Qi Zheng, PhD, Department of Bioinformatics and Biostatistics, University of Louisville

"Spatiotemporal mixed effect modeling and its applications"

Forward regression, a classical variable screening method, has been widely used for model building when the number of covariates is relatively low compared to the sample size. However, forward regression is seldom used in high-dimensional settings, when the predictor dimension is substantially larger than the sample size, because of cumbersome computation and unknown theoretical properties. Recently, Wang (2009) and Chen et al (2016) have shown that forward regression can identify all relevant predictors consistently in high-dimensional linear regression settings. However, it is unclear whether forward regression can be applied to more general regression settings, such as Cox proportional hazards models. We introduce a forward variable selection procedure for survival data. It selects important variables sequentially according to the increment of partial likelihood, with an extended Bayesian information criterion (EBIC)-based stopping rule. To our knowledge, this is the first study that investigates the partial likelihood-based forward regression in high-dimensional settings and establishes rigorous selection consistency results. As partial likelihood is not a regular density-based likelihood, we develop some new theoretical results on partial likelihood and use these results to establish the desired sure screening properties. The practical utility of the proposed method is examined via extensive simulations and analyses of two real datasets. We envision the established theoretical framework will facilitate the extension of the procedure to other general settings, such as generalized linear models.

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