Institute for Data Analysis and Visualization

We consider the detennination of an unknown quantity-for example, the concentration of a particular chemical in a given sample or samples-using controlled calibration. Here several samples are prepared with concentrations chosen to cover a required range, and these are used to establish the relationship between concentration and the measured response to an assay method. This relationship is then used to estimate the concentration in the unknown samples from their measured responses. Confidence intervals for the estimated concentrations can usually be calculated by inverting a prediction interval, but in some situations this method becomes intractable. We explore the use of the bootstrap as an alternative in linear, nonlinear, and multivariate controlled calibration, using both simulation and real datasets from the field of immunoassay. We also discuss the alternatives afforded by replication of the design points. The bootstrap is found to be comparable to the standard method in simple situations and is easy to apply even in complex situations in which standard approaches perform poorly or are intractable.