William A. Sadler

Estimation of Imprecision in Immunoassay Quality Assessment Programmes

A computer was used to produce and store a large body of simulated thyroxine and thyrotropin radioimmunoassay results over wide concentration ranges. Sets of 24 results, designed to represent results returned to an external quality assessment survey, were randomly drawn from the stored results in order to compare limited data survey estimates of imprecision with the ‘true’ values obtained from the population data. Results show that estimation of an imprecision profile has advantages over the usual index of imprecision, but that neither form of estimate is particularly reliable when the available data is limited. Results suggest that survey organisers should place considerably less emphasis on results from any one survey and greater emphasis on analysing cumulative data and method comparison data.

Error models for immunoassays

Background For nearly 20 years, we and others have used a three-parameter power function as a direct estimation error model for immunoassays. The main application is imprecision profile plots (after translating from variance to coefficient of variation) but other uses include weighting functions for regression analysis and variance stabilizing transformations. Although generally successful, the intrinsic monotonicity of the function means that it fails to describe small but distinct increases in variance that occasionally occur near the assay detection limit. Methods A systematic comparison of five variance functions was undertaken, using randomly drawn samples from a large body of real immunoassay data. Results Variance function accuracy (hence imprecision profile accuracy) can be markedly improved, particularly near the assay detection limit, by employing a pair of complementary three-parameter power functions, together with a constrained four-parameter function, which provides for a variance turning point. Conclusions A set of rules, based on an objective goodness-of-fit statistic, can be used to automate presentation of the most appropriate function for any particular data-set. Flexibility is easily incorporated into the selection rules and is actually highly desirable to encourage ongoing evaluation with a wider variety of data. A Win32 computer program that performs the variance function estimation and plotting is freely available.

Preparation of 125I-labelled arginine vasopressin for radioimmunoassay

Despite the common use of gel chromatography for separation of products from radioiodination of arginine vasopressin, reported specific activities of the material used as radioimmunoassay label cover a very wide range. We present evidence that, while the choice of iodination reducing agent is critical in the case of arginine vasopressin, the volume of the gel bed is almost certainly the major reason for this discordance. On a suitably large column essentially carrier-free mono and diiodinated arginine vasopressin are readily separated from other iodination products, and when the arginine vasopressin antiserum is primarily directed toward the three amino acid tail of the molecule, the diiodinated label can be successfully employed in a radioimmunoassay. This observation is of particular significance in arginine vasopressin radioimmunoassay, where a detection limit less than 1 fmol is required to distinguish subnormal from normal plasma concentrations.

Using the variance function to estimate limit of blank, limit of detection and their confidence intervals

Background Implementing International Organization for Standardization definitions of limit of blank and limit of detection requires precision estimates from specimens devoid of analyte (blank specimens) and also from specimens located close to zero. Calculations are straightforward if errors are constant over the relevant concentration range but estimation of the relationship between variability and concentration (variance function) is necessary in the general case when errors are not constant. This study investigated the efficacy of incorporating the variance function into estimation of limit of blank, limit of detection and their confidence intervals. Methods Simulated data, designed to encompass the range of properties that would typically be observed in practice, consisted of four distinct relationships between variance and concentration, in combination with large and small variances and three concentration ranges. Four methods of estimating limit of blank were evaluated together with the accuracy of variance function derived estimates of limit of detection and the accuracy of symmetrical 95% confidence intervals constructed from limit of blank and limit of detection constituent variables. Results Most limit of blank estimates and all limit of detection estimates showed systematic negative bias but, provided the data concentration range is not too small, the biases were consistently <1% with confidence interval coverages ranging from 92% to 95%. Estimating limit of blank by extrapolating the variance function to zero lost little in comparison with methods based on blank specimen data. Conclusions The variance function provides a convenient and reliable way of analyzing data from experiments evaluating detection capability and, provided certain assumptions are tenable, of estimating limit of blank and limit of detection as part of routine internal quality control.

Monoclonal antibody purified beta2-microglobulin: Heterogeneity revealed by radioimmunoassay1

&NA; A monoclonal antibody, CMRF1, to human β2‐microglobulin (β2m) was used to purify antigen to develop an in‐house β2m radioimmunoassay. This immunoadsorption purified material was used to prepare a rabbit anti‐β2m serum and was radiolabeled for the radioimmunoassay. The assay compared favourably with a widely used commercial radioimmunoassay but the immunological potency of the in‐house standard was lower than that of the commercial reagent. This potency difference was not accounted for by antigenic denaturation. Subsequent two‐dimensional gel electrophoresis revealed a second 12,000 dalton protein with a higher isoelectric point than β2m in the immunoadsorption purified material, which was also present, although in lesser amounts, in the commercial product. The different relative content of the additional 12,000 dalton protein appeared to explain the immunological potency difference between the in‐house and the commercial standard. These results strengthen suggestions that there may be some heterogeneity or polymorphism in human β2m.

Variance functions, detectability and bias: a re-evaluation

Background A recent study used simulated internal quality control data (4 specimens × 40 replicates) to investigate the use of variance functions in estimating limit of blank and limit of detection, as per ISO definitions. Small systematic negative biases were found (typically <1%), but subsequent investigation has shown that these estimates had unacceptably large uncertainties because of an inadequate simulation size. Methods The previous data generation and variance function estimations were repeated 25 times using a different random number generator seed on each occasion. The study was further extended by increasing data quantities 100-fold and by reducing the number of replicates per specimen (40 through 20, 10, 5 and 2). Results The previously reported negative biases were shown to be an artefact, and this was confirmed by simulations using 100-fold more data. Biases were <|0.1%| throughout with replication ≥20, but positive biases were found at lower replication; up to + 1.23% in the case of duplicates and large variances (e.g. some immunoassays) and up to + 0.2% in the case of duplicates and small variances. Conclusions The variance function provides essentially unbiased estimates of limit of blank and limit of detection at data replication ≥20 (bias: <1 part in 1000) and minimal biases at lower replication when measurement errors are small.

ANNALS EXPRESS: Using the variance function to generalise Bland-Altman analysis

Background Bland–Altman analysis is a popular and widely used method for assessing the level of agreement between two analytical methods. An important assumption is that paired method differences exhibit approximately constant (homogeneous) scatter when plotted against pair means. This allows estimation of limits of agreement which retain validity across the entire range of mean values. In practice, pair differences often increase systematically with the mean and Bland and Altman used log transformed data to achieve approximately homogeneous scatter. Unfortunately, a logarithmic transformation fails when data are located near the detection limit of an assay (a region that is often of considerable clinical importance). Methods Simulated thyrotropin data are used to illustrate how a variance function, estimated from pair differences, can be used to transform problematic data into a form suitable for traditional Bland–Altman analysis. Simulated and real data sets are used in a supplementary file to illustrate and offer practical solutions to potential problems. Results Following transformation by variance function, Bland–Altman results can be readily interpreted by back-transformation either to the original measurement scale or as percentage values. Limits of agreement are no longer horizontal straight lines, but their shapes simply reflect error characteristics which are (or should be) thoroughly familiar to laboratory analysts. Conclusions The method is completely general and in principle requires only the estimation of a variance function that reliably describes the relationship between the variances of pair differences and their mean values. A computer program is available which performs the necessary calculations.