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Statistical inference for data-adaptive doubly robust estimators with survival outcomes.

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This study introduces a novel doubly robust estimator for survival analysis. It achieves reliable estimation even when nuisance parameters are estimated with less precision, improving statistical inference.

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Doubly robust estimators require consistent estimation of nuisance parameters.
  • In complex models, achieving this consistency can be challenging.
  • Existing methods may lack guaranteed n1/2-consistency if one nuisance estimator is inconsistent.

Purpose of the Study:

  • To develop a doubly robust estimator for survival analysis with improved consistency properties.
  • To relax the stringent conditions on nuisance parameter estimation.
  • To provide a method with guaranteed n1/2-convergence under weaker assumptions.

Main Methods:

  • Developed a novel doubly robust estimator for survival data.
  • Applied semiparametric inference techniques, including Gaussianization of a drift term.
  • Utilized cross-fitting to mitigate entropy conditions on nuisance estimators.
  • Derived the formula for the asymptotic variance of the new estimator.

Main Results:

  • The proposed estimator achieves n1/2-rate convergence for a broad range of data-adaptive nuisance estimators.
  • This convergence holds if at least one nuisance estimator is consistently estimated at an n1/4-rate.
  • The derived asymptotic variance enables computation of doubly robust confidence intervals and p-values.

Conclusions:

  • The new estimator offers enhanced robustness and reliability in survival analysis.
  • It provides a valuable tool for statistical inference, particularly in complex settings.
  • Demonstrated utility in a phase III clinical trial for HER2-positive breast cancer therapy evaluation.