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Author Notes:

Robert H. Lyles: rlyles@sph.emory.edu

Acknowledgments The authors greatly appreciate valuable input from Drs. Larry Kupper and Dana Flanders, as well as the helpful comments of the editor, associate editor, and two referees.


Research Funding:

This work was partially supported by National Institute of Environmental Health Sciences grant 2R01-ES012458-5 (R.H.L.) and by National Institutes of Health grant R01-MH079448-01 (Y.G.).


  • Bias
  • Efficiency
  • Logistic regression
  • Minimum variance unbiased estimator

A Fresh Look at the Discriminant Function Approach for Estimating Crude or Adjusted Odds Ratios


Journal Title:

American Statistician


Volume 63, Number 4


Type of Work:

Article | Post-print: After Peer Review


Assuming a binary outcome, logistic regression is the most common approach to estimating a crude or adjusted odds ratio corresponding to a continuous predictor. We revisit a method termed the discriminant function approach, which leads to closed-form estimators and corresponding standard errors. In its most appealing application, we show that the approach suggests a multiple linear regression of the continuous predictor of interest on the outcome and other covariates, in place of the traditional logistic regression model. If standard diagnostics support the assumptions (including normality of errors) accompanying this linear regression model, the resulting estimator has demonstrable advantages over the usual maximum likelihood estimator via logistic regression. These include improvements in terms of bias and efficiency based on a minimum variance unbiased estimator of the log odds ratio, as well as the availability of an estimate when logistic regression fails to converge due to a separation of data points. Use of the discriminant function approach as described here for multivariable analysis requires less stringent assumptions than those for which it was historically criticized, and is worth considering when the adjusted odds ratio associated with a particular continuous predictor is of primary interest. Simulation and case studies illustrate these points.

Copyright information:

© 2009 American Statistical Association

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