A likelihood and resampling based approach to dichotomizing a continuous biomarker in medical research

Dichotomizing a continuous biomarker is a common practice in medical research. Various methods exist in the literature for dichotomizing continuous biomarkers. The most widely adopted minimum p-value approach uses a sequence of test statistics for all possible dichotomizations of a continuous biomarker, and it chooses the cutpoint that is associated with the maximum test statistic, or equivalently, the minimum p-value of the test. We herein propose a likelihood and resampling-based approach to dichotomizing a continuous biomarker. In this approach, the cutpoint is considered as an unknown variable in addition to the unknown outcome variables, and the likelihood function is maximized with respect to the cutpoint variable as well as the outcome variables to obtain the optimal cutpoint for the continuous biomarker. The significance level of the test for whether a cutpoint exists is assessed via a permutation test using the maximum likelihood values calculated based on the original as well as the permutated data sets. Numerical comparisons of the proposed approach and the minimum p-value approach showed that the proposed approach was not only more powerful in detecting the cutpoint but also provided markedly more accurate estimates of the cutpoint than the minimum p-value approach in all the simulation scenarios considered.