Inference for smooth curves in longitudinal data with application to an AIDS clinical trial

We discuss a longitudinal study where data for many subjects are collected at irregular intervals. The study is a randomized trial of HIV infected subjects and the response variable of interest is serum neopterin. The mean of the outcome variable, taken over patients in each treatment group, is assumed to follow a smooth curve. Piecewise cubic polynomials with a moderate number of knots are used to model the curves. A general parametric form is assumed for the covariance structure. Maximum penalized likelihood estimation is used to smooth the over-parameterized curves. Statistical inference for the mean curves, including confidence bands and hypothesis tests, is discussed. Two approaches, one using a Bayesian interpretation of the penalized likelihood and the other based on the asymptotic distribution of the maximum penalized likelihood estimates, are discussed and contrasted. The properties of the confidence bands obtained from these two approaches are evaluated by examining their coverage rates in a simulation study.