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Area of Science:

  • Biostatistics
  • Clinical Trials
  • Statistical Modeling

Background:

  • Randomization in clinical trials ensures unbiased estimation of treatment effects when using mean differences.
  • However, bias can occur when assessing treatment effects with other summaries, such as odds ratios, if important covariates are omitted, irrespective of randomization or trial size.

Purpose of the Study:

  • To present accurate closed-form approximations for asymptotic bias arising from omitted covariates in logistic regression.
  • To compare these approximations with existing methods and derive more convenient forms.

Main Methods:

  • Development of closed-form approximations for asymptotic bias in logistic regression models.
  • Comparison of derived approximations with existing literature.
  • Simulation studies to assess the applicability of the approximations for various distributions.

Main Results:

  • Accurate closed-form approximations for asymptotic bias due to omitted normally distributed covariates in logistic regression were derived.
  • The derived approximations offer insights into the nature of the bias.
  • Simulations indicated the utility of these approximations for non-normal distributions as well.

Conclusions:

  • Omitting important covariates can lead to bias in treatment effect estimation (e.g., odds ratios) in clinical trials, even with randomization.
  • The developed approximations provide a valuable tool for understanding and quantifying this bias.
  • The findings are applicable even when the logistic regression model includes additional binary covariates.