Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data

Semiparametric models are becoming increasingly attractive for longitudinal data analysis. Often there is lack of knowledge of the covariance structure of the response variable. Although it is still possible to obtain consistent estimators for both parametric and nonparametric components of a semipatrametric model by assuming an identity structure for the covariance matrix, the resulting estimators may not be efficient. We conducted extensive simulation studies to investigate the impact of an unknown covariance structure on estimators in semiparametric models for longitudinal data. In some situations the loss of efficiency could be substantial. A two-step estimator is thus proposed to improve the efficiency. Our study was motivated by a population based data analysis to examine the temporal relationship between systolic blood pressure and urinary albumin excretion.