Correlation models for monitoring child growth

Growth measurements of children, such as weight and height, are monitored regularly, particularly in infancy, to assess whether or not a child's growth is normal when compared with a reference population of the same age and sex. Here, after a suitable power transformation to normality of the reference population, we model temporal evolution of the standardized deviation (Z-score) of the transformed measurement of a normal child from the reference population as a Gaussian process with zero mean and unit variance. This paper concentrates on modelling and fitting the serial correlation structure of the process, with the benefit that monitoring growth at specific ages is not crucial, statistically. Exploratory analysis of various observed correlation matrices has suggested that a particular two-parameter Markovian form is a good representation of the correlation function in infancy. The main implication for growth monitoring is that we only need to condition on the most recent Z-score to inform a clinician's judgement about a child's growth based on its current Z-score. Inferences about the correlation parameters derive from likelihood methods based either on observed Z-scores or, if raw data are unavailable, on an observed correlation matrix. The Markov model is compared with a previously studied six-parameter correlation model. Data from major child growth studies in Newcastle and Cambridge are used to illustrate the methods and compare predictions from the two models. We argue that the Markov model serves as a pragmatic choice for growth monitoring in infancy.