Non-normal random effects models for immunogenicity assay cut point determination

Administration of biological therapeutics can generate undesirable immune responses that may induce anti-drug antibodies (ADAs). Immunogenicity can negatively affect patients, ranging from mild reactive effect to hypersensitivity reactions or even serious autoimmune diseases. Assessment of immunogenicity is critical as the ADAs can adversely impact the efficacy and safety of the drug products. Well-developed and validated immunogenicity assays are required by the regulatory agencies as tools for immunogenicity assessment. Key to the development and validation of an immunogenicity assay is the determination of a cut point, which serves as the threshold for classifying patients as ADA positive(reactive) or negative. In practice, the cut point is determined as either the quantile of a parametric or nonparametric empirical distribution. The parametric method, which is often based on a normality assumption, may lead to biased cut point estimates when the normality assumption is violated. The non-parametric method, which yields unbiased estimates of the cut point, may have low efficiency when the sample size is small. As the distribution of immune responses are often skewed and sometimes heavy-tailed, we propose two non-normal random effects models for cut point determination. The random effects, following a skew-t or log-gamma distribution, can incorporate the skewed and heavy-tailed responses and the correlation among repeated measurements. Simulation study is conducted to compare the proposed method with the current normal and nonparametric alternatives. The proposed models are also applied to a real dataset generated from assay validation studies.