Shrinkage estimation analysis of correlated binary data with a diverging number of parameters

For analyzing correlated binary data with high-dimensional covariates, we, in this paper, propose a two-stage shrinkage approach. First, we construct a weighted least-squares (WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations (GEE) model. Second, we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter estimation. The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters. Moreover, we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified. For the selection of tuning parameter, we develop a consistent penalized quadratic form (PQF) function criterion. The performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.