Modelling HIV-RNA viral load in vertically infected children

Human immunodeficiency virus (HIV) ribo-nucleic acid (RNA) viral load is a measure of actively replicating virus and is used as a marker of disease progression. For a thorough understanding of the dynamics of the evolution of the virus in the early life of HIV-1 vertically infected children, it is important to elucidate the pattern of HIV-RNA viral load over age. An aspect of assay systems used in the quantification of RNA viral load is that they measure values above particular cut-off values for detection, below which the assays used are not sufficiently sensitive. In this way, measurements are potentially left-censored. Recent adult studies suggest that to adequately model RNA pattern over age, it is necessary to account for within-subject correlation, due to repeated measures, and censoring. The aim of this study, therefore, was to establish whether it is necessary to use complex methods to allow for repeated measures within individuals and censoring of the HIV-RNA viral load in children enrolled in a cohort study. The approach involved the identification of an appropriate model for the basic pattern of RNA viral load by age and subsequent assessment of various estimation procedures accounting for repeated measures and censoring in different ways. Methods developed by Hughes involving the expectation-maximization (EM) algorithm and the Gibbs sampler were taken as the benchmark for comparison of simpler alternatives. Other approaches considered involve linear mixed-effects and ordinary least squares in which censoring is dealt with informally by taking the cut-off value as absolute or taking the mid-point between cut-off and zero. Fractional polynomials provided a substantially superior approach for modelling the dynamics of viral load over age compared to conventional polynomials or change-point models. Allowing for repeated measures was necessary to improve the power of the likelihood ratio tests required to establish the final model, but methods beyond taking the mid-point for censored values did not further improve the fit. Although Hughes' methodology is the best approach, its implementation is not necessary for the identification of the optimal model.