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Generalized linear mixed models are commonly used to describe relationships between correlated responses and covariates in medical research. In this paper, we propose a simple and easily implementable regularized estimation approach to select both fixed and random effects in generalized linear mixed model. Specifically, we propose to construct and optimize the objective functions using the confidence distributions of model parameters, as opposed to using the observed data likelihood functions, to perform effect selections. Two estimation methods are developed. The first one is to use the joint confidence distribution of model parameters to perform simultaneous fixed and random effect selections. The second method is to use the marginal confidence distributions of model parameters to perform the selections of fixed and random effects separately. With a proper choice of regularization parameters in the adaptive LASSO framework, we show the consistency and oracle properties of the proposed regularized estimators. Simulation studies have been conducted to assess the performance of the proposed estimators and demonstrate computational efficiency. Our method has also been applied to two longitudinal cancer studies to identify demographic and clinical factors associated with patient health outcomes after cancer therapies. 

Abstract Multivariate failure time data are frequently analyzed using the marginal proportional hazards models and the frailty models. When the sample size is extraordinarily large, using either approach could face computational challenges. In this paper, we focus on the marginal model approach and propose a divide‐and‐combine method to analyze large‐scale multivariate failure time data. Our method is motivated by the Myocardial Infarction Data Acquisition System (MIDAS), a New Jersey statewide database that includes 73,725,160 admissions to nonfederal hospitals and emergency rooms (ERs) from 1995 to 2017. We propose to randomly divide the full data into multiple subsets and propose a weighted method to combine these estimators obtained from individual subsets using three weights. Under mild conditions, we show that the combined estimator is asymptotically equivalent to the estimator obtained from the full data as if the data were analyzed all at once. In addition, to screen out risk factors with weak signals, we propose to perform the regularized estimation on the combined estimator using its combined confidence distribution. Theoretical properties, such as consistency, oracle properties, and asymptotic equivalence between the divide‐and‐combine approach and the full data approach are studied. Performance of the proposed method is investigated using simulation studies. Our method is applied to the MIDAS data to identify risk factors related to multivariate cardiovascular‐related health outcomes.