Modeling anti-KLH ELISA data using two-stage and mixed effects models in support of immunotoxicological studies

During preclinical drug development, the immune system is specifically evaluated after prolonged treatment with drug candidates, because the immune system may be an important target system. The response of antibodies against a T-cell-dependent antigen is recommenced by the FDA and EMEA for the evaluation of immunosuppression/enhancement. For that reason, we developed a semiquantitative enzyme-linked immunosorbent assay to measure antibodies against keyhole limpet hemocyanin. To our knowledge, the analysis of this kind of data is at this moment not yet fully explored. In this article, we describe two approaches for modeling immunotoxic data using nonlinear models. The first is a two-stage model in which we fit an individual nonlinear model for each animal in the first stage, and the second stage consists of testing possible treatment effects using the individual maximum likelihood estimates obtained in the first stage. In the second approach, the inference about treatment effects is based on a nonlinear mixed model, which accounts for heterogeneity between animals. In both approaches, we use a three-parameter logistic model for the mean structure.