A total of 97 transvaginal scans were performed from 4 to 12 weeks' gestation in normal and accurately dated gestations. The sequential appearance of six structures were examined: (1) the gestational sac only was present during week 4; (2) the yolk sac appeared in week 5; (3) the fetal pole with detectable heart motion was first seen in week 6; (4) the single unpartitioned ventricle in the brain marked week 7; (5) the falx cerebri appeared during week 9; and (6) the appearance and the disappearance of the physiologic midgut herniation were seen in week 8 and week 11, respectively. Inasmuch as the time in gestation at which these structures appear characterizes the gestational age more than any measurement at this age, we propose a practical method to determine the correct gestational age in early first-trimester pregnancy. (AM J OBSTET GYNECOl 1989;161 :747-53.)
Key words: Transvaginal ultrasonography, embryologic development, pregnancy, first trimester Pregnancy dating is an important consideration in several diagnostic and therapeutic processes in perinataology. The later in pregnancy the "dating" process is performed, the larger the confidence limits become. l Measurement of the crown-rump length by ultrasonography is considered to be the most accurate method to establish gestational age in the first trimester. However, crown-rump length is measurable by abdominal
From the Department of Obstetrics and Gynecology, and the DivisIOn of Ultrasound, Columbia University College of Physicians and Surgeons. Presented at the Ninth Annual Meeting of the Society of Perinatal Obstetricians, New Orleans, Louisiana, February 2-4, 1989. Reprint requests: [Ian E. Timor, MD, Department of Obstetrics and Gynecology, Columbia Presbyterian Medical Center, 622 W. 168th St., Room 1212, New York, NY 10032. 616114092
ultrasonography only after 6Y2 weeks' gestation!-5 The accuracy of early first-trimester crown-rump length measurements by abdominal ultrasonography has been estimated to be ± 5 days at best. 6 Attempts have been made to date the very early gestation by measuring the size of the gestational sac. 1. 7 However this was not widely accepted as a useful clinical tool because the confidence limits of these measurements are ± 12 days and the size of the sac varies because of variable influences of the bladder and scanning plane. l In earlier publications we described the ability of a 6.5 MHz transvaginal transducer probe to image embryonic and extraembryonic structures in the first trimester. 8 In early anatomic studies of human embryos, the structures of developing embryos have been used as a method to determine their postconceptional age. 9 • lO We hypothesize that the sequential appearance
747