Determining the Cutoff Based on a Continuous Variable to Define Two Populations

Abstract

In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate. The distribution of a continuous variable can differ between two populations defined by the case status. Under such a scenario, the dichotomization process can be based on distributions of the continuous variable in two distinct populations. The resulting dichotomous variable can be used as an endpoint in future studies. Even though dichotomization has not been extensively studied, dichotomization has been commonly carried out in clinical trials. We developed a methodology on dichotomization based on maximizing the correlation between the two populations and the dichotomous variable. We have investigated several commonly assumed distributions (e.g., normal, log-normal and gamma distribution) of the continuous variable for the two populations and developed a numerical algorithm for the proposed method to determine the optimal cutoff point. The two populations can differ in form and/or parameters. The proposed method of finding the optimal cutoff was also extended to adjust for covariates. In real world scenarios where the two samples from the two populations are not completely identified, we recommended using the EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. The performance of the proposed method with the numerical algorithm and the EM method has been studied for several theoretical distributions and using simulated data. These methods were also applied to a varicella vaccine example.