Multi-state models and missing covariate data: expectation–maximization algorithm for likelihood estimation

Multi-state models have been widely used to analyse longitudinal event history data obtained in medical and epidemiological studies. The tools and methods developed recently in this area require completely observed data. However, missing data within variables of interest are very common in practice, and they have been an issue in applications. We propose a type of expectation–maximization (EM) algorithm, which handles missingness within multiple binary covariates efficiently, for multi-state model applications. Simulation studies show that the EM algorithm performs well for both missing completely at random and missing at random covariate data. We apply the method to a longitudinal aging and cognition study data-set, the Klamath Exceptional Aging Project, whose data were collected at Oregon Health & Science University and integrated into the Statistical Models of Aging and Risk of Transition database at the University of Kentucky.