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We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed-effects model framework for model fitting, prediction and inference. The proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals. Use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates.

These data define the slowest rise in serial hCG values for a potentially viable gestation and will aid in distinguishing a viable early pregnancy from a miscarriage or ectopic pregnancy. The minimal rise in serial hCG values for women with a viable intrauterine pregnancy is "slower" than previously reported, suggesting that intervention to diagnosis and treat an abnormal gestation should be more conservative.