Bayesian updating in reference centile charts

Reference centile charts, used for monitoring the health of an individual over time (e.g. the weight gain of pregnant women over successive periods in their pregnancy) do not take into account the longitudinal nature of the individual profiles. There is also generally more than one variable which affects the outcome of interest, and information regarding the path of a group of variables over time may prove advantageous in terms of sensitivity. We propose a Bayesian approach to this problem in which the successive deviations of the individual's observations from the mean of the corresponding reference distribution are used to compute updated reference centiles for future measurements on the individual. The univariate and multivariate situations are discussed, and consideration is given to non-normal cross-sectional distributions. The theory is illustrated on data obtained from the records of weight gain and fundal height of pregnant women visiting a clinic at intervals during pregnancy.