A cautionary note on the use of autoregressive models in analysis of longitudinal data

Rosner et al. presented a simple, easily implemented modelling method for retaining time order relationships in analyses of longitudinal data when successive measures are correlated. Evaluation of time order is particularly useful in epidemiologic studies concerned with exposure to potentially toxic substances and subsequent outcome, but may also have use in more traditional growth studies that relate intake to subsequent development. The analysis allows for unequally spaced measures and missing data. The estimation method permits varying numbers of observations per subject and, with measures equally spaced, one can fit the model with use of ordinary least squares regression software. We report on a potential false association that can result when both exposure and outcome are related to time. We illustrate this problem with a small scale simulation and example. We also note a more serious problem with Rosner's approach in interpreting parameters. Although the model may be useful for prediction, parameters depend on the autocorrelation and are not readily interpretable. We recommend alternative modelling strategies be used when autocorrelation of errors is suspected.