The one-sided three sigma rule: is it a beauty or a beast in serological data analysis
ฝัง
- เผยแพร่เมื่อ 17 ก.ย. 2024
- This is my rehearsal for a talk that I will deliver in the LIII International Biometrical Colloquium, Poznań 8-11 September 2024.
Abstract:
Many epidemiological studies aim at estimating the proportion of individuals currently or previously infected by a given microorganism. Given that an infection leads to an immune response, this estimation exercise often requires identifying individuals who reach a minimal level of microbe-specific antibodies in their serum (Vainionpää et al, 2015). This threshold typically is defined by the three-sigma rule: mean plus three times the standard deviation from the hypothetical antibody-negative population (Sepúlveda et al, 2015). Notwithstanding not being linked to a specific parametric distribution, it has the most intuitive interpretation in the context of a normal distribution (Dias Domigues et al, 2024). I will then discuss the problems of estimation bias and apparent control of specificity arising from applying this rule to nonnormal distributions for the seronegative population. I will use serological data on SARS-CoV2 to illustrate these problems. I finally pose the question whether the three-sigma rule is a beautiful statistical concept or, instead, a little beast hidden in serological data analysis.
Keywords: Gaussian mixture models, seropositivity, serological data.
References
Dias Domingues , T., Mouriño, H., Sepúlveda, N. 2024. Analysis of Antibody Data Using Skew-normal and Skew-T Mixture Models. REVSTAT-Statistical Journal 22(1): 111-132.
Sepúlveda, N., Stresman, G., White, M. T., & Drakeley, C. J. 2015. Current Mathematical Models for Analyzing Anti-Malarial Antibody Data with an Eye to Malaria Elimination and Eradication. Journal of Immunology research 2015:738030.
Vainionpää, R., Waris, M., Leinikki, P. 2015. Diagnostic Techniques: Serological and Molecular Approaches. Reference Module In Biomedical Science Approaches 2015:B978-0-12-801238-3.02558-7.
Acknowledgements
The author acknowledges partial funding from FCT - Fundação para a Ciência e Tecnologia, Portugal (grant ref. UIDB/00006/2020)
