Incorporating correlations between measurements into the estimation of age-related reference ranges

An LMS-based maximum likelihood method of fitting age-related reference ranges is extended to incorporate non-independent measurements by including the matrix of the correlations between standard normalized repeat measurements into the likelihood. The likelihood is maximized via iterative re-estimation of the correlation structure and the reference range parameters until convergence is achieved. The correlation structure is explicitly modelled and the extent to which the estimated centiles depend on the adequacy with which the correlation structure is modelled is investigated. The method is illustrated using CD4 counts of uninfected children born to HIV-1 infected women. This data set consists of 5063 CD4 counts taken from 745 children at irregular ages between birth and 10 years of age. The data exhibited a strong correlation structure with correlations decreasing with increasing time between measurements and being lower for younger measurement ages. However, incorporation of the correlation had little effect on the choice of model for the median or on the fitted centiles or their precision.