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Abstract This paper discusses regression analysis of incomplete event history studies with a focus on simultaneous estimation and variable selection. Such studies are commonly performed in areas such as medical studies and social sciences, and a great deal of literature has been devoted to their analysis except for the problem considered here (Sun and Zhao, 2013). We develop a new method, which will be referred to as a broken adaptive ridge regression approach. We establish its asymptotic properties, including the oracle property and clustering effect. We also report simulation results which indicate that the proposed method performs well, and better than the existing methods, in practice. In addition, an application is provided. [ABSTRACT FROM AUTHOR]