Multiple Imputation for Missing Data in Repeated Measurements Using MCMC and Copulas

This paper presents two imputation methods: Markov Chain Monte Carlo (MCMC) and Copulas to handle missing data in repeated measurements. Simulation studies were performed using the Monte Carlo technique to generate datasets in different situations. Each subject unit in each dataset was measured on three occasions under the following conditions: 1. data had a multivariate normal distribution under two types of correlation structures: Compound Symmetry (CS) and Autoregressive (AR (1)), 2. the correlation among repeated observations under each subject was determined at low level (rho = 0.3), middle level (rho = 0.5), and high level (rho = 0.7), 3. sample sizes consisted of 30, 70, and 100 subject units, and 4. data were assigned missing at random (MAR) at the last occasion of measurement with missing rate of 5%, 10%, 20% and 30%, respectively. All possible combinations of these conditions gave rise a total of 72 different situations. Each defined situation was repeated 1,000 times by SAS programming and each missing value was replaced with a set of five plausible values that represent the uncertainty about the right value to impute under the MCMC method. The performance of each imputation method was evaluated using mean square error (MSE). The lower MSE would indicate the more effective method. The results from the simulation studies showed that the Copulas method was superior effective than other methods in all situations. The MCMC method was more effective than the simple mean imputation method when the correlation structure was AR1. For application, both imputation methods were applied with two datasets in practices: 1) waist circumference data on healthy project and 2) monthly rainfall data. The results also confirmed that the Copulas was the most effective method which was consistent with the simulation studies.