Statistical measures of foetal growth using linear mixed models applied to the foetal origins hypothesis

Statistical models of the relationship between the distribution of each of five foetal dimensions and gestational age are developed based on serial ultrasound biometric data from a prospective longitudinal study in Perth, Western Australia. Both the response variable and the gestational age timescale are transformed to establish an approximately linear relationship within subjects. This relationship is modelled using a linear mixed effects model that accounts for between-subject heterogeneity by incorporating subject specific random effects for both intercept and gradient. These models are used to motivate three measures of foetal growth: the conditional centile or z-score of a current measurement given an earlier value for the same measurement; the best linear unbiased predictor (BLUP) of the subject specific random effect gradient (which is shown to be invariant to transformations of location and scale), and the standardized residual at a given gestational age, which characterizes departures from the modelled growth trajectory. We illustrate how these three measures of growth might be applied to subsequent health outcomes in later life by relating growth in foetal abdominal circumference to blood pressure in children from the same cohort at six years of age. Foetuses whose summary measures indicate poor growth in abdominal circumference have higher blood pressure in early childhood, supporting the 'foetal origins' hypothesis that many chronic diseases of adulthood have their origins before birth.