Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Super doubly robust and efficient estimator for informative covariate censoring

Zhewei Zhang, Yanyuan Ma, Karen Marder, Tanya P. Garcia

TL;DR

This work tackles the challenge of estimating pre-diagnosis decline when the time of diagnosis $X$ is right-censored by study exit $C$, with informative censoring potentially present. It introduces SPIRE, a semi-parametric, super doubly robust estimator that remains consistent without correctly specifying $f_{C|{f Z}}$ or $f_{X|C,{f Z}}$, and achieves semiparametric efficiency when the latter is correctly specified. The authors derive the efficient score via projection onto the orthogonal nuisance space, provide a practical discretization-based implementation, and develop a chi-square test to detect noninformative censoring. Through simulations and an Enroll-HD analysis, SPIRE demonstrates robustness to model misspecification, improved efficiency, and reliable detection of informative censoring, offering a principled tool for identifying rapid pre-diagnosis decline and informing intervention windows in neurodegenerative research.

Abstract

Early intervention in neurodegenerative diseases requires identifying periods before diagnosis when decline is rapid enough to detect whether a therapy is slowing progression. Since rapid decline typically occurs close to diagnosis, identifying these periods requires knowing each patient's time of diagnosis. Yet many patients exit studies before diagnosis, making time of diagnosis right-censored by time of study exit -- creating a right-censored covariate problem when estimating decline. Existing estimators either assume noninformative covariate censoring, where time of study exit is independent of time of diagnosis, or allow informative covariate censoring, but require correctly specifying how these times are related. We developed SPIRE (Semi-Parametric Informative Right-censored covariate Estimator), a super doubly robust estimator that remains consistent without correctly specifying densities governing time of diagnosis or time of study exit. Typical double robustness requires at least one density to be correct; SPIRE requires neither. When both densities are correctly specified, SPIRE achieves semiparametric efficiency. We also developed a test for detecting informative covariate censoring. Simulations with 85% right-censoring demonstrated SPIRE's robustness, efficiency and reliable detection of informative covariate censoring. Applied to Huntington disease data, SPIRE handled informative covariate censoring appropriately and remained consistent regardless of density specification, providing a reliable tool for early intervention.

Super doubly robust and efficient estimator for informative covariate censoring

TL;DR

This work tackles the challenge of estimating pre-diagnosis decline when the time of diagnosis is right-censored by study exit , with informative censoring potentially present. It introduces SPIRE, a semi-parametric, super doubly robust estimator that remains consistent without correctly specifying or , and achieves semiparametric efficiency when the latter is correctly specified. The authors derive the efficient score via projection onto the orthogonal nuisance space, provide a practical discretization-based implementation, and develop a chi-square test to detect noninformative censoring. Through simulations and an Enroll-HD analysis, SPIRE demonstrates robustness to model misspecification, improved efficiency, and reliable detection of informative censoring, offering a principled tool for identifying rapid pre-diagnosis decline and informing intervention windows in neurodegenerative research.

Abstract

Early intervention in neurodegenerative diseases requires identifying periods before diagnosis when decline is rapid enough to detect whether a therapy is slowing progression. Since rapid decline typically occurs close to diagnosis, identifying these periods requires knowing each patient's time of diagnosis. Yet many patients exit studies before diagnosis, making time of diagnosis right-censored by time of study exit -- creating a right-censored covariate problem when estimating decline. Existing estimators either assume noninformative covariate censoring, where time of study exit is independent of time of diagnosis, or allow informative covariate censoring, but require correctly specifying how these times are related. We developed SPIRE (Semi-Parametric Informative Right-censored covariate Estimator), a super doubly robust estimator that remains consistent without correctly specifying densities governing time of diagnosis or time of study exit. Typical double robustness requires at least one density to be correct; SPIRE requires neither. When both densities are correctly specified, SPIRE achieves semiparametric efficiency. We also developed a test for detecting informative covariate censoring. Simulations with 85% right-censoring demonstrated SPIRE's robustness, efficiency and reliable detection of informative covariate censoring. Applied to Huntington disease data, SPIRE handled informative covariate censoring appropriately and remained consistent regardless of density specification, providing a reliable tool for early intervention.

Paper Structure

This paper contains 21 sections, 3 theorems, 64 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. A class of consistent estimators
  3. Model assumptions and identifiability
  4. Constructing the class of consistent estimators
  5. The super doubly robust and efficient estimator
  6. Development and properties of SPIRE
  7. Implementation of SPIRE
  8. Test for noninformative covariate censoring
  9. Simulation studies
  10. Evaluation of robustness and efficiency
  11. Evaluation of power to detect differences between noninformative and informative covariate censoring
  12. Application to Enroll-HD data
  13. Discussion
  14. Proof of Lemma \ref{['lem:1']}
  15. Specific form of the nuisance tangent space $\Lambda$ and its proof
  16. ...and 6 more sections

Key Result

Proposition 1

The orthogonal complement $\Lambda^\perp$ takes the form

Figures (2)

  • Figure 1: Simulation results of the empirical power and the empirical size based on 1000 replicates. ${\rm cc}$: when $\widehat{{\boldsymbol\beta}}_1$ is the CC estimator; ${\rm spire}$: when $\widehat{{\boldsymbol\beta}}_1$ is the SPIRE estimator; ${\rm ipw}$: when $\widehat{{\boldsymbol\beta}}_1$ is the IPW estimator. The horizontal dashed line represents the 0.05 significance level.
  • Figure 2: $95\%$ Confidence intervals for all parameters where the working model is the localized Kaplan-Meier (K-M) estimator (left) and the uniform model (right).

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • proof