Variable Selection for Length-Biased and Interval-Censored Failure Time Data

Length-biased failure time data occur often in various biomedical fields, including clinical trials, epidemiological cohort studies and genome-wide association studies, and their analyses have been attracting a surge of interest. In practical applications, because one may collect a large number of candidate covariates for the failure event of interest, variable selection becomes a useful tool to identify the important risk factors and enhance the estimation accuracy. In this paper, we consider Cox’s proportional hazards model and develop a penalized variable selection technique with various popular penalty functions for length-biased data, in which the failure event of interest suffers from interval censoring. Specifically, a computationally stable and reliable penalized expectation-maximization algorithm via two-stage data augmentation is developed to overcome the challenge in maximizing the intractable penalized likelihood. We establish the oracle property of the proposed method and present some simulation results, suggesting that the proposed method outperforms the traditional variable selection method based on the conditional likelihood. The proposed method is then applied to a set of real data arising from the Prostate, Lung, Colorectal and Ovarian cancer screening trial. The analysis results show that African Americans and having immediate family members with prostate cancer significantly increase the risk of developing prostate cancer, while having diabetes exhibited a significantly lower risk of developing prostate cancer.