INFERENCE FOR THE ASSOCIATION BETWEEN COEFFICIENTS IN A MULTIVARIATE GROWTH CURVE MODEL

This paper generalizes the work of Blomqvist (1977, Journal of the Ame rican Statistical Association 72, 746-749) on inference for the relati onship between the individual-specific slope and the individual-specif ic intercept in a linear growth curve model. The paper deals with long itudinal data involving one or more response variables and irregular f ollow-up times, with each response variable postulated to follow a lin ear 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 fo r all remaining coefficients among all of the response variables. An i nferential 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 metho dology to allow polynomial growth curves and baseline covariates are o utlined. The methodology is illustrated with a practical example arisi ng from a clinical trial in lung disease.