Generalized linear modeling of flow cytometry data to analyze immune responses in tuberculosis vaccine research

Abstract

Tuberculosis (TB) caused by Mycobacterium tuberculosis (Mtb) kills ~1.3 million people annually. Accordingly, vaccines and sophisticated analytical tools are necessary to evaluate their effectiveness. To address these challenges, we created a Generalized Linear Model (GLM) framework to evaluate high-dimensional flow cytometry data and the multivariable influences on immune responses, accommodating proportional and non-normal data, and violations of assumptions set by classical statistical evaluations. In naïve mice vaccinated with BCG boosted with ID93-GLA-SE, we used GLMs to assess the impact of sex, vaccination, and days post-infection on probabilities of immune cell phenotypes following Mtb challenge. We demonstrate enhanced T cell responses in the lung following BCG + ID93-GLA-SE compared to BCG or ID93-GLA-SE alone, with notable sex differences in humoral immunity. This framework highlights GLMs in assessing complex datasets while enhancing our comprehension of independent continuous and categorical variables on vaccine efficacy, and serves as a foundation for deeper, more complex scenarios.

Fig. 1. Distribution and observed proportions of immune populations in vaccinated female and male C57Bl/6 mice infected with Mtb.

Mice were vaccinated with either Saline (control), BCG, ID93-GLA-SE, or BCG+ID93-GLA-SE and infected with Mtb. Lungs were processed for flow cytometry 14-, 56-, and 90-days post infection, and stained for A, B CD4+ CD44+, C, D CD8+, and E, F CD19+. A, C, E Distributions immune cell “success” in mice within each vaccination group. B, D, F Observed proportions of immune populations normalized to live leukocytes.

Fig. 2. Estimated coefficients and odds ratios for immune responses in the infected mouse lung.

A, C, E Estimated coefficients on the outcome of immune responses for CD4+ CD44+, CD8+, and CD19+ cells for each one-, two-, and three-way interactions of group, day and sex derived from GLM logistical model output. B, D, F Odds ratios for exponentiated estimated effects.

Fig. 3. Probability of immune phenotypes in the lung during Mtb infection.

A–C Predicted probabilities of immune cell responses in the lung considering combinations of vaccination groups, days post-infection, and sex. A CD4+ CD44+, B CD8+, and) CD19+. All values were derived from the inverse of the logit function in our logistic regression model in R.

Fig. 4. GLM framework workflow.

Our computational framework is comprised of four sequential data analysis steps which include, (1) Data acquisition from high dimensional flow cytometry and analysis software. (2) Initial data processing and exploration/visualization. (3) Logistical modeling withing the GLM framework. (4) Visualization of computed probabilities of outcomes based on variable interactions.