Empirical Bayes estimation of random effects parameters in mixed effects logistic regression models

We extend an approach for estimating random effects parameters under a rand om intercept and slope logistic regression model to include standard errors , thereby including confidence intervals. The procedure entails numerical i ntegration to yield posterior empirical Bayes (EB) estimates of random effe cts parameters and their corresponding posterior standard errors. We incorp orate an adjustment of the standard error due to Kass and Steffey (KS; 1989 , Journal of the American Statistical Association. 84, 717-726) to account for the variability in estimating the variance component of the random effe cts distribution. In assessing health care providers with respect to adult pneumonia mortality, comparisons are made with the penalized quasi-likeliho od (PQL) approximation approach of Breslow and Clayton (1993, Journal of th e American Statistical Association 88, 9-25) and a Bayesian approach. To ma ke comparisons with an EB method previously reported in the literature, we apply these approaches to crossover trials data previously analyzed with th e estimating equations EB approach of Waclawiw and Liang (1994, Statistics in Medicine 13, 541-551). We also perform simulations to compare the propos ed KS and P&L approaches. These two approaches lead to EB estimates of rand om effects parameters with similar asymptotic bias. However, for many clust ers with small cluster size, the proposed KS approach does better than the PQL procedures in terms of coverage of nominal 95% confidence intervals for random effects estimates. For large cluster sizes and a few clusters, the PQL approach performs better than the KS adjustment. These simulation resul ts agree somewhat with those of the data analyses.