Analysis of longitudinal data in case-control studies

Case-control studies for longitudinal data are considered. Among repeated binary measurements of disease status in each subject, the exposure levels of risk factors for all diseased cases are identified and the exposure levels for only a small fraction of disease-free cases, to be regarded as controls, are identified. Case-control studies for longitudinal data bring about economies in cost and time when the disease is rare and when assessing the exposure level of risk factors is difficult. We propose a way of using an ordinary logistic model to analyse case-control longitudinal data. We prove that the proposed estimator is consistent and asymptotically normally distributed provided that the choice of control observations is independent of the covariates for those subjects. We also discuss the validity of the generalised estimating equation method for case-control longitudinal data. Simulation results are provided, and a real example is presented.