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Using the jackknife for estimation in log link Bernoulli regression models.

Stuart R Lipsitz1, Garrett M Fitzmaurice, Alex Arriaga

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|November 13, 2014
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Summary
This summary is machine-generated.

Bernoulli regression with a log link offers interpretable relative risks for common outcomes. A novel jackknife bias-reduction method improves upon the COPY method for prevalent outcomes in generalized linear models.

Keywords:
bias-reductioncopy methodmaximum likelihoodnon-convergencerelative risk regression

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Bernoulli regression with a log link is preferred over logistic regression for prospective studies with common outcomes, as it yields relative risks.
  • Relative risks are often considered more interpretable than odds ratios.
  • A challenge arises with the log link when outcomes are highly prevalent, potentially leading to non-unique likelihood maxima.

Purpose of the Study:

  • To address the bias in the COPY method for Bernoulli regression when outcomes are prevalent.
  • To propose and evaluate the jackknife as a bias-reduction technique for the COPY method.
  • To enhance the accuracy of relative risk estimation in generalized linear models for common outcomes.

Main Methods:

  • The study proposes using the jackknife technique to reduce bias.
  • The COPY method, which involves creating a pseudo-observation with interchanged outcome values, is utilized.
  • The proposed jackknife approach is applied to the COPY method to mitigate estimation bias.

Main Results:

  • The COPY method, while ensuring convergence, can produce biased estimates for prevalent outcomes or small sample sizes.
  • The jackknife bias-reduction approach is investigated as a solution to the limitations of the COPY method.
  • The study evaluates the performance of the jackknife-enhanced COPY method in scenarios with common outcomes.

Conclusions:

  • The jackknife offers a viable bias-reduction strategy for the COPY method in Bernoulli regression.
  • This approach improves the reliability of relative risk estimates, particularly in studies with prevalent outcomes.
  • The findings are relevant for statistical analysis in fields like colorectal cancer surgery research.