Robust and Efficient Assessment of Potency (REAP): A Quantitative Tool for Doseresponse Curve Estimation
Abstract
The medianeffect equation has been widely used to describe the doseresponse relationship and identify compounds that activate or inhibit specific disease targets in contemporary drug discovery. However, the experimental data often contain extreme responses, which may significantly impair the estimation accuracy and impede valid quantitative assessment in the standard estimation procedure. To improve the quantitative estimation of the doseresponse relationship, we introduce a novel approach based on robust beta regression. Substantive simulation studies under various scenarios demonstrate solid evidence that the proposed approach consistently provides robust estimation for the medianeffect equation, particularly when there are extreme outcome observations. Moreover, simulation studies illustrate that the proposed approach also provides a narrower confidence interval, suggesting a higher power in statistical testing. Finally, to efficiently and conveniently perform common lab data analyses, we develop a freely accessible webbased analytic tool to facilitate the quantitative implementation of the proposed approach for the scientific community.
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Evaluation Summary:
This article proposes methodology and accompanying software for robustly fitting doseresponse curves where response is a number between 0 and 1. When response is transformed using the common logistic transformation, values close to 0 or 1 become large in magnitude, unduly influencing the fitted curve after backtransformation and introducing bias in the estimate of certain parameters. The proposed approach, called Robust and Efficient Assessment of Potency, is less perturbed by these extreme measurements.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
This article considers the common scenario wherein it is desired to construct a doseresponse curve. Response is a continuously valued number between 0 and 1, e.g. % cell viability. A typical approach is to transform response using a logistic function, log(x/[1x]), so that the transformed response spans the real number line and then applying linear regression models. However, when some responses are very close to 0 (or very close to 1), this typical approach will be susceptible to these highly influential values, and the fitted model will not estimate well parameters of usual interest, such as the slope or intercept of the regression or the IC50 or the backtransformed dose response curve.
The proposed approach is an adaptation of Beta regression. The underlying systematic component of the generalized …
Reviewer #1 (Public Review):
This article considers the common scenario wherein it is desired to construct a doseresponse curve. Response is a continuously valued number between 0 and 1, e.g. % cell viability. A typical approach is to transform response using a logistic function, log(x/[1x]), so that the transformed response spans the real number line and then applying linear regression models. However, when some responses are very close to 0 (or very close to 1), this typical approach will be susceptible to these highly influential values, and the fitted model will not estimate well parameters of usual interest, such as the slope or intercept of the regression or the IC50 or the backtransformed dose response curve.
The proposed approach is an adaptation of Beta regression. The underlying systematic component of the generalized linear model is the same as in the standard case described above but the random component is based upon the beta distribution. Further, rather than using maximum likelihood to fit the model, the authors propose to use 'robust minimum density power divergence estimators'. This method is called REAP, for Robust and Efficient Assessment of Potency. The authors present an online, interactive application where users can upload data and fit the authors' method.
Overall, the REAP methodology seems useful and achieves exactly what they are intended to achieve: robustly fitting doseresponse curves subject to extreme measurement error. The mathematical arguments are sound and further supported by simulation. A potentially straightforward alternative solution to this problem would be to directly model the measurement error process by using a heavytailed Cauchy distribution to model the measurement error process, thereby downweighting the influence of extreme responses but not removing them altogether. This would seem to have a 'familiarity advantage' over the authors' method.
The current version of the interactive application, although relatively easy to use, seems a little buggy. For example, the 'width of CI' argument accepts any positive number, including those greater than 1, and it's not clear how to interpret the different choices that one can plug in for this parameter. Also, even if there is just one 'Agent' provided in the data, the numerical comparisons below the plot are still presented in triplicate.
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Reviewer #2 (Public Review):
Zhou et al. investigate a robust estimation for the medianeffect equation and develop a freely accessible webbased analytic tool to facilitate the quantitative implementation of the proposed approach for the scientific community. In the paper, substantive simulation studies under various scenarios are carried out to show that the proposed approach consistently provides robust estimation for the medianeffect equation, particularly when there are extreme outcome observations. The proposed approach also provides a narrower confidence interval, suggesting a higher power in statistical testing. The case studies provide the visualization of the doseresponse curves for different drugs or under different conditions, and the case studies also show the usefulness of the proposed method.
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