Nonparametric multistate representations of survival and longitudinal data with measurement error

This paper proposes a nonparametric procedure to describe the progression of longitudinal cohorts over time from a population averaged perspective, leading to multistate probability curves with the states defined jointly by survival and longitudinal outcomes measured with error. To account for the challenges of informative dropout and nonlinear shapes of the longitudinal trajectories, we apply a bias corrected penalized spline regression to estimate the unobserved longitudinal trajectory for each subject. We then estimate the multistate probability curves on the basis of the survival data and the estimated longitudinal trajectories. We further use simulation-extrapolation method to reduce the estimation bias caused by the randomness of the estimated trajectories. We develop a bootstrap test to compare multistate probability curves between groups. We present theoretical justification of the estimation procedure along with a simulation study to demonstrate finite sample performance. We illustrate the procedure by data from the African American Study of Kidney Disease and Hypertension, and it can be widely applied in longitudinal studies.