Agreement and error of titration assays

Titration assays can be used to define positivity either in terms of a change over time, i.e. seroconversion, or relative to a fixed threshold. The operating characteristics of these definitions depend on the precision of the assay. We present methods for estimating the distribution of errors, at the level of a single replicate, from the distribution of within-pair agreement. When the maximum replicate-level error is one dilution, a simple probability argument is used, with estimation by method of moments. For the more general case, a discretized Gaussian model is used, with maximumum likelihood estimation. These models fit well to eight published datasets. The discretized Gaussian model also allows the potential performance of alternative dilution factors to be assessed. For influenza hemagglutination-inhibition, the approach is compared to a previous Markov chain Monte Carlo data augmentation model. These methods allow the estimation of the underlying error distribution from observed between-replicate differences under repeatability conditions. The results can be used to guide the choice of the fold change necessary to infer seroconversion. Finer dilution factors, e.g. 1.5 rather than 2, could facilitate a better balance between the sensitivity and specificity of titration assays.