A mixture model with detection limits for regression analyses of antibody response to vaccine

Antibody concentration values as determined by quantitative assays often are left-censored due to detection limits or limits established for purpose of specificity. Standard analyses which assume the data arise from a single lognormal response distribution may not be appropriate, when more observations are censored than would be expected under such a model. Interference from maternal antibodies due to vaccination at an early age, for example, could result in a high proportion of nonresponders to vaccine. A mixture model consisting of a censored lognormal distribution and a point distribution located below the detection limit is proposed for such situations. Antibody data from a study of measles vaccine are used to illustrate the utility of this approach and the interpretation of the model parameters.