Predicting allergy and postpartum depression from an incomplete compositional microbiome

Time series of compositional data are a common format for many high-throughput studies of biological molecules, e.g., analyzing the response to a treatment or with the aim of predicting an outcome. However, data from some time points may be missing, which reduces the size of the complete dataset. We propose a method for binary classification that includes imputation for missing values, dimensionality reduction, and logarithmic transformation of compositional data. Imputation approaches entail models that incorporate artificial data alongside true measurements, thereby supplementing the dataset. In the application part, we consider two case studies with longitudinal data and associated target labels, aiming to improve prediction accuracy. We predict infants' food allergies from their gut microbiome with a balanced accuracy of 0.72. We forecast postpartum depression based on gut microbiome data collected during pregnancy, with a balanced accuracy of 0.62. Features extracted from the microbiome time series, specifically ratios of bacterial abundance, are statistically significant indicators of depression.