Use of zero-inflated mixture models to compare antibody titers in response to H1N1 vaccination

Abstract

Pandemic H1N1 vaccine was administered to participants with mild/moderate and severe asthma to investigate quantitative and qualitative differences in immunogenicity among subgroups. H1N1 antibody titers were measured pre-vaccination (Day 1) and post-vaccination (Days 8, 21, 28 and 41). A second vaccination of the same dose (15 or 30 mcg) was administered after blood samples were taken on Day 21. H1N1 antibodies at Day 1 and three weeks post-vaccination (Day 21) were of primary interest for the current article. A preponderance of titers below the lower detection limit was observed (36% - 75% of observations at Day 1, depending on subgroup). Titers above the upper detection limit (6 - 52% at Day 21) were also observed. Because of this preponderance of censored values, assumptions of Gaussian data are not appropriate, and traditional modeling approaches could produce biased estimates of differences in immunogenicity. Zero-inflated log-normal models that accounted for left- and right-censoring and a “point mass” below the lower limit of detection were utilized to compare subgroups with respect to antibody titers. Results derived from traditional analytical methods such as imputation of censored values were compared to results from zero-inflated methods. By formal criteria, zero-inflated models provided a better fit to data and yielded results that were qualitatively and quantitatively different from traditional models. Zero-inflated models yielded geometric mean titers that were 2- to 3-fold different from traditional models and elucidated differences among subgroups that were obscured by traditional methods.