Improving Power by Dichotomizing (Even Under Normality)

Abstract

This article reviews controversies surrounding dichotomization in biopharmaceutical research. Despite known loss of power following dichotomization in the univariate case, it is shown that dichotomizing continuous data can greatly improve the power of multiple testing procedures. To illustrate such gains, the apparently under-appreciated discrete multiple comparisons method is reviewed and applied to the case of dichotomization. The resulting method has precise control of the familywise error rate, and specific power gains relative to comparable methods that use the continuous data are demonstrated. Cases where such power gains are likely (even with normally distributed data) are identified, and applications to biopharmaceutical research are discussed. The first application is to gene expression analysis, where it is shown that power of classical multiple comparisons methods with normally distributed data (even false discovery rate controlling methods) can be arbitrarily low, while the dichotomized familywise error rate controlling method maintains a constant 0.92 power. A second application shows that multiple tests for endpoints in clinical trials can benefit by using dichotomization. Finally, in an analysis of multiple dichotomous thresholds to classify prostate cancer, it is shown that a discrete Boole inequality-based method can be quite powerful, even with highly correlated data.

Keywords: :

• Bonferroni-Holm method
• Closed testing
• Discrete distribution
• Familywise error rate
• Fisher exact test
• Multiple comparisons