dr4pl: A stable convergence algorithm for the 4 parameter logistic model

Abstract

The 4 Parameter Logistic (4PL) model has been recognized as a major tool to analyze the relationship between doses and responses in pharmacological experiments. A main strength of this model is that each parameter contributes an intuitive meaning enhancing interpretability of a fitted model. However, implementing the 4PL model using conventional statistical software often encounters numerical errors. This paper highlights the issue of convergence failure and presents several causes with solutions. These causes include outliers and a non-logistic data shape, so useful remedies such as robust estimation, outlier diagnostics and constrained optimization are proposed. These features are implemented in a new R package dr4pl (Dose-Response analysis using the 4 Parameter Logistic model) whose code examples are presented as a separate section. Our R package dr4pl is shown to work well for data sets where the traditional dose-response modelling packages drc and nplr fail.