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A measure of partial association for generalized estimating equations. (English) Zbl 07257678
Summary: 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 \(x' = [x_1, \ldots, x_K]\). 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.
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