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Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Targeted maximum likelihood estimation for causal inference in survival and competing risks analysis.

Helene C W Rytgaard1, Mark J van der Laan2

  • 1Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark. hely@sund.ku.dk.

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|November 6, 2022
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Summary

Targeted maximum likelihood estimation (TMLE) offers a robust method for causal inference in survival and competing risks analysis. This approach effectively estimates treatment effects on survival and risk, even with complex data structures.

Keywords:
Average treatment effectsCausal inferenceCompeting risksHighly adaptive lassoSemiparametric efficiencySuper learningSurvival analysisTMLE

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Area of Science:

  • Causal Inference
  • Biostatistics
  • Survival Analysis
  • Competing Risks

Background:

  • Targeted Maximum Likelihood Estimation (TMLE) is a powerful methodology for estimating causal parameters, particularly when dealing with high-dimensional nuisance parameters.
  • TMLE combines data-adaptive estimation of nuisance parameters with semiparametric efficiency and rigorous statistical inference through a targeted update.
  • Existing methods often face limitations in continuous-time survival and competing risks settings.

Purpose of the Study:

  • To demonstrate the practical application of TMLE for causal inference in continuous-time survival and competing risks analysis.
  • To estimate the causal effects of time-fixed treatment decisions on survival probabilities and absolute risks.
  • To provide guidance on extending TMLE with super learning for conditional hazard estimation.

Main Methods:

  • Applied Targeted Maximum Likelihood Estimation (TMLE) to survival and competing risks data.
  • Focused on estimating causal effects of time-fixed treatments on survival and absolute risk probabilities.
  • Incorporated super learning (loss-based cross-validation) for estimating conditional hazards.

Main Results:

  • Successfully demonstrated the practical applicability of TMLE in complex survival and competing risks scenarios.
  • Estimated various univariate and multidimensional causal parameters related to treatment effects.
  • Illustrated the methods using real-world data from a colon cancer adjuvant chemotherapy trial.

Conclusions:

  • TMLE provides a versatile and effective framework for causal inference in continuous-time survival and competing risks settings.
  • The integration of super learning enhances the estimation of nuisance parameters, improving causal effect estimation.
  • The study provides practical guidance and reproducible R code for applying these advanced causal inference techniques.