Fitting subject-specific curves to grouped longitudinal data

In longitudinal studies, a response variable measured over time, may vary across subgroups. A typical example is illustrated by the first three panels of Figure 1; these display simulated growth data (based on the model in Durban et al. 2005) of 197 children who suffer from acute lymphoblastic leukaemia, and have received three different treatments. In some cases, a parametric mixed model is sufficient to summarize this type of data. However in Figure 1, a parametric approach does not seem appropriate, so smoothing is incorporated into the modelling process in order to extract the correct patterns from the data. In this setting, the mixed model representation of truncated polynomials is widely used,
with a well known covariance structure for the random effects. In this paper, we outline this approach, demonstrate its limitations, and describe a more
appropriate approach via penalty arguments.