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<p>In this article, we consider nonparametric estimation of the cumulative incidence function (CIF) for left-truncated and interval-censored competing risks (LT-ICC) data. We propose two estimators and show that they are asymptotically equivalent and consistent. The first estimator is the non-parametric maximum likelihood estimator (NPMLE) derived from the likelihood functions for LT-ICC data. In particular, we correctly formulate the innermost intervals for developing self-consistent equations and establish consistency of the NPMLE. The second estimator, called the pseudo-likelihood estimator (PLE), is obtained by implementing a suitable constraint on the procedure from Hudgens et al. (2001), leading to the asymptotic equivalence of the PLE and the NPMLE. Simulation studies show that both estimators perform well.</p>

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The NPMLE of cumulative incidence function for competing risks survival data subject to interval censoring and left truncation

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Pao-sheng Shen,
  • Raf Loreto

摘要

In this article, we consider nonparametric estimation of the cumulative incidence function (CIF) for left-truncated and interval-censored competing risks (LT-ICC) data. We propose two estimators and show that they are asymptotically equivalent and consistent. The first estimator is the non-parametric maximum likelihood estimator (NPMLE) derived from the likelihood functions for LT-ICC data. In particular, we correctly formulate the innermost intervals for developing self-consistent equations and establish consistency of the NPMLE. The second estimator, called the pseudo-likelihood estimator (PLE), is obtained by implementing a suitable constraint on the procedure from Hudgens et al. (2001), leading to the asymptotic equivalence of the PLE and the NPMLE. Simulation studies show that both estimators perform well.