Deriving bio‐equivalents from in vitro bioassays: Assessment of existing uncertainties and strategies to improve accuracy and reporting

Abstract

Bio-equivalents (e.g., 17β-estradiol or dioxin equivalents) are commonly employed to quantify the in vitro effects of complex human or environmental samples. However, there is no generally accepted data analysis strategy for estimating and reporting bio-equivalents. Therefore, the aims of the present study are to 1) identify common mathematical models for the derivation of bio-equivalents from the literature, 2) assess the ability of those models to correctly predict bio-equivalents, and 3) propose measures to reduce uncertainty in their calculation and reporting. We compiled a database of 234 publications that report bio-equivalents. From the database, we extracted 3 data analysis strategies commonly used to estimate bio-equivalents. These models are based on linear or nonlinear interpolation, and the comparison of effect concentrations (ECX ). To assess their accuracy, we employed simulated data sets in different scenarios. The results indicate that all models lead to a considerable misestimation of bio-equivalents if certain mathematical assumptions (e.g., goodness of fit, parallelism of dose-response curves) are violated. However, nonlinear interpolation is most suitable to predict bio-equivalents from single-point estimates. Regardless of the model, subsequent linear extrapolation of bio-equivalents generates additional inaccuracy if the prerequisite of parallel dose-response curves is not met. When all these factors are taken into consideration, it becomes clear that data analysis introduces considerable uncertainty in the derived bio-equivalents. To improve accuracy and transparency of bio-equivalents, we propose a novel data analysis strategy and a checklist for reporting Minimum Information about Bio-equivalent ESTimates (MIBEST).

The advantages of linear concentration–response curves for in vitro bioassays with environmental samples

“…However, because many in vitro assays do not report toxicity but some defined biological effect, bioequivalents or bioanalytical equivalent concentrations have become more popular for in vitro bioassays. Wagner et al (2013) reviewed 234 peer-reviewed publications on that topic and came to a very FIGURE 3: If the slopes of the log-concentration-response curves (CRCs) are not the same for the reference compound and chemical i, then the relative effect potency values of chemical i (REP i ) are dependent on the effect level (A). For log-CRC with the same slope (B) and linear CRCs (C), the REP i values are independent of the effect level.…”

“…similar conclusion as Villeneuve et al (2000) did for REP i , that nonparallel log-CRCs and the variability of the maximum effect were the largest impediments, as well as the extrapolation to untested enrichment factors. After this analysis, Wagner et al (2013) recommended the definition of bioequivalents from nonlinear interpolations of log-CRC and proposed a checklist to assess the validity of the approach in practical applications when often only single point estimates were available. At the time of that publication the use of linear CRCs for environmental samples was already emerging (Escher et al 2012b(Escher et al , 2013, but they were not accounted for in that review, which included literature up to 2010 and discussed only log-CRCs with linear models relating to the middle linear portion of the log-CRC (Wagner et al 2013).…”

When the Whole is Not Greater than the Sum of the Parts: A Critical Review of Laboratory Bioassay Effects Testing for Insecticidal Protein Interactions

“…This is particularly relevant for certain insecticidal proteins (e.g., Vip3A, Lee et al 2003 ) that were not even identified at the time of the Tabashnik (1992) reference; in addition, a number of other Cry proteins had been identified but not yet cloned and purified for in vitro studies at that early date. In other fields of biology, restricting the use of the CA model to agents which have been demonstrated to be mutually exclusive in their action is a bit more consistent, but not perfect ( Wagner et al 2013 , Geary 2013 ); likely the complexity of Bt insecticidal protein MoA has hindered applying a similar restrictive principle for use of the CA model within entomology.…”

“…If the dose–responses of any two agents being compared are not parallel, then a single number does not accurately describe their relative potency. It is readily apparent that when similar slopes are not observed, the deviations can cause large errors in predictions of the relative potency of any two (or more) agents ( Villeneuve et al 2000 , Ritz et al 2006 , Wagner et al 2013 ).…”

Bioanalytical tools: half a century of application for potable reuse

“…For specific toxicity assays, results are often expressed as toxic equivalents, based on the assay's reference compound (positive control). 47,48 For example, estrogenic activity is generally reported as Estradiol Equivalent (EEQ) 49 or aryl hydrocarbon receptor-mediated dioxin activity is reported as TCDD equivalent (TCDDEQ). 50 This is because the response in specific toxicity assays can often be explained by a relatively small subset of chemicals, 39,41,45,51 while the response in the other assays classes discussed above (reactive and nonspecific toxicity, adaptive stress and xenobiotic metabolism) can often be induced by a very large number of chemicals.…”