A comparison of joint dichotomization and single dichotomization of interacting variables to discriminate a disease outcome

Abstract

Dichotomization is often used on clinical and diagnostic settings to simplify interpretation. For example, a person with systolic and diastolic blood pressure above 140 over 90 may be prescribed medication. Blood pressure as well as other factors such as age and cholesterol and their interactions may lead to increased risk of certain diseases. When using a dichotomized variable to determine a diagnosis, if the interactions with other variables are not considered, then an incorrect threshold for the continuous variable may be selected. In this paper, we compare single dichotomization with joint dichotomization; the process of simultaneously optimizing cutpoints for multiple variables. A simulation study shows that simultaneous dichotomization of continuous variables is more accurate in recovering both 'true' thresholds given they exist.

Keywords: Youden’s; cutpoints; dichotomization; disease prediction; odds ratio.

Figure 1:

Values of statistics from Table 2 for different thresholds, $t_{x_1}$; for $X_1$ under single or joint thresholding in the case where two continuous variables $X_1$ and $X_2$ are associated with a binary outcome $Y$ the relationship in the Equation 2. Here $X~N_2\left(0,I_2\right),P_{X_1\ge T_1}>0.2,P_{X_2\ge T_2}>0.2,P_{Y=1}=0.2$, $P_{Y\mid T}=0.2$, and $P_{Y\mid F}=0.094$. The solid line represents the value of each statistic for values of $t_{x_1}$ in $[-\mathrm{4,4}]$ under joint thresholding where $t_{x_2}=T_2$. The dashed line represents the values of each statistic for values of $t_{x_1}$ under single thresholding. The vertical line occurs at the true threshold $T_1$ for $X_1$.

Figure 2:

Numeric estimation of the first derivative of the six statistics from Table 2 for different values of threshold, $t_{x_1}$ for continuous variable $X_1$ under single or joint dichotomization. Here $P_{X_1\ge T_1}=0.2,P_{X_2\ge T_2}=0.2,P_{Y=1}=0.2$ and $OR=3$. Under joint dichotomization we assume that $t_{x_1}$ varies while $t_{x_2}=T_2$

Figure 3:

The results from the simulation study comparing joint and single dichotomization of independent continuous variables. Each plot shows MSE by bias squared for the different values of $P_{X_1\ge T_1}$ and $P_{X_2\ge T_2}$ and strength of association with $Y$.

Figure 4:

The results from the simulation study comparing joint and single dichotomization of interacting continuous variables. Each plot shows MSE by bias squared for the different values of $P_{X_1\ge T_1}$ and $P_{X_2\ge T_2}$ and strength of association with $Y$.