Abstract
Many modern serial dilution assays are based on fluorescence intensity (FI) readouts. We study the optimal transformation model choice for fitting five-parameter logistic curves (5PL) to FI-based serial dilution assay data. We first develop a generalized least squares-pseudolikelihood type algorithm for fitting heteroscedastic logistic models. Next, we show that the 5PL and log 5PL functions can approximate each other well. We then compare four 5PL models with different choices of log transformation and variance modeling through a Monte Carlo study and real data. Our findings are that the optimal choice depends on the intended use of the fitted curves. Supplementary materials for this article are available online.
Highlights
Nonlinear regression models are commonly used to fit dose-response curves to measure immune response biomarkers, and have important applications in immune correlates studies, which seek to identify immune response biomarkers associated with infectious disease transmission (Gilbert et al, 2008)
In order to quantify the amount of antibodies from a serum sample that shows specific binding to an antigen, an enzyme-linked immunosorbent assay (ELISA) is often performed on serial dilution of the serum sample
A dilution-response curve is fitted to the optical density readouts at each dilution; the dilution that corresponds to the optical density just above the background level is called endpoint titer and is often used to quantify the amount of binding antibody in the sample
Summary
Nonlinear regression models are commonly used to fit dose-response curves to measure immune response biomarkers, and have important applications in immune correlates studies, which seek to identify immune response biomarkers associated with infectious disease transmission (Gilbert et al, 2008). To ensure that the quality of curve fits obtained using our algorithm is on par with grid search, we apply both methods to a real dataset from the RV144 immune correlates study (Haynes et al, 2012). We use 100 sets of serial dilution assay data from this dataset to compare the GLS-PL algorithm with grid search in fitting 5PL models. We have shown that some log 5PL curves can be well approximated with 5PL curves and some 5PL curves can be well approximated with log 5PL curves These results help explain our empirical observations that both the 5PL and log 5PL models provide good fits to many real datasets. The 5PL and log 5PL models may produce curve fits of different quality for some real datasets
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