This paper discusses nonparametric estimation of a survival function when one observes only current status data (McKeown and Jewell, Lifetime Data Anal 16:215–230, 2010; Sun, The statistical analysis of interval-censored failure time data, 2006; Sun and Sun, Can J Stat 33:85–96, 2005). In this case, each subject is observed only once and the failure time of interest is observed to be either smaller or larger than the observation or censoring time. If the failure time and the observation time can be assumed to be independent, several methods have been developed for the problem. Here we will focus on the situation where the independent assumption does not hold and propose two simple estimation procedures under the copula model framework. The proposed estimates allow one to perform sensitivity analysis or identify the shape of a survival function among other uses. A simulation study performed indicates that the two methods work well and they are applied to a motivating example from a tumorigenicity study.
Copula models Current status data Dependent censoring Nonparametric estimation
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