Nonparametric Estimation from Current Status Data with Competing Risks

Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Tanya Henneman, Department of Biostatistics, University of California, Los Angeles

Abstract

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, motivated by an example in Krailo and Pike (1983). We briefly consider simple parametric models as a backdrop to nonparametric procedures. We make some brief comparisons and remarks regarding the nonparametric maximum likelihood estimators. The ideas are illustrated on the data of Krailo and Pike (1983) which considers 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.