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

Abstract

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. By simultaneously inferring the classification and the batch-correction our method is more robust to dependence between batch and class than pre-processing steps such as ComBat. 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 750 samples with 2 measurements each in 11.7 seconds for the MVN mixture model and 14.7 seconds for the MVT mixture model. We further validate our model on gene expression data where cell type (class) is known and simulate batch effects. 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, available in the R package batchmix. Scripts to recreate our analysis are at https://github.com/stcolema/BatchClassifierPaper.