Non-linear random effects models with continuous time autoregressive errors: A Bayesian approach

Measurements on subjects in longitudinal medical studies are often collected at several different times or under different experimental conditions. Such multiple observations on the same subject generally produce serially correlated outcomes. Traditional regression methods assume that observations within subjects are independent which is not true in longitudinal data. In this paper we develop a Bayesian analysis for the traditional non-linear random effects models with errors that follow a continuous time autoregressive process. In this way, unequally spaced observations do not present a problem in the analysis. Parameter estimation of this model is done via the Gibbs sampling algorithm. The method is illustrated with data coming from a study in pregnant women in Santiago, Chile, that involves the non-linear regression of plasma volume on gestational age.