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.

Weighted cumulative sum tests for random effect models with binary responses.

Correlated binary responses are very commonly encountered in many disciplines like, for example, medical studies. The development of goodness-of-fit tests is essential for examining the adequacy of the fitted models. The objective of this article is to provide weighted modifications of cumulative sums or moving cumulative sums of residuals for testing goodness-of-fit of random effects logistic regression models. The proposed weights can be interpreted as the residuals of a weighted linear regression of an omitted covariate on the covariates already included in the fixed part of the model. These processes lead to supremum statistics whose null distribution is derived using simulation. Results from a simulation study suggest better performance of the weighted when compared to the unweighted supremum statistics. The proposed tests are illustrated using a real data example.