Comment and reply on: Prediction of the date of delivery based on first trimester ultrasound measurements: an independent method from estimated date of conception

We read with interest the paper ‘Prediction of the date of delivery based on first trimester ultrasound measurements: an independent method from estimated date of conception’ by Salomon et al. [1]. It is very interesting to see the median-based direct prediction method that we developed for second trimester measurements [2,3] being applied to first trimester data. Although the size of their study is much smaller than ours, it illustrates the strength of our population-based method; when high-quality registry data are available, the direct method provides a prediction model adapted to the clinical setting that the data were collected under, whether it is firstor second trimester routine scans. To avoid obscuring the central concept, it should be stressed that the essence of the authors’ approach is precisely the one developed in our paper, namely a direct estimation of median (and other centiles) of remaining time of pregnancy. This is the basis for deriving all the clinically useful estimates such as term prediction and prediction interval. The obvious statistical approach to the estimation is then to use a non-linear quantile regression model. A plethora of such models is available in the literature, and both the local linear quantile regression (LLQR) [4] employed by us and the spline-smoothed quantile regression employed by the authors fall in this category. Our reason for avoiding the spline smoothing approach was that it is inherently polynomial. This is clearly seen, for instance, in Figure 1 [1], where the spline approach ends up with a single knot at the median crown-rump length (CRL) value, and straight lines on each side, which may seem a bit odd. The LLQR method is to a larger extent truly non-linear in its kernel smoothing approach. However, we believe that such technical differences are of secondary importance to the overarching principle of direct median prediction. As the authors point out, centiles of remaining time is a potentially useful tool in pregnancy management, and one of the advantages of the direct prediction method. In Figures 1, 2, 5, and 6 [2], we provided values for the 10th, 25th, 50th, 75th, and 90th centiles, avoiding the most extreme centiles for which the precision is more questionable. The authors are correct in claiming that the LLQR method does not provide means (meaning, presumably, a formula) of computing centiles. We fail to see, however, that the authors’ suggested spline method provides such means. Regardless, a specific formula is not really needed. For any practical application of the model, the required centiles can be estimated from raw data and tabulated. Furthermore, since the shape of the residual distribution in our second trimester predictions is quite stable over the prediction range, useful and stable centile estimates can easily be obtained from the overall distribution (Figure 3), even for the more extreme centiles. The authors refer to our study [2] as using ‘less accurate second trimester measurements’. The conventional thinking is that in the first trimester the variability in fetal size is smaller, thus estimates made during the first trimester should be more precise than second trimester estimates. However, since the primary outcome is time of birth, not time of conception, this is not as obvious as it may seem. In fact, this is precisely one of the important empirical questions that can be addressed with our direct prediction method. If direct prediction curves were constructed both for firstand second trimester measurements, preferably on the same population, their precisions could be compared. This would effectively avoid uncertainties arising from comparing different populations and different dating formulas. Indeed, in Figures 1, 2, 5, and 6 [2] there are no obvious signs of increased precision at the lower end of the prediction range, which goes down to about week 13. Unfortunately, the authors miss the opportunity to study this in more detail and only refer to two previous publications. Their first reference is Taipale and Hiilesmaa [5], which in fact does not contain data after week 16; the paper only points onward to a paper on gestational age by Bergsjø et al. [6], which has no data on ultrasound at all, using only the last menstrual period (LMP). Their second reference is Saltvedt et al. [7], which is The Journal of Maternal-Fetal and Neonatal Medicine, August 2010; 23(8): 944–947