Bias correction in random effects models with sparse binary responses

Sparse correlated binary data are frequently encountered in many applications involving either rare event cases or small sample sizes. In this study, we consider correlated binary data and a logit random effects model framework. We discuss h-likelihood estimates and how the computational procedure is affected by sparseness. We propose an adjustment to the fitting process that involves the adaption of the regression calibration method to the estimation of random effects. Using this adjustment, we correct for the bias in the random effects estimates resulting in better properties for the fixed effects estimates of the model. This is supported by the results of the simulation study that was conducted under different sparseness levels. The proposed adjusted h-likelihood estimation approach is also used for the analysis of two real meta-analyses data sets.