An evaluation of common methods for dichotomization of continuous variables to discriminate disease status

Abstract

Dichotomization of continuous variables to discriminate a dichotomous outcome is often useful in statistical applications. If a true threshold for a continuous variable exists, the challenge is identifying it. This paper examines common methods for dichotomization to identify which ones recover a true threshold. We provide mathematical and numeric proofs demonstrating that maximizing the odds ratio, Youden's statistic, Gini Index, chi-square statistic, relative risk and kappa statistic all theoretically recover a true threshold. A simulation study evaluating the ability of these statistics to recover a threshold when sampling from a population indicates that maximizing the chi-square statistic and Gini Index have the smallest bias and variability when the probability of being larger than the threshold is small while maximizing Kappa or Youden's statistics is best when this probability is larger. Maximizing odds ratio is the most variable and biased of the methods.

Figure 1

Graphical representation of possible thresholds for X presented in equations 1–3.

Figure 2

Simulation results showing mean-squared error (MSE) by Bias² under the case-control study design for the estimated threshold obtained by maximizing the statistics: odds ratio, Youden’s, chi-square, Gini Index, and kappa. Rows represent strength of association between X and Y and columns represent the probability that the independent variable X is greater than the true threshold T.

Figure 3

Simulation results showing mean-squared error (MSE) by Bias² under the case-control study design for the estimated threshold obtained by maximizing the statistics: Youden’s, chi-square, Gini Index, and kappa, excluding P(X ≥ T)=0.05. Rows represent strength of association between X and Y and columns represent the probability that the independent variable X is greater than the true threshold T.