Inference for the association between coefficients in a multivariate growth curve model

This paper generalizes the work of Blomqvist (1977, Journal of the American Statistical Association 72, 746-749) on inference for the relationship between the individual-specific slope and the individual-specific intercept in a linear growth curve model. The paper deals with longitudinal data involving one or more response variables and irregular follow-up times, with each response variable postulated to follow a linear growth curve model. The problem considered is inference concerning the association between one growth curve coefficient and another--for example, the slope and intercept for a selected response variable, or the two slopes for two different response variables--after adjusting for all remaining coefficients among all of the response variables. An inferential approach based on the method of moments and an inferential approach based on maximum likelihood are described, and the asymptotic properties of these procedures are presented. Extensions of the methodology to allow polynomial growth curves and baseline covariates are outlined. The methodology is illustrated with a practical example arising from a clinical trial in lung disease.