Classification Methods for the Serological Status Based on Mixtures of Skew-Normal and Skew-t Distributions

Gaussian mixture models are widely employed in serological data analysis to discern between seropositive and seronegative individuals. However, serological populations often exhibit significant skewness, making symmetric distributions like Normal or Student-t distributions unreliable. In this study, we propose finite mixture models based on Skew-Normal and Skew-t distributions for serological data analysis. Although these distributions are well established in the literature, their application to serological data needs further exploration, with emphasis on the determination of the threshold that distinguishes seronegative from seropositive populations. Our previous work proposed three methods to estimate the cutoff point when the true serological status is unknown. This paper aims to compare the three cutoff techniques in terms of their reliability to estimate the true threshold value. To attain this goal, we conducted a Monte Carlo simulation study. The proposed cutoff points were also applied to an antibody dataset against four SARS-CoV-2 virus antigens where the true serological status is known. For this real dataset, we also compared the performance of our estimated cutoff points with the ROC curve method, commonly used in situations where the true serological status is known.