This chapter focuses on the multiple imputation methods and the expectation-maximization algorithm for handling missing data when mixture models are applied for cluster analysis. In medical and health sciences research, always inevitably face the problem of missing data. Due to the presence of missing data, studies are prone to bias and loss of statistical power, imposing an enormous challenge for interpretation and generalization of research findings. Concerning methodological approaches to handle missing data, the difficulty in obtaining valid and reliable estimates of model parameters depends on the mechanism that induces missing data. There are a number of approaches to handling missing values in statistical analyses of data acquired from medical and health sciences research, as summarized in Bennett. Most of these existing methods for handling missing data focus on the case of ignorable missing at random mechanism and continuous variables under the normality assumption.