Time-series of compositional data are a common format for many high-throughput studies of biological molecules, analyzing e.g. response to a treatment or with the aim to predict 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 and logarithmic transformation of compositional data. Imputation approaches entail models that incorporate artificial data alongside true measurements, thereby supplementing the dataset. We consider two datasets from prospective analyses with associated target labels, aiming to improve prediction accuracy. We predict infants\' food allergy 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.