Covariate-Adjusted Regression for Distorted Longitudinal Data with Informative Observation Times

In many longitudinal studies, repeated response and predictors are not directly observed, but can be treated as distorted by unknown functions of a common confounding covariate. Moreover, longitudinal data involve an observation process which may be informative with a longitudinal response process in practice. To deal with such complex data, we propose a class of flexible semiparametric covariate-adjusted joint models. The new models not only allow for the longitudinal response to be correlated with observation times through latent variables and completely unspecified link functions, but they also characterize distorted longitudinal response and predictors by unknown multiplicative factors depending on time and a confounding covariate. For estimation of regression parameters in the proposed models, we develop a novel covariate-adjusted estimating equation approach which does not rely on forms of link functions and distributions of frailties. The asymptotic properties of resulting parameter estimators are established and examined by simulation studies. A longitudinal data example containing calcium absorption and intake measurements is provided for illustration. Supplementary materials for this article are available online.