Evaluation of immunogenicity is a key step in the clinical development of novel vaccines. T-cell responses to vaccine candidates are typically assessed by intracellular cytokine staining (ICS) using multiparametric flow cytometry. A conventional statistical approach to analyze ICS data is to compare, between vaccine regimens or between baseline and post-vaccination of the same regimen depending on the trial design, the percentages of cells producing a cytokine of interest after ex vivo stimulation of peripheral blood mononuclear cells (PBMC) with vaccine antigens, after subtracting the non-specific response (of unstimulated cells) of each sample. Subtraction of the non-specific response is aimed at capturing the specific response to the antigen, but raises methodological issues related to measurement error and statistical power. We describe here a new statistical approach to analyze ICS data from vaccine trials. We propose a bivariate linear random-effect regression model for estimating the nonspecific and antigen-specific ICS responses. We benchmarked the performance of the model in terms of both bias and control of type-I and -II errors in comparison with conventional approaches, and applied it to simulated data as well as real pre- and post-vaccination data from two recent HIV vaccine trials (ANRS VRI01 in healthy volunteers and therapeutic VRI02 ANRS 149 LIGHT in HIV-infected participants). The model was as good as the conventional approaches (with or without subtraction of the non-specific response) in all simulation scenarios in terms of statistical performance, whereas the conventional approaches did not provide robust results across all scenarios. The proposed model estimated the T-cell responses to the antigens without any effect of the nonspecific response on the specific response, irrespective of the correlation between the nonspecific and specific responses. This novel method of analyzing T-cell immunogenicity data based on bivariate modelling allows consideration of all T-cell data and is more flexible than conventional methods, and so yields more detailed results and enables accurate interpretation of vaccine efficacy.