Consequences of dichotomization

Authors

  • Valerii Fedorov,

    1. Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, Collegeville, PA, USA
    Search for more papers by this author
  • Frank Mannino,

    Corresponding author
    1. Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, Collegeville, PA, USA
    • Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, 1250 South Collegeville Road, Collegeville, PA 19426, USA
    Search for more papers by this author
  • Rongmei Zhang

    1. Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, Collegeville, PA, USA
    2. Department of Biostatistics and Epidemiology, School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
    Search for more papers by this author

Abstract

Dichotomization is the transformation of a continuous outcome (response) to a binary outcome. This approach, while somewhat common, is harmful from the viewpoint of statistical estimation and hypothesis testing. We show that this leads to loss of information, which can be large. For normally distributed data, this loss in terms of Fisher's information is at least 1 − 2/π (or 36%). In other words, 100 continuous observations are statistically equivalent to 158 dichotomized observations. The amount of information lost depends greatly on the prior choice of cut points, with the optimal cut point depending upon the unknown parameters. The loss of information leads to loss of power or conversely a sample size increase to maintain power. Only in certain cases, for instance, in estimating a value of the cumulative distribution function and when the assumed model is very different from the true model, can the use of dichotomized outcomes be considered a reasonable approach. Copyright © 2008 John Wiley & Sons, Ltd.

Ancillary