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Estimation of separable direct and indirect effects in continuous time.

Torben Martinussen1, Mats Julius Stensrud2

  • 1Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark.

Biometrics
|September 10, 2021
PubMed
Summary

This study introduces new methods for estimating separable direct and indirect causal effects in time-to-event data with competing risks. These methods offer clearer interpretation of treatment effects, aiding in medical research.

Keywords:
competing eventshazard functionsinfluence functionseparable effectssurvival analysis

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Area of Science:

  • Biostatistics
  • Causal Inference
  • Survival Analysis

Background:

  • Time-to-event outcomes with competing risks pose challenges for causal interpretation.
  • Classical statistical measures like hazard ratios are difficult to interpret causally.
  • Cumulative incidence functions capture total effects but not disentangled pathways.

Purpose of the Study:

  • To develop and evaluate methods for estimating separable direct and indirect causal effects in continuous-time settings.
  • To provide robust estimators for disentangling treatment effects on an event of interest and competing events.

Main Methods:

  • Derivation of the nonparametric influence function for continuous-time data.
  • Construction of a robust estimator based on the influence function.
  • Proposal of a semiparametric estimator using cause-specific hazard functions.
  • Analysis of asymptotic properties and simulation studies.

Main Results:

  • New estimators for separable direct and indirect effects in continuous time are presented.
  • The proposed estimators demonstrate satisfactory performance in finite samples.
  • The influence function provides a foundation for robust estimation in this complex setting.

Conclusions:

  • The developed methods enable clearer causal interpretation of treatment effects in the presence of competing risks.
  • These advancements are crucial for accurately assessing interventions in medical research, such as in prostate cancer trials.