Advances in flow cytometry and other single-cell technologies have enabled high-dimensional, high-throughput measurements of individual cells as well as the interrogation of cell population heterogeneity. However, in many instances, computational tools to analyze the wealth of data generated by these technologies are lacking. Here, we present a computational framework for unbiased combinatorial polyfunctionality analysis of antigen-specific T-cell subsets (COMPASS). COMPASS uses a Bayesian hierarchical framework to model all observed cell subsets and select those most likely to have antigen-specific responses. Cell-subset responses are quantified by posterior probabilities, and human subject-level responses are quantified by two summary statistics that describe the quality of an individual's polyfunctional response and can be correlated directly with clinical outcome. Using three clinical data sets of cytokine production, we demonstrate how COMPASS improves characterization of antigen-specific T cells and reveals cellular 'correlates of protection/immunity' in the RV144 HIV vaccine efficacy trial that are missed by other methods. COMPASS is available as open-source software.