Statistical approaches for the determination of cut points in anti-drug antibody bioassays

Cut points in immunogenicity assays are used to classify future specimens into anti-drug antibody (ADA) positive or negative. To determine a cut point during pre-study validation, drug-naive specimens are often analyzed on multiple microtiter plates taking sources of future variability into account, such as runs, days, analysts, gender, drug-spiked and the biological variability of un-spiked specimens themselves. Five phenomena may complicate the statistical cut point estimation: i) drug-naive specimens may contain already ADA-positives or lead to signals that erroneously appear to be ADA-positive, ii) mean differences between plates may remain after normalization of observations by negative control means, iii) experimental designs may contain several factors in a crossed or hierarchical structure, iv) low sample sizes in such complex designs lead to low power for pre-tests on distribution, outliers and variance structure, and v) the choice between normal and log-normal distribution has a serious impact on the cut point. We discuss statistical approaches to account for these complex data: i) mixture models, which can be used to analyze sets of specimens containing an unknown, possibly larger proportion of ADA-positive specimens, ii) random effects models, followed by the estimation of prediction intervals, which provide cut points while accounting for several factors, and iii) diagnostic plots, which allow the post hoc assessment of model assumptions. All methods discussed are available in the corresponding R add-on package mixADA.