Derivation of combination birth‐weight prediction equations to identify fetal macrosomia

We agree with Hart et al.1 that fetal macrosomia is best predicted using a combination of fetal ultrasound measurements and maternal characteristics. We have advocated this approach previously2-4 and demonstrated its superiority to methods that rely on ultrasonographic fetal biometry or maternal characteristics alone2, 5. However, despite our agreement with their general conclusions, they used highly questionable methods that violate accepted practices. In their regression analyses, head circumference is calculated directly from biparietal diameter (BPD) and occipitofrontal diameter, and abdominal circumference (AC) directly from abdominal transverse diameter and abdominal anteroposterior diameter. High levels of multicollinearity result when predictor variables are derived from other predictors, as was done here; this can lead to significant modeling errors6. Stepwise regression is also notorious for generating incorrect formulae6. A far better approach is to combine stepwise methods with theory-guided variable selection, then cross-validate the findings with multiple samples of unrelated newborns6, 7. Because all the fetuses used to derive the present formula were macrosomic (birth weight 4000–5050 g), the present equation is optimized to predict fetal weights ≥ 4000 g. Thus, the primary evaluation sample (birth weight 4000–4900 g) grossly underestimates the actual prediction errors that will occur in clinical practice, where the great majority of fetuses have birth weights in the range for which the equation is not optimized (< 4000 g). This bias renders it impossible to reconcile the current findings with the very extensive prior literature on birth-weight prediction8. To their credit, the authors also tested their formula on fetuses with birth weights of 3500–3999 g; the mean error and mean absolute prediction error were 4.15 and 10.28%, respectively. These results are poor but still remain overly optimistic, because practitioners regularly encounter fetuses with term birth weights below 3500 g (the mean for term birth weight is substantially lower). This constitutes a severe limitation, as the present formula is only clinically useful after having determined—by independent means and with sufficient confidence—that a fetus is, in fact, macrosomic. But this is, after all, the reason that most such ultrasonographic studies are performed. The positive predictive value of the proposed new formula for predicting fetal macrosomia is only 32%. Previously, we routinely achieved positive predictive values exceeding 50% using equations that combine maternal characteristics with fetal ultrasonographic measurements obtained within 11 weeks of delivery (over a much wider birth-weight range of 2285–4850 g)2. By using our previously derived combination equation that incorporates fetal ultrasonographic biometric information (AC, BPD), maternal characteristics (height, weight at 26 weeks of pregnancy, rate of third-trimester weight gain, parity) and gestational age, fetal macrosomia can be predicted with up to 75% sensitivity, 93% specificity, 67% positive predictive value, and 95% negative predictive value, with a likelihood ratio of 10.3 and an overall classification accuracy (macrosomic vs. non-macrosomic) of 90%2. The present formula is much more limited in its clinical utility, far less accurate, and can be used only within 7 days of delivery. Clinicians can intervene to prevent fetal macrosomia only if it can be predicted long before the final week of pregnancy. This requires sophisticated prediction methods, such as the algorithmic system that we have previously developed to accurately predict fetal macrosomia beginning from the start of the third trimester2, 4, 9, 10. We disclose that we are the co-inventors of the birth-weight prediction algorithms described in the issued United States Patent entitled ‘Methods, systems, and computer program products for estimating fetal weight at birth and risk of macrosomia’ (US Patent No. 6 695 780; issued February 24, 2004), the issued Australian Patent entitled ‘Estimating fetal birth weight and risk of macrosomia’ (Australia Patent No. 2 003 287 084; accepted November 21, 2006), and the issued Canadian Patent entitled ‘Methods, systems, and computer program products for estimating fetal weight at birth and risk of macrosomia’ (Canada Patent No. CA 2 501 763; accepted September 1, 2009), as well as similar patents pending in Europe, in addition to being shareholders in the United States corporations Algorithmic Bioscience Inc. and Biomedical Decision Support Corporation. G. G. Nahum*, H. Stanislaw , * Department of Obstetrics and Gynecology, Uniformed Services University of the Health Sciences, Bethesda, MD, USA, Department of Psychology, California State University, Stanislaus, 1 University Circle, Turlock, CA 95382, USA

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