Quantifying intraclass correlations for count and time‐to‐event data

Abstract

The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter-rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non-Gaussian outcomes. The focus here is on count and time-to-event outcomes where so-called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed-form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies.

Describing the association between socioeconomic inequalities and cancer survival: methodological guidelines and illustration with population-based data

“…However, in our final explanatory model, we rarely retained a single parameter for each prognostic factor, which makes impossible such a comparison. So, though the MEHR has the merit of simplicity, an interesting perspective would be to extend the approach proposed by Oliveira et al 51 These authors derived an intra-class correlation coefficient for time-to-event regression models with a random effect (frailty). As in a linear model, this coefficient is defined as a ratio of variance components, which allows interpreting the coefficient as the proportion of the total variance due to the between-IRIS variability.…”

“… 52 However, the approach proposed by Oliveira et al suits their specific models that include closed forms of marginal variance, which leads to closed forms of intraclass correlation. 51 A future work would check whether their approach may be applied to our model.…”

Adolescent birth rates and the urban social environment in 363 Latin American cities

“…To assess the degree of clustering within cities and countries we estimated intraclass correlations coefficients (ICC) based on the formula for negative binomial models described by Oliveira et al . 26 Given that the mean and variance for the negative binomial distribution are related, the ICC was calculated holding the mean ABR constant as the overall mean ABR across subcities.…”

“…To examine the variability across subcities, within cities and across cities within the same country we fitted a three-level negative binomial model with random intercepts for cities and countries (subcities nested within cities nested within countries). To assess the degree of clustering within cities and countries we estimated intraclass correlations coefficients (ICC) based on the formula for negative binomial models described by Oliveira et al 26. Given that the mean and variance for the negative binomial distribution are related, the ICC was calculated holding the mean ABR constant as the overall mean ABR across subcities.…”