Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

We discuss the problem of estimating the correlation coefficient between two variables observed in a longitudinal study where some observations are missing completely at random. We propose several estimators: the group weighted mean, the marginal mean, the weighted fisheris z and the weighted marginal mean. In the first approach we group data based on the missing pattern, estimate the correlation for each group, and take their weighted average. In the last three approaches we obtain the correlations based on cross-sectional data and combine those marginal information in different ways. We obtain the asymptotic distributions of these estimators. Using simulation we compare them with the MLE. We find that except the group weighted mean these estimators are as good as the MLE while they are much easier to compute. The robustness of the five estimators as the nuisance parameters vary is discussed. We also discuss how to test the equality of correlations over time. Further, we use data from an AIDS study to illustrate the advantage of the proposed estimators.