Analysis of antibody data using Finite Mixture Models based on Scale Mixtures of Skew-Normal distributions

Abstract

Finite mixture models have been widely used in antibody (or serological) data analysis in order to help classifying individuals into either antibody-positive or antibody-negative. The most popular models are the so-called Gaussian mixture models which assume a Normal distribution for each component of a mixture. In this work, we propose the use of finite mixture models based on a flexible class of scale mixtures of Skew-Normal distributions for serological data analysis. These distributions are sufficiently flexible to describe right and left asymmetry often observed in the distributions associated with hypothetical antibody-negative and antibody-positive individuals, respectively. We illustrate the advantage of these alternative mixture models with a data set of 406 individuals in which antibodies against six different human herpesviruses were measured in the context of Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.

Herpesviruses Serology Distinguishes Different Subgroups of Patients From the United Kingdom Myalgic Encephalomyelitis/Chronic Fatigue Syndrome Biobank

“…In our association analysis, we allowed the seropositivity cutoff to vary within a given range of possible values, similarly done in a recent study of molecular mimicry between Anoctamin 2 and EBNA1 in multiple sclerosis (55). This analytical approach seems reasonable given the difficulty to choose the best seropositivity cutoff among the different criteria and methods available, as illustrated in the earlier analyses of the same data (38,39). This approach is also in line with several discussions about seropositivity estimation and the sensibility to use a fixed cutoff (56)(57)(58)(59).…”

“…We previously performed thorough analyses of different cutoff values for seropositivity to each viral antigen ( 38 , 39 ). These earlier analyses were based on the comparison and the selection of different scale mixtures of skew-normal distributions and four different criteria to define seropositivity.…”

Analysis of cutoff point estimation for determining seropositivity in the context of SARS-CoV-2 infections

“…This method is more adequate when the antibody distribution of the seronegative population is normally distributed ( [4]). However, our previous studies of different serological data ( [9,30]) showed evidence against a normality assumption for the antibody levels associated with a putative seronegative population. In the case where the true infection (or disease) status is known, ROC curve-based methods are most commonly used to determine the cutoff point for defining seropositivity.…”

“…The presence of antibodies in a serum sample can be regarded as an indicator of immunity against a given infectious agent or as an indicator of past infection in the absence of vaccination ( [10]). The detection of antibodies in the serum samples is classically done via enzyme linked immunosorbent assays (ELISA), where the resulting data are light intensities, also called optical density, which reflects the underlying antibody concentration in the samples ( [9]). For statistical convenience, the analysis of serological data proceeds by dichotomizing the amount of antibodies present in the serum of an individual using an arbitrary cutoff point in the antibody distribution to achieve a certain sensitivity and specificity.…”

“…Alternatively, finite mixture models can be used to determine the seropositivite cutoff directly from the data ( [4,9,13,21,29]). In our previous work, three methods for determining seropositivity cutoff were explored using the so-called scale mixtures of Skew-normal distributions in the case where the true infection status is unknown ( [9]). In this paper we applied the same methods and models in order to evaluate their performance in freely available serological data concerning SARS-CoV-2 virus ( [26]).…”