Flexible methods for analysing longitudinal data using piecewise cubic polynomials

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Abstract
We investigate a method for the analysis of repeated observations, that could arise in a clinical trial, in which there are many treatment groups, the number of observations per subject is variable, and the observations are unequally spaced. Changes in the mean of the outcome variable are described by curves defined on the follow-up period. We develop a practical and computationally feasible approach in which piecewise cublic polynomials with a large and fixed number of knots are used to parametrize the curves. Penalized likelihood estimates are used to reduce the variability and obtain smooth curves for different treatment groups. A leave-out-one-subject weighted cross-validation scheme is developed to choose the smoothing parameter λ which controls the smoothness of the curves. Some simplifying approximations to the cross-validation criterion are discussed. A simulation study is performed to evaluate the method. The result shows that using the λ chosen by cross-validation, the maximum penalized likelihood fit gives a smooth and acceptable estimate of the curves. The method is applied to AIDS clinical trial data.

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