The effect of missing data on sample sizes for repeated measures models

Researchers involved with longitudinal studies are faced with the problem of trying to get study subjects to return for every follow-up visit. There is always some amount of missing data when looking at these types of studies. The MIXED procedure of the SAS(R) enables examination of correlational structures and variability changes between repeated measurements on experimental units across time. While PROC MIXED has the capacity to handle unbalanced data when the data are missing at random, a question arises as to when the degree of sparseness jeopardizes inference. Simulation is a tool that can be used to answer these types of questions. This paper show how to simulate sets of data where an assumption of a Toeplitz structure has been made for the variance-covariance (V-C) relationship of the repeated measurements. Then observations are systematically deleted at rates of 10%, 20% and 25% in specific patterns. Comparisons of the suitability of the Toeplitz versus the unstructured or compound symmetric models were made using Likelihood Ratio Tests (LRTs). Sample sizes can be increased in the simulations until the underlying covariance structure is determined 95% of the time (the p-value for the LRT is set at 0.05).