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The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
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Improving estimation efficiency for case-cohort studies with a cure fraction.

Qingning Zhou1, Xu Cao2

  • 1Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States.

Biometrics
|May 14, 2025
PubMed
Summary

This study introduces a novel statistical method for analyzing time-to-event data with a cure fraction using a generalized case-cohort design. The proposed approach enhances efficiency and accuracy in estimating cure rates and event probabilities, even with missing covariate data.

Keywords:
auxiliary variablemissing datamixture cure modelrobust estimationsemiparametric inferencesurvival analysis

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Epidemiology

Background:

  • Time-to-event studies often include subjects who never experience the event (cure fraction).
  • Low event rates in such studies can reduce statistical power and increase costs.
  • Two-phase sampling designs, like the generalized case-cohort design, are efficient for handling expensive covariates.

Purpose of the Study:

  • To propose a statistical estimation procedure for semiparametric transformation mixture cure models under a generalized case-cohort design.
  • To develop an efficient and consistent estimation method that accounts for a cure fraction and utilizes two-phase sampling.
  • To provide a robust method for analyzing time-to-event data with potential cures and expensive covariates.

Main Methods:

  • A two-step estimation procedure involving sieve maximum weighted likelihood and an Expectation-Maximization (EM) algorithm.
  • Updating the initial estimator using a working model with auxiliary variables for improved efficiency.
  • Developing a weighted bootstrap procedure for reliable variance estimation.

Main Results:

  • The proposed update estimator is shown to be consistent and asymptotically efficient.
  • The method performs well even if the working model is misspecified.
  • Simulation studies confirm the superior finite-sample performance of the proposed method.

Conclusions:

  • The generalized case-cohort design combined with the proposed semiparametric cure model offers an efficient approach for time-to-event data analysis.
  • The method provides accurate and robust estimates, particularly valuable in studies with cure fractions and costly covariates.
  • The approach is applicable to real-world epidemiological studies, as demonstrated by its application to the National Wilms' Tumor Study.