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Bayesian Regressions

  • Ton J. Cleophas
  • Aeilko H. Zwinderman
Chapter

Abstract

In studies with two unpaired samples of continuous data as outcome and a binary predictor like treatment modality the difference of the two means and their pooled standard error is usually compared to zero. Instead of the above tests a Bayesian regression analysis is possible.

A traditional regression analysis with a single binary predictor provided a linear correlation coefficient of 0.643, p-value = 0.002, and a linear regression coefficient of −1.720, t = −3.558, p-value = 0.002. A Bayesian regression of these data did not compute “supporting null versus alternative hypothesis” but, in contrast, the other ways around, and it provided support in favor of the traditional test with a Bayes factor of 17.329.

A traditional regression analysis with multiple binary predictors provided a linear correlation coefficient of 0.669, p-value = 0.021, and only one significant linear regression coefficients of −1.642, t = −3.223, p-value = 0.005. A Bayesian regression of these data did again not compute “supporting null versus alternative hypothesis” but, in contrast, the other ways around, and it provided support in favor of the traditional test with a Bayes factor of 1.626.

A traditional regression analysis with a single continuous predictor provided a linear correlation coefficient of 0.975, p-value = 0.000, and a linear regression coefficient of 0.093, t = 18.443, p-value = 0.000. A Bayesian regression of these data again did not compute “supporting null versus alternative hypothesis” but, in contrast, the other ways around, and it provided support in favor of the traditional test with a Bayes factor of 2.28410.

A disadvantage of Bayesian analysis may be an increased risk of overfitting, but in the regression examples in this chapter this was virtually not observed.

Suggested Reading1,2

  1. Statistics applied to clinical studies 5th edition, 2012Google Scholar
  2. Machine learning in medicine a complete overview, 2015Google Scholar
  3. SPSS for starters and 2nd levelers 2nd edition, 2015Google Scholar
  4. Clinical data analysis on a pocket calculator 2nd edition, 2016Google Scholar
  5. Understanding clinical data analysis from published research, 2016Google Scholar
  6. Modern Meta-analysis, 2017, Regression Analysis in Clinical Research, 2018Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ton J. Cleophas
    • 1
  • Aeilko H. Zwinderman
    • 2
  1. 1.Department Medicine Albert Schweitzer HospitalAlbert Schweitzer HospitalSliedrechtThe Netherlands
  2. 2.Department Biostatistics and EpidemiologyAcademic Medical Center Department Biostatistics and EpidemiologyAmsterdamThe Netherlands

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