A stochastic regression model for general trend analysis of longitudinal continuous data.

A predictive continuous time model is developed for continuous panel data to assess the effect of time-varying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an Ornstein-Uhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time first-order autoregressive regression model with time-varying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasi-likelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasi-likelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a follow-up study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.