Geoffrey Jones

Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard

We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215-231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158-167). Subsequently, we further develop Goodmans technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.

An immunoarray for the simultaneous determination of multiple triazine herbicides

An immunochemical method for simultaneous analysis of cross-reacting analytes is presented. We demonstrate the general principle using triazine herbicides as the model system. The analysis is based on a combination of individual enzyme immunoassays (immunoarray) for triazine herbicides using antibodies with different cross-reactivity patterns towards the selected analytes. The assay signals obtained can be mathematically evaluated to estimate concentrations of each analyte out of a ternary or quaternary mixture. The mathematical model utilizes an extension of the empirical four parameter log-logistic fit. Using mono- and polyclonal antibodies it was possible to quantify the four analytes atrazine, simazine, cyanazine, and prometon in the low to sub-ppb range simultaneously.

Extension of the four-parameter logistic model for ELISA to multianalyte analysis

The standard implementation of enzyme-linked immunosorbent assay (ELISA) for single analytes can lead to false conclusions if cross reacting compounds are present in the sample. This paper discusses the extension of the usual four-parameter logistic model for ELISA to the case of multiple cross-reacting analytes. The use of the extended model in multianalyte analysis (MELISA) is illustrated and compared with a more simplistic approach. Data on the analysis of a binary mixture of s-triazines suggests the superiority of the proposed model. This model is also suitable for other forms of immunoassay that use the four-parameter logistic curve.

An approach to the construction of an immunoarray for differentiating and quantitating cross reacting analytes

Abstract We demonstrate the construction of an immunoarray to categorize, identify and quantitate different triazine herbicides or their environmental metabolites in water. In a first step cluster analysis is used to examine the performance of a small subset of antibodies out of a larger library, and hence to select a small array that is capable of categorizing the triazine herbicides into different groups. At the 1 ppb level it is possible to categorize an analyte as a chloro-s-triazine, a hydroxy metabolite, or as a methoxy/methylthio substituted triazine when using only 2–4 antibodies. At higher concentrations even the identity of the triazine can be determined with the same number of antibodies. A selected combination of antibodies is then used to identify and quantify unknowns by comparing their immunoassay responses to an array of calibration curves and using the maximum likelihood criterion.

Bootstrapping in controlled calibration experiments

We consider the determination 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 ea...

Optimal design for ELISA and other forms of immunoassay

In enzyme-linked immunosorbent assay (ELISA), as well as in many other kinds of immunoassay, a log-logistic or similar-shaped calibration curve is fit using standards at a series of known levels and then used to transform the measured values for the unknowns into estimated concentrations. The choice of the number of standards, the concentration of the standards, and the number of replicates of the standards and of the unknowns all affect the precision of the measurement. This article develops an optima1 design paradigm for this type of problem and shows how optimal choices can be calculated so that the system achieves the maximum precision of which it is capable. Although exact calculation of optimal designs requires use of a computer program, close approximations to the optimum can be derived from simple rules for hand calculation.

Prior Elicitation: Interactive Spreadsheet Graphics With Sliders Can Be Fun, and Informative

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.

A procedure for the immunoanalysis of samples containing one or more members of a group of cross-reacting analytes

The information obtained from a single-antibody immunoassay can be ambiguous when the identity of the analyte is unknown and could be one of a group of compounds all having different affinities for the antibody. If we allow the possibility of mixtures of analytes the difficulty of the situation is aggravated. However, additional information can sometimes be obtained by assaying with a number of different antibodies. We demonstrate a rationale for identifying and quantifying analytes from a group of candidates, and illustrate the application of our method with an example from the class of s-triazine herbicides. Using a four-antibody array, correct identification and accurate quantification were usually achieved for singleanalytes samples in the low ppb range. Mixtures of analytes were recognized as such but were more difficult to classify correctly, with some confusion arising between members of subgroups, particularly within the methoxy/methylthio substituted triazines. The mathematical perspective is used to suggest directions for improving the experimental performance of multianalyte immunoassay.

Sources of experimental variation in calibration curves for enzyme-linked immunosorbent assay

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.

Innovative approach to investigating the microstructure of calcified tissues using specular reflectance Fourier transform-infrared microspectroscopy and discriminant analysis.

Although bone fracture has become a serious global health issue, current clinical assessments of fracture risk based on bone mineral density are unable to accurately predict whether an individual is likely to suffer a fracture. There is increasing recognition that the chemical structure and composition, or microstructure, of mineralized tissues has an important role to play in determining the fracture resistance of bone. The objective of this preliminary study was to evaluate the use of specular reflectance Fourier transform infrared (SR FT-IR) microspectroscopy in conjunction with discriminant analysis as an innovative technique for providing future insights into the origins of orthopedic abnormalities. The impetus for this approach was that SR FT-IR microspectroscopy would offer several advantages over conventional transmission methods. Bone samples were obtained from young racehorses at known fracture predilection sites and spectra were successfully obtained from calcified cartilage and subchondral bone for the first time. By applying discriminant analysis to the spectral data set in biologically relevant regions, microstructural differences between groups of individuals were found to be related to features associated with both the mineral and organic components of the bone. The preliminary findings also suggest that differences in bone microstructure may exist between healthy individuals of the same age, raising important questions around the normal limits of individual variation and whether individuals may be predisposed to later fracture as a result of detrimental microstructural changes during early growth and development.