A semi-supervised Bayesian mixture modelling approach for joint batch correction and classification

Systematic differences between batches of samples present significant challenges when analysing biological data. Such batch effects are well-studied and are liable to occur in any setting where multiple batches are assayed. Many existing methods for accounting for these have focused on high-dimensional data such as RNA-seq and have assumptions that reflect this. Here we focus on batch-correction in low-dimensional classification problems. We propose a semi-supervised Bayesian generative classifier based on mixture models that jointly predicts class labels and models batch effects. Our model allows observations to be probabilistically assigned to classes in a way that incorporates uncertainty arising from batch effects. We explore two choices for the within-class densities: the multivariate normal and the multivariate t. A simulation study demonstrates that our method performs well compared to popular off-the-shelf machine learning methods and is also quick; performing 15,000 iterations on a dataset of 500 samples with 2 measurements each in 7.3 seconds for the MVN mixture model and 11.9 seconds for the MVT mixture model. We apply our model to two datasets generated using the enzyme-linked immunosorbent assay (ELISA), a spectrophotometric assay often used to screen for antibodies. The examples we consider were collected in 2020 and measure seropositivity for SARS-CoV-2. We use our model to estimate seroprevalence in the populations studied. We implement the models in C++ using a Metropolis-within-Gibbs algorithm; this is available in the R package at https://github.com/stcolema/BatchMixtureModel. Scripts to recreate our analysis are at https://github.com/stcolema/BatchClassifierPaper. ### Competing Interest Statement The authors have declared no competing interest.