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

Author

Listed:
  • Tiago Dias-Domingues

    (Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
    These authors contributed equally to this work.)

  • Helena Mouriño

    (Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
    These authors contributed equally to this work.)

  • Nuno Sepúlveda

    (Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662 Warsaw, Poland
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Tiago Dias-Domingues & Helena Mouriño & Nuno Sepúlveda, 2024. "Classification Methods for the Serological Status Based on Mixtures of Skew-Normal and Skew-t Distributions," Mathematics, MDPI, vol. 12(2), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:217-:d:1315752
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    References listed on IDEAS

    as
    1. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    2. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    3. Tong, Donald D.M. & Buxser, Stephen & Vidmar, Thomas J., 2007. "Application of a mixture model for determining the cutoff threshold for activity in high-throughput screening," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4002-4012, May.
    4. Rota, Matteo & Antolini, Laura, 2014. "Finding the optimal cut-point for Gaussian and Gamma distributed biomarkers," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 1-14.
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