Application of multilevel models to morphometric data. Part 2. Correlations

Multilevel organization of morphometric data (cells are "nested" within patients) requires special methods for studying correlations between karyometric features. The most distinct feature of these methods is that separate correlation (covariance) matrices are produced for every level in the hierarchy. In karyometric research, the cell-level (i.e., within-tumor) correlations seem to be of major interest. Beside their biological importance, these correlation coefficients (CC) are compulsory when dimensionality reduction is required. Using MLwiN, a dedicated program for multilevel modeling, we show how to use multivariate multilevel models (MMM) to obtain and interpret CC in each of the levels. A comparison with two usual, "single-level" statistics shows that MMM represent the only way to obtain correct cell-level correlation coefficients. The summary statistics method (take average values across each patient) produces patient-level CC only, and the "pooling" method (merge all cells together and ignore patients as units of analysis) yields incorrect CC at all. We conclude that multilevel modeling is an indispensable tool for studying correlations between morphometric variables.