Modeling Correlation in Incomplete Longitudinal Data: The Case of Fruit Fly Mortality Data

Longitudinal studies are prevalent in clinical trials, biological and social sciences where subjects are measured repeatedly over time. Modeling the correlations of repeated measurements on the same subject and handling missing data are challenging problems in the statistical analysis of such data. The situation is exacerbated knowing that the presence of missing data can hamper modeling of dependence, and improper accounting of dependence can negatively affect imputation of the missing values. Methods for handling missing data have been thoroughly studied, but data-based and graphical methods for modeling the covariance matrix of longitudinal data are relatively new. Our work illustrates the insensitivity of formulating models for the covariance matrix to different methods of handling missing values in longitudinal studies for the fruit fly mortality data which has about 22% missing values. We emphasize the role of graphical tools like the regressograms in formulating models for covariance matrices under different methods of handling missing data. Surprisingly, for five of commonly used methods, the regressograms remain robust and consistent in suggesting the same class of cubic polynomial models for the components of the modified Cholesky decomposition of the sample covariance matrix. We hope this aspect of the success of the regressograms will encourage statisticians to use them in conjunction with other graphical tools for displaying dependence in longitudinal data and formulating parametric models for the covariance matrix in the presence of missing data.