Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of variable selection using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial likelihood estimator, and show that the proposed variable selection procedure is consistent and has an asymptotic oracle property. Simulation studies compare the finite sample performance of the procedure with Akaike information criterion- and Bayesian information criterion-based tuning parameter selection methods. We make recommendations for use of the procedures in case-cohort studies, and apply them to the Busselton Health Study.



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