The relationship between tumor immune responses and tumor neoantigens is one of the most fundamental and unsolved questions in tumor immunology, and is the key to understanding the inefficiency of immunotherapy observed in many cancer patients. However, the properties of neoantigens that can elicit immune responses remain unclear. This biological problem can be represented and solved under a multiple instance learning framework, which seeks to model multiple instances (neoantigens) within each bag (patient specimen) with the continuous response (T cell infiltration) observed for each bag. To this end, we develop a Bayesian multiple instance regression method, named BMIR, using a Gaussian distribution to address continuous responses and latent binary variables to model primary instances in bags. By means of such Bayesian modeling, BMIR can learn a function for predicting the bag-level responses and for identifying the primary instances within bags, as well as give access to Bayesian statistical inference, which are elusive in existing works. We demonstrate the superiority of BMIR over previously proposed optimization-based methods for multiple instance regression through simulation and real data analyses. Our method is implemented in R package entitled "BayesianMIR" and is available at https://github.com/inmybrain/BayesianMIR.
Keywords: Bayesian inference; Multiple instance learning; T cell infiltration; neoantigen; primary instance assumption.