The correlation between any two random variables can be estimated using a variety of techniques including parametric methods based on the Pearson correlation coefficient, nonparametric methods, and regression analysis. While these estimators have been widely used, the computation of these estimates in the presence of missing data has not been as widely studied. There has been some work addressing the estimation of parameters in the presence of missing data for regression analysis; including imputation, inverse probability weighted regression and weighted estimating equations. However, there has been little work focused on the estimation of the correlation coefficient. To assess the usefulness of these methods in a practical setting, we present simulation studies comparing imputation, inverse probability weighting and complete cases and provide recommendations on the basis of these results. Furthermore, computation of Partial Least Squares (PLS) scores with the correlation matrix computed using the above mentioned techniques are also presented. We apply these results in a positron emission tomography data set consisting of several different brain regions as response variables and cognitive tasks as covariates of interest. Alzheimer's disease is a progressive and fatal health disease. The application presented in this work is significant for public health since it provides us with a better understanding of variability in different brain regions as it relates to neuropsychological tests that are helpful in diagnosis of progressive brain disease (i.e Alzheimer's disease).
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