  The intraclass correlation coefficient (ICC) is a classical index of
measurement reliability. With the advent of new and complex types of data for
which the ICC is not defined, there is a need for new ways to assess
reliability. To meet this need, we propose a new distance-based intraclass
correlation coefficient (dbICC), defined in terms of arbitrary distances among
observations. We introduce a bias correction to improve the coverage of
bootstrap confidence intervals for the dbICC, and demonstrate its efficacy via
simulation. We illustrate the proposed method by analyzing the test-retest
reliability of brain connectivity matrices derived from a set of repeated
functional magnetic resonance imaging scans. The Spearman-Brown formula, which
shows how more intensive measurement increases reliability, is extended to
encompass the dbICC.
