Maximum Likelihood Estimation of Titer via a Power Family of Four-Parameter Logistic Model

For many laboratory assays, the readouts are presence or absence of a particular function, and the binary outcomes are correlated. The research interest is often focused on the estimation of titers, at which 50% positivity occurs. The classical approach by Reed and Muench (RM) assumes linear dose-response relationship around the potential titer, and uses only information from two points around the potential titer, which is inefficient in both precision and accuracy. While the model-based methods such as four-parameter logistic regression (4PL) use all the data, they do not consider the correlation among binary outcomes from same identities, which may lead to estimates with overstated precision. We propose estimating titers from two different anchors: independent responses from same identities or exchangeable responses from same identities. Marginal distributions of responses are linked to covariates of dilution factors by the 4PL model for independent responses and by a power family of the 4PL models for exchangeable responses. The maximum-likelihood procedure is used to get estimates of parameters and titers. The superiority of proposed methods over the classical approach is demonstrated both in simulation studies and in analysis of real data from hemagglutination assays.