Within group and between group correlation : Application to noninvasive estimation of intracranial pressure

The linear association between two continuous quantities is often assessed in terms of Pearson’s correlation coefficient, r. However, if the data are not homogeneous, i.e., consist of groups, then it is important to decompose r into components that measure the correlation within the groups, and the correlation between the groups. We point out the importance of examining these components, and present a method for computing them. Our approach has several attractive features. First, all three measures of correlation are computed in a unified framework based on the analysis of (co)variance in a single linear model. Second, it allows one to measure nonlinear correlations. Finally, p-values, traditionally computed in linear modeling can be utilized to test the statistical significance of the three measures of correlation. The method is applied to assess the correlation between invasive observations and noninvasive estimates of intracranial pressure (ICP), with individual patients representing each group. The total correlation is 0.506, while the within-group and between-group correlations are 0.053 and 0.518, respectively. As such, the ICP predictions are useful for estimating/predicting the mean (over time) ICP for any patient, but they are useless for monitoring an individual’s ICP at any time.