Consequences of Dichotomization
Consequences of Dichotomization
Valerii Fedorov, Frank Mannino and Rongmei Zhang
ABSTRACT Dichotomization is the transformation of a continuous outcome (response) to a binary outcome. This approach, while somewhat common, is not harmless from the viewpoint of statistical estimation and hypothesis testing. We show that this leads to a loss of information, which can be large. For normally distributed data, this loss in terms of Fisher’s information is at least 1 − 2/pi (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 a 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 analysis model is very different from the true model, can the use of dichotomized outcomes be considered a reasonable approach.
