Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models. Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the observed data likelihood function is based on the model of a joint distribution of the response longitudinal event history data and the discrete covariate with missing values. Secondly, we proposed a maximum simulated likelihood method to deal with the missing continuous covariate when applying multi-state models. The observed data likelihood function was approximated by using the Monte Carlo simulation method. At last, an EM algorithm was used to deal with multiple missing covariates when estimating the parameters of multi-state model. The EM algorithm would be able to handle multiple missing discrete covariates in general missing pattern efficiently. All the proposed methods are justified by simulation studies and applications to the datasets from the SMART project, a consortium of 11 different high-quality longitudinal studies of aging and cognition.