Statistical methods for constructing gestational age‐related reference intervals and centile charts for fetal size

Many fetal size variables, for example head measurements, abdominal measurements and femur length, increase over the course of gestation. Reference intervals (RIs) and centile charts provide a means of assessing these measurements, at a given gestational age (GA) or across a range of GAs, respectively, and are tools of great importance in clinical medicine. RIs (sometimes, misleadingly, called ‘normal ranges’) represent the interval between a pair of symmetrically placed extreme centiles (such as the 5th and 95th for a 90% interval) of a size variable, denoted y, at a given GA. Centile charts plot the values of y corresponding to one or more RIs against the relevant GA over a range of GAs. In the field of fetal size, values which lie outside the RI are regarded as extreme and may indicate the presence of a disorder such as intrauterine growth restriction1 or macrosomia2. More informative, however, than this forced dichotomy is the calculation of a value’s centile position, or Z-score, relative to the reference population, estimated from knowledge of the distribution of y at a given GA. For a given observation, the proximity of the centile position to 0% or 100% (alternatively the magnitude and sign of the Z-score) is then a measure of how extreme the observation is compared to the reference data at that GA. A centile position above 50% (equivalently a positive Z-score) signifies a measurement greater than average for that GA, and a centile position below 50% (or a negative Z-score) one less than average. While recent years have seen the publication of a variety of strategies for the construction of RIs, incorrect methods have still been used for fetal measurements of all kinds1. The choice of suitable methodology in this field is especially crucial as inaccurate centiles may lead to false conclusions regarding the development of the fetus, resulting in suboptimal clinical care. In an article in this issue of the Journal, Sherer et al.3 construct centile charts of the axial cerebellar hemisphere circumference (CHC) and area (CHA) through gestation using one such method, based upon regression modelling of both the mean and the standard deviation (SD) across GA, as detailed by Altman and Chitty4 and Royston and Wright1. It is the aim of the present article to further examine the statistical approach used by Sherer et al.3, while taking a more general look at the problem of constructing GArelated RIs and considering alternative approaches to this problem. Techniques for longitudinal data, where each subject contributes repeated observations, as opposed to cross-sectional data, where they contribute only one, require a different approach and are not considered here. Further information on this area can be found in, for example, Royston and Altman5 and Royston6. While many of the techniques explored here could be, and indeed have been, used in the context of anthropometric measurements, the focus here is on applications in the field of fetal size.