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On nonparametric maximum likelihood estimation with double truncation.

J Xiao1, M G Hudgens2

  • 1SPHERE Institute, 500 Airport Blvd #340, Burlingame, California 94010, USA.

Biometrika
|November 23, 2019
PubMed
Summary
This summary is machine-generated.

Graphical conditions determine the existence and uniqueness of nonparametric maximum likelihood estimates for doubly truncated survival data. A new graphical method helps assess these estimates, revealing non-existence in an AIDS incubation time dataset analysis.

Keywords:
GraphNonparametric estimatorTruncation

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Data Science

Background:

  • Doubly truncated survival data occur when observations are limited to specific time intervals.
  • The nonparametric maximum likelihood estimator (NPMLE) is a standard method for estimating failure time distributions.
  • Assessing the existence and uniqueness of NPMLEs is crucial for reliable survival data analysis.

Purpose of the Study:

  • To introduce graphical conditions for determining the existence and uniqueness of NPMLEs for doubly truncated data.
  • To propose a practical method for checking these graphical conditions using existing software.
  • To re-evaluate an AIDS incubation time dataset using the proposed graphical approach.

Main Methods:

  • Utilizing a directed graph representation of survival data, inspired by Vardi (1985).
  • Defining and applying specific graphical conditions to assess NPMLE existence and uniqueness.
  • Conducting a reanalysis of a published AIDS incubation time dataset.

Main Results:

  • A graphical condition was identified that precisely indicates when the NPMLE exists and is unique.
  • If the primary condition fails, a secondary graphical condition can determine if an NPMLE exists at all.
  • The reanalysis of the AIDS incubation time data demonstrated that a valid NPMLE does not exist for this dataset.

Conclusions:

  • The proposed graphical conditions offer a straightforward method for evaluating NPMLEs in doubly truncated survival data.
  • These conditions are computationally simple and can be implemented with current graphical software.
  • The findings highlight potential issues with NPMLE application in certain real-world datasets, as exemplified by the AIDS incubation time data.