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Penalized logistic regression with low prevalence exposures beyond high dimensional settings

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  • Sam Doerken
  • Marta Avalos
  • Emmanuel Lagarde
  • Martin Schumacher

Abstract

Estimating and selecting risk factors with extremely low prevalences of exposure for a binary outcome is a challenge because classical standard techniques, markedly logistic regression, often fail to provide meaningful results in such settings. While penalized regression methods are widely used in high-dimensional settings, we were able to show their usefulness in low-dimensional settings as well. Specifically, we demonstrate that Firth correction, ridge, the lasso and boosting all improve the estimation for low-prevalence risk factors. While the methods themselves are well-established, comparison studies are needed to assess their potential benefits in this context. This is done here using the dataset of a large unmatched case-control study from France (2005-2008) about the relationship between prescription medicines and road traffic accidents and an accompanying simulation study. Results show that the estimation of risk factors with prevalences below 0.1% can be drastically improved by using Firth correction and boosting in particular, especially for ultra-low prevalences. When a moderate number of low prevalence exposures is available, we recommend the use of penalized techniques.

Suggested Citation

  • Sam Doerken & Marta Avalos & Emmanuel Lagarde & Martin Schumacher, 2019. "Penalized logistic regression with low prevalence exposures beyond high dimensional settings," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-14, May.
    • Handle: RePEc:plo:pone00:0217057
    DOI: 10.1371/journal.pone.0217057
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    1. Gerhard Tutz & Harald Binder, 2006. "Generalized Additive Modeling with Implicit Variable Selection by Likelihood-Based Boosting," Biometrics, The International Biometric Society, vol. 62(4), pages 961-971, December.
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