Age-related reference ranges: significance tests for models and confidence intervals for centiles

A method of fitting age-related reference ranges using maximized likelihood is presented. The method is illustrated using CD4 counts of uninfected children born to HIV-1 infected women. The likelihood incorporates exponential functions to describe the Box-Cox transformation parameter that induces Normality and the mean and standard deviation of the transformed data, at all ages in the range. This guarantees that the centiles are asymptotic to notional adult values and avoids edge effects. Likelihood ratio tests were used to assess the significance of the model parameters, and profile likelihood confidence intervals were constructed around the fitted centiles. The asymptotes of the resulting CD4 reference range for the childhood dataset were compared with CD4 counts available from a group of uninfected adults. The proposed approach limits the need for arbitrary decisions about grouping of the data, degree of smoothing or choice of model.