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Confidence intervals for the cumulative incidence function via constrained NPMLE. (English) Zbl 1437.62361

Summary: The cumulative incidence function (CIF) displays key information in the competing risks setting, which is common in medical research. In this article, we introduce two new methods to compute non-parametric confidence intervals for the CIF. First, we introduce non-parametric profile-likelihood confidence intervals. The method builds on constrained non-parametric maximum likelihood estimation (NPMLE), for which we derive closed-form formulas. This method can be seen as an extension of that of D. R. Thomas and G. L. Grunkemeier [J. Am. Stat. Assoc. 70, 865–871 (1975; Zbl 0331.62028)] to the competing risks setting, when the CIF is of interest instead of the survival function. Second, we build on constrained NPMLE to introduce constrained bootstrap confidence intervals. This extends an interesting approach introduced by S. Barber and C. Jennison [Biometrics 55, No. 2, 430–436 (1999; Zbl 1059.62603)] to the competing risks setting. A simulation study illustrates how these methods can perform as compared to benchmarks implemented in popular software. The results suggest that more accurate confidence intervals than usual Wald-type ones can be obtained in the case of small to moderate sample sizes and few observed events. An application to melanoma data is provided for illustration purpose.

MSC:

62N01 Censored data models
62G15 Nonparametric tolerance and confidence regions
62G07 Density estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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