On casting random‐effects models in a survival framework

Summary. Logistic random‐effects models are often employed in the analysis of correlated binary data. However, fitting these models is challenging, since the marginal distribution of the response variables is analytically intractable. Often, the random effects are treated as missing data for constructing traditional data augmentation algorithms. We create a novel alternative data augmentation scheme that simplifies the likelihood‐based inference for logistic random‐effects models. We cast the random‐effects model in a ‘survival framework’, where each binary response is the censoring indicator for a survival time that is treated as additional missing data. Under this augmentation framework, the conditional expectations are free of unknown regression parameters. Such a construction has a particular advantage that, in the case of discrete covariates, the score equations for regression parameters have analytical solutions. Consequently, one does not need to resort to a search algorithm in estimating the regression parameters. We further create a parameter expansion scheme for logistic random‐effects models under this survival data augmentation framework. The proposed data augmentation is illustrated when the random‐effects distribution follows a multivariate Gaussian and multivariate t‐distribution. The performance of the method is assessed through simulation studies and a real data analysis.