Numerous biological factors can modify an individual's degree of immune response to vaccine. Such factors may complicate an immunogenicity trial by acting as counfounding variables; alternatively, their relationship to the measured antibody response may be the primary focus of an investigation. Standard regression analyses can adjust for many variables simultaneously and assess their relative importance, but require several conditions or assumptions. To reduce these requirements, we present a flexible regression model that allows for: (1) a broad class of shapes for the response distribution; (2) censoring of observations due to detection limits; and (3) the existence of a separate distribution of low-responders. We illustrate this modeling approach with neutralizing antibody data from a factorial study of measles vaccine. The effects of vaccine dose and strain, obscured by standard analyses, are elucidated by the new model.