Analysis of Longitudinal Data with Intermittent Missing Values using The Stochastic EM Algorithm

Abstract

In longitudinal studies each unit is measured on several occasions. In practice, some intended measurements may not available for some subjects resulting in a missing data pattern. Dropout pattern occurs when some subject are withdrawn from the study prematurely. The missing data pattern is defined as intermittent if a missing value followed by an observed value. When the probability of missingness depends on the missing value, and may be on the observed values, the missing data mechanism termed as nonrandom. Ignoring the missing values mechanism in this case leads to biased inference. In this study, the stochastic EM algorithm is proposed and developed to find parameters estimates to normal response distribution in the presence of intermittent missing values. Also, in this setting, the Monte Carlo method is developed to find the standard errors of parameters estimates. Assumptions about the distribution of the response can have a large effect on inference about parameters that govern the dropout process. So, it is important to consider the sensitivity of conclusions to distributional assumptions. We apply the proposed method to non­ normal response distribution. This enables us to examine the effect of the distributional assumptions of the response on the parameters that characterize the dropout process. Finally, the proposed techniques are applied to a real data from the International Breast Cancer Study Group.