A measure of partial association for generalized estimating equations

In a regression setting, the partial correlation coefficient is often used as a measure of 'standardized' partial association between the outcome y and each of the covariates in x′ = [x₁,..., x_K ]. In a linear regression model estimated using ordinary least squares, with y as the response, the estimated partial correlation coefficient between y and x_k can be shown to be a monotone function, denoted f(z), of the Z-statistic for testing if the regression coefficient of x_k is 0. When y is non-normal and the data are clustered so that y and x are obtained from each member of a cluster, generalized estimating equations are often used to estimate the regression parameters of the model for y given x. In this paper, when using generalized estimating equations, we propose using the above transformation f(z) of the GEE Z-statistic as a measure of partial association. Further, we also propose a coefficient of determination to measure the strength of association between the outcome variable and all of the covariates. To illustrate the method, we use a longitudinal study of the binary outcome heart toxicity from chemotherapy in children with leukaemia or sarcoma.