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Yongdai Kim (Seoul National University)

12 December 2013 @ 11:00

 

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Date:
12 December 2013
Time:
11:00
Event Category:

Deviance Information Criteria for the frailty model

We are concerned with model selection for the frailty model by use of the deviance information criterion (DIC). The DIC is a Bayesian model selection criterion proposed by Spiegelhalter et al. (2002).  A difficulty in applying the DIC to the frailty model lies on the unspecified baseline hazard function. While the DIC has been studied mostly for parametric models, it is unclear how the DIC is defined for semiparametric models. We propose various versions of the DIC for the frailty model and compare their performance by simulation. We illustrate the proposed DICs by analyzing the data set of the cluster-randomized trial conducted in Kolkata, India. In many case-control studies, a central goal is to test for association or dependence between the predictors and the response. Relevant covariates must be conditioned on to avoid false positives and loss in power. Conditioning on covariates is easy in parametric frameworks such as the logistic regression—by incorporating the covariates into the model as additional variables. In contrast, nonparametric methods such as the Cochran-Mantel-Haenszel test accomplish conditioning by dividing the data into strata, one for each possible covariate value. In modern applications, this often gives rise to numerous strata, most of which are sparse due to the multi-dimensionality of the covariate and/or predictor space, while in reality, the covariate space often consists of just a small number of subsets with differential response-predictor dependence. We introduce a Bayesian approach to inferring from the data such an effective stratification and testing for association accordingly. The core of our framework is a recursive mixture model on the retrospective distribution of the predictors, whose mixing distribution is a prior on the partitions on the covariate space. Inference under the model can proceed efficiently in closed form through a sequence of recursions, striking a balance between model flexibility and computational tractability. Simulation studies show that our method substantially outperforms classical tests under various scenarios.