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Inverse probability weighted (IPW) estimates for Cox marginal structural models (MSMs) can be unbiased even with time-varying confounders. This study introduces a data generation method to compare IPW bias against standard regression bias without model misspecification.

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Causal Inference

Background:

  • Standard regression estimates can be biased by time-varying confounders affected by prior treatment.
  • Inverse probability weighted (IPW) methods offer potential unbiasedness for Cox marginal structural models (MSMs).
  • Existing simulation methods for Cox MSMs often require knowledge of outcome-dependent past data, limiting bias isolation.

Purpose of the Study:

  • To develop a data generation approach for comparing bias in IPW versus standard regression estimates for Cox MSMs.
  • To isolate and quantify bias stemming from time-varying confounding, distinct from model misspecification.
  • To demonstrate that standard regression bias is a function of time-varying confounder effects.

Main Methods:

  • Simulate data from a standard likelihood parametrization.
  • Solve for the underlying Cox MSM parameters.
  • Analytically and through simulations, compare bias of IPW and standard regression estimates.

Main Results:

  • The proposed data generation method allows for unbiased comparison of estimation methods.
  • Bias in standard regression estimates for Cox MSM parameters is shown to be dependent on time-varying confounder effects.
  • Computations are tractable under various data-generating mechanisms.

Conclusions:

  • The developed method effectively isolates bias due to time-varying confounding in Cox MSMs.
  • Standard regression estimates are susceptible to bias from time-varying confounders, even when the outcome model is correctly specified.
  • This approach aids in understanding and mitigating bias in causal effect estimation.