One- and two-sample nonparametric inference procedures in the presence of a mixture of independent and dependent censoring

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Abstract
In survival analysis, the event time T is often subject to dependent censorship. Without assuming a parametric model between the failure and censoring times, the parameter Θ of interest, for example, the survival function of T, is generally not identifiable. On the other hand, the collection Ω of all attainable values for Θ may be well defined. In this article, we present nonparametric inference procedures for Ω in the presence of a mixture of dependent and independent censoring variables. By varying the criteria of classifying censoring to the dependent or independent category, our proposals can be quite useful for the so-called sensitivity analysis of censored failure times. The case that the failure time is subject to possibly dependent interval censorship is also discussed in this article. The new proposals are illustrated with data from two clinical studies on HIV-related diseases.

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