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.

In calibration experiments, an estimated relationship between covariate information for a sample and an observed response is used to infer the covariate information for unknown samples from their responses. In some situations, this covariate information comprises a nominal variable (e.g., identity of a chemical, sex of an animal) and a real-valued variable (e.g., concentration of the chemical, age of animal). If the calibrating relationship can be estimated separately for each candidate identity, the first step in analyzing unknown samples is to correctly determine their identity. A discrimination statistic is suggested for use in this situation and its asymptotic distribution is derived. The investigation is motivated by the possibility of using multiple immunoassays in environmental monitoring to identify and quantitate contaminated samples in situations where there are several candidate pollutants that cross-react significantly to single assays. An example is given of the use of a four-antibody assay for the simultaneous monitoring of the levels in water samples of several of the commonly used triazine herbicides and their derivatives.

Fibrodysplasia ossificans progressiva is a rare genetic disorder in which the joints of patients become disabled by the formation of heterotopic bone. Data are available on the status of 11 joints of each of 21 patients before, during and after treatment with Accutane. These are compared with data obtained by questionnaire from 40 untreated patients to determine the efficacy of the treatment. Both left- and right-censoring are present in each group, which, together with the multivariate nature of the data and the time-dependent treatment covariate, makes analysis difficult. We consider two alternative parametric models for incorporating within-subject dependence: a marginal model and a frailty model. Both analyses suggest that Accutane treatment is effective. We discuss and illustrate the differences between the two approaches. We also discuss the extent to which the conclusions are compromised by the observational nature of the study.

There are several approaches to setting priors in Bayesian data analysis. Some attempt to minimize the impact of the prior on the posterior, allowing the data to "speak for themselves," or to provide Bayesian inferences that have good frequentist properties. In contrast, this note focuses on priors where scientific knowledge is used, possibly partially informative. There are many articles on the use of such subjective information. We focus on using standard software for eliciting priors from subject-matter specialists, in the form of models such as the binomial, Poisson, and normal. Our approach uses a common spreadsheet package with the facility to display dynamic pictures of prior distributions as the user toggles scroll bars or "sliders" that manipulate parameters of particular distributions. This allows interactive exploration of the shape of a probability distribution. We have found this a useful tool when eliciting priors for Bayesian data analysis. We present examples to illustrate the scope and flexibility of the method. Supplementary materials for this article are available online. © 2014 American Statistical Association.

Enzyme-linked immunosorbent assays are usually performed by running standard and Unknown concentrations together on the same microtiter plate, because the standard curve is known to vary considerably from one assay to the next. Here we examine experimentally the sources and nature of this variation, and discuss the possibility of reducing the cost of the assay by using a batch of plates, only one of which is used to generate the calibration curve. We present a method for doing this, and test it empirically.