Assessing correlation of clustered mixed outcomes from a multivariate generalized linear mixed model

Abstract

The classic concordance correlation coefficient measures the agreement between two variables. In recent studies, concordance correlation coefficients have been generalized to deal with responses from a distribution from the exponential family using the univariate generalized linear mixed model. Multivariate data arise when responses on the same unit are measured repeatedly by several methods. The relationship among these responses is often of interest. In clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different methods on the same subjects. Indices for measuring such association are needed. This study proposes a series of indices, namely, intra-correlation, inter-correlation, and total correlation coefficients to measure the correlation under various circumstances in a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. The proposed indices are natural extensions of the concordance correlation coefficient. We demonstrate the methodology with simulation studies. A case example of osteoarthritis study is provided to illustrate the use of these proposed indices.

Consistent Maximum Likelihood Estimation Using Subsets with Applications to Multivariate Mixed Models

“…That is, the probability that there exists a maximizer of the likelihood outside an arbitrarily small ball around the true parameter tends to zero. We now discuss the use of subcollections and the assumptions used to achieve (3), which eventually leads to the main results in Theorems 2.3 and 2.4 presented at the end of the section.…”

“…Unfortunately, in many practically relevant settings, it is not clear that any such convergence holds and proving that it does is arguably the main obstacle to establishing consistency of MLEs. Let us illustrate using an MGLMM, commonly considered both in statistics and applied sciences [3,4,11,19,29].…”

Comments on ‘Assessing correlation of clustered mixed outcomes from a multivariate generalized linear mixed model’

“…As pointed out by McCulloch [2] and Inan [3], when the link function associating binary responses with covariates is the logit link function and the distribution for the random effects is the normal distribution within generalized linear mixed models, closed-form expression for marginal variance, covariance, and correlation functions cannot be obtained. , we can show that these functions can be approximated through a first-order Taylor series expansion.To illustrate, we follow the conventional notation used in Chen and Wehrly [1] and assume that Y ijt , which is the binary outcome of subject i at measurement t for method j, is associated with some set of covariates x ijt = (x 1,ijt , … , x p j ,ijt ) T through the logit link function. Then, a MGLMM for bivariate clustered binary data with subject and response-specific random-intercepts can be specified as follows [7]:…”

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Chen and Wehrly [1] have recently proposed intra-correlation, inter-correlation, and total correlation coefficients to assess the correlations under different circumstances for multivariate clustered data with mixed outcomes under multivariate generalized linear mixed models (MGLMMs). However, they restricted their theoretical derivations and numerical computations to joint modeling of clustered data with Gaussian and non-Gaussian continuous outcomes (e.g., exponential and gamma variables) and count outcomes (e.g., Poisson variables) because they were able to derive closed-form solution for marginal variance of outcomes and that for marginal covariance and correlation between outcomes.

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“…Now, following Chen and Wehrly [1], we can present approximate expression for intra-correlation, inter-correlation, and total correlation coefficients for bivariate clustered data with binary outcomes under MGLMMs, respectively, as follows:…”