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Nonparametric estimation from current status data with competing risks. (English) Zbl 1034.62034

Summary: A great deal of recent attention has focused on the estimation of survival distributions based on current status data, an extreme form of interval censored data. This particular data structure arises in a wide variety of applications where cross-sectional observation either naturally occurs or is preferred to more traditional forms of follow-up.
Here, we consider current status data in the context of competing risks. We briefly consider simple parametric models as a backdrop to nonparametric procedures. We make some brief comparisons and remarks regarding the nonparametric maximum likelihood estimator. The ideas are illustrated on the data of M. D. Krailo and M. C. Pike [Am. J. Epidem. 117, 356–361 (1983)] which consider estimation of the age distribution at both natural and operative menopause. We also consider the case where there is exact observation of failure times due to one of the competing risks when failure occurs prior to the monitoring time.

MSC:

62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis
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