A restricted b-spline basis for S-shaped calibration curves

S-shaped curves arise in many calibration assays. They are typically modeled using an empirically chosen nonlinear function. Nonparametric alternatives usually perform poorly because there are often insufficient data points and there are difficulties in enforcing the required asymptotic behavior. We propose an alternative approach using a b-spline basis adapted to produce lower and upper asymptotes in the fitted curves. Its main advantage is that, with pre-determined knot positions, the model is linear in the parameters and so is more numerically stable than a nonlinear model; this has advantages in, for example, fitting a mixed model to multiple curves. We explore the performance of this approach using data from a single radioimmunoassay for cortisol and from a set of 96 ELISA assays for the herbicide atrazine. Copyright © 2012 John Wiley & Sons, Ltd.