An Analysis of Paediatric CD4 Counts for Acquired Immune Deficiency Syndrome Using Flexible Random Curves

Abstract

SUMMARY In this paper we analyse CD4 counts from infants born to mothers who are infected with the human immunodeficiency virus. A random effects model with linear or low order polynomials in time is unsatisfactory for these longitudinal data We develop an alternative approach based on a flexible family of models for which both the fixed and the random effects are linear combinations of B-splines. The fixed and random parts are smooth functions of time and the covariance structure is parsimonious. The procedure allows estimates of each individual's smooth trajectory over time to be exhibited. Model selection, estimation and computation are discussed. Centile curves are presented that take into account the longitudinal nature of the data. We emphasize a graphical approach to the presentation of results.