Determining the cutoff based on a continuous variable to define two populations with application to vaccines

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 with patients. The distribution of the continuous variable can differ between two populations defined by a disease 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 for determining the optimal cutoff point based on maximizing the correlation between the two populations and the dichotomous variable. In some real-world scenarios where outcome status in samples from two populations is not completely identified, we recommend using EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. In addition, we have investigated the performance of the proposed method for several common distributions (e.g., normal, log-normal and exponential distribution) of the continuous variable. Finally, we applied the proposed methods to a varicella vaccine example.