In this article, we presented a new, flexible, sex-specific model for fetal weight for gestational age, and systematically compared the model to other proposed approaches. We established that at most gestational ages, the choice of model does not have a meaningful impact on the median estimates of fetal weight for gestational age, insomuch as the models’ 95% pointwise confidence bands have a large degree of overlap. However, the greater accuracy of estimates of weight-for-gestational-age medians at late term of the proposed model is important, because information on fetal growth at post-term ages may inform clinical decision-making on induction of labour. Overestimation of the median is likely to lead to an overestimation of the SGA threshold as well, which would produce an overestimation of the number of pregnancies with abnormal fetal growth. This being said, due to the quickly diminishing number of data points after 40 completed weeks, obtaining low-variance estimates at very late ages becomes difficult. While focusing on the estimation of the 10th percentile would be valuable, larger sample sizes than are currently available would be needed to obtain reasonable accuracy. Estimation of the median weight for gestational age is nevertheless useful, since an understanding of normal fetal growth is needed to be able to define and identify abnormal growth.
The differences between median estimates from the different methods before late term remain small and are therefore unlikely to be of clinical significance. Therefore, the selection process can safely be guided by the model-specific features that make a given model best suited to the underlying characteristics or objectives of a study. For instance, Hooper et al. (2002)
proposed a way to isolate the measurement error from the latent weight component of estimated fetal weight, as to allow for the derivation of latent weight percentiles. The proposed model also presents several advantages. Its flexibility, in comparison to polynomial regression models for instance, makes it an obvious candidate for modelling growth. Its parsimony also makes it very appealing. Further it readily offers a concise and straightforward parametrization of variance and covariance. The mixed spline regression model is commonly taught in statistics and epidemiology programs, and scholars are very familiar with its formulation, implications and limitations. It has become a very popular approach to handle non-linear relationships, such as the one between gestational age and fetal weight. For the first time, this standard approach has been systematically compared to methods especially tailored to the problem of fetal growth. Spline regression methods are readily available in most software packages (as compared to some of the specialized approaches used previously). The practical implication of this work for epidemiologists and statisticians interested in modeling fetal growth is that these models mostly provide similar estimates of median weight-for-gestational-age, so that modeling strategies may be selected based on other criteria such as ease of use.
In general, fitting a model to a dataset in which the response variable has been transformed may produce results that are hard to interpret. For instance, fixed-effect coefficient values will not be expressible on the original scale and the retransformed mean will be biased. (Duan, 1983
) However, percentile estimators, which are generally of greater relevance in the study of fetal growth and identification of intrauterine growth restriction, (McIntire et al., 1999
) still remain unbiased. In this context, we are more interested in the estimation of median weight for gestational age than in interpreting the coefficients themselves.
Estimates of individual weight-for-gestational-age trajectories are strongly affected by measurement error in estimated fetal weight, which results from the use of a formula to estimate fetal weight from ultrasound biometric measurements, as well as operator-error at the time of ultrasound. Fortunately, this source of error has been shown to be mostly non-systematic (Dudley, 2005
), so that while individual-level estimation of fetal weight may be error-prone, population medians should not be greatly affected. Uncertainty in gestational age is a second source of measurement error in longitudinal modeling of fetal weight. However, in our data, the gestational age estimates were validated by the use of both the ultrasound and the LNMP estimates, providing confidence that the measurement error on gestational age remains small on average.
Two different kinds of weight data are being used in the model-fitting process, namely ultrasound-based estimates and precise measurements made at birth. We would expect the coefficient of variation for ultrasound-based estimates to be higher, due to measurement error. Model variance estimates may also be affected. However, the Box-Cox transformation dampens changes in variance, irrespective of their patterns. Therefore, since we fitted models on the transformed scale, it seems unlikely that the median fits were significantly biased by the reduced variance of birth weight data.
Most models proposed to date were only adjusted for the influence of gestational age on fetal weight. It is worth considering if other adjustment terms in addition to sex should be considered. Parity, ethnicity and maternal BMI have all been shown to be significant predictors of fetal weight (Gardosi et al., 1995b
, Mongelli and Gardosi, 1995
). However, the clinical relevance of customization for maternal characteristics remains controversial (Hutcheon et al., 2008b
). Another way to further personalize a weight-for-gestational-age curve would be to make it conditional on attained weight. Such an approach has been advocated by Royston (1995)
. A conditional estimate of weight becomes in essence an estimate of growth. However, temporal distance between successive weight measurements tends to dampen correlation and conceal the effects conditioning might have on the variance of individual predicted weights on the short term. Since successive measurements in our dataset are often more than four weeks apart, a weight estimate conditioned on a measurement taken less than a month earlier would essentially rely on an arbitrarily imposed covariance structure. Measurement error, too, would negatively impact the predictive power of an individual conditional weight estimate. Results by Hutcheon et al. (2010)
indicate that the potential theoretical gains from conditioning are practically negligible when evaluated in the clinical setting.
While the goal of this study was to compare different methods for characterizing normal fetal growth, the methodologies examined in this paper could also be applied to the study of pediatric and adolescent growth. Further, the models could easily be modified to take other predictors into account. %For instance, maternal serum folate concentration in the second trimester and third trimester has been shown to be associated with birth weight (Goldenberg, Tamura, Cliver, Cutter, Hoffman, and Copper, 1992
, Scholl, Hediger, Schall, Khoo, and Fischer, 1996
) and therefore, measuring this predictor routinely during pregnancy might be warranted.
The dataset used in this study has several advantages, notably its relatively large sample size, the four longitudinal measurements resulting from unselected ultrasound scans and the quality of its weight and gestational age estimates. However, it would be of interest to be able to generate estimates applicable to different obstetrical populations, e.g. a North American population. Future work should determine whether the model can be adapted or rescaled to reflect fetal growth in different obstetrical populations.
Efforts are currently being made to update weight-for-gestational-age reference charts through the creation of a US national ultrasound standard for fetal growth (Zhang et al., 2010a
). On the other hand, a new method could also be proposed to improve reference charts by combining data from difference sources that are already available such as data from routine clinical ultrasounds, serial ultrasound research studies, and population birthweight data. As both approaches will require selecting a model for median weight for gestational age, we believe that our work will be especially useful in this context.