Evaluation of methacholine dose-response curves by linear and exponential mathematical models: goodness-of-fit and validity of extrapolation (original) (raw)
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Current modeling practice may lead to falsely high benchmark dose estimates
Regulatory Toxicology and Pharmacology, 2014
Benchmark dose (BMD) modeling is increasingly used as the preferred approach to define the point-of-departure for health risk assessment of chemicals. As data are inherently variable, there is always a risk to select a model that defines a lower confidence bound of the BMD (BMDL) that, contrary to expected, exceeds the true BMD. The aim of this study was to investigate how often and under what circumstances such anomalies occur under current modeling practice. Continuous data were generated from a realistic dose-effect curve by Monte Carlo simulations using four dose groups and a set of five different dose placement scenarios, group sizes between 5 and 50 animals and coefficients of variations of 5-15%. The BMD calculations were conducted using nested exponential models, as most BMD software use nested approaches. ''Non-protective'' BMDLs (higher than true BMD) were frequently observed, in some scenarios reaching 80%. The phenomenon was mainly related to the selection of the non-sigmoidal exponential model (Effect = a Á e bÁdose ). In conclusion, non-sigmoid models should be used with caution as it may underestimate the risk, illustrating that awareness of the model selection process and sound identification of the point-of-departure is vital for health risk assessment.
The analysis of dose-response curves-a practical approach
British Journal of Clinical Pharmacology, 1987
1 The rationale for the objective assessment of dose-response curves (DRCs) is presented. 2 Using data derived from isoprenaline/heart rate responses studies, two new statistical methods of objectively defining the terminal linear segment of an incomplete DRC are presented. 3 Using data derived from phenylephrine/diastolic blood pressure response studies, the parallel shift quadratic model of has been extended to include a measure of the suitability of the quadratic model for each individual data set using the Akaike information criterion. 4 A parallel shift Emax model is proposed for complete DRCs.
A Comparative study of the Estimation of the Maximum Tolerated Dose
Dose-response analysis (DRA) has been a very popular topic within statistical estimation especially in biomedical areas. In addition to estimating the entire dose-response relationship, assessing the risk itself at a certain dose level has been of much interest in some applications, such as in estimating the maximum tolerated dose (MTD) in Phase I clinical trials. Although a variety of parametric dose-response models have been proposed and successfully used in practice, many of the exiting models may not be appropriate in terms of capturing the underlying shape of the dose-response curve.
Benchmark dose (BMD) modeling: current practice, issues, and challenges
Critical reviews in toxicology, 2018
Benchmark dose (BMD) modeling is now the state of the science for determining the point of departure for risk assessment. Key advantages include the fact that the modeling takes account of all of the data for a particular effect from a particular experiment, increased consistency, and better accounting for statistical uncertainties. Despite these strong advantages, disagreements remain as to several specific aspects of the modeling, including differences in the recommendations of the US Environmental Protection Agency (US EPA) and the European Food Safety Authority (EFSA). Differences exist in the choice of the benchmark response (BMR) for continuous data, the use of unrestricted models, and the mathematical models used; these can lead to differences in the final BMDL. It is important to take confidence in the model into account in choosing the BMDL, rather than simply choosing the lowest value. The field is moving in the direction of model averaging, which will avoid many of the ch...
Linear low-dose extrapolation for noncancer health effects is the exception, not the rule
Critical Reviews in Toxicology, 2011
The nature of the exposure-response relationship has a profound influence on risk analyses. Several arguments have been proffered as to why all exposure-response relationships for both cancer and noncarcinogenic endpoints should be assumed to be linear at low doses. We focused on three arguments that have been put forth for noncarcinogens. First, the general "additivity-to-background" argument proposes that if an agent enhances an already existing disease-causing process, then even small exposures increase disease incidence in a linear manner. This only holds if it is related to a specific mode of action that has nonuniversal properties-properties that would not be expected for most noncancer effects. Second, the "heterogeneity in the population" argument states that variations in sensitivity among members of the target population tend to "flatten out and linearize" the exposure-response curve, but this actually only tends to broaden, not linearize, the dose-response relationship. Third, it has been argued that a review of epidemiological evidence shows linear or no-threshold effects at low exposures in humans, despite nonlinear exposure-response in the experimental dose range in animal testing for similar endpoints. It is more likely that this is attributable to exposure measurement error rather than a true nonthreshold association. Assuming that every chemical is toxic at high exposures and linear at low exposures does not comport to modern-day scientific knowledge of biology. There is no compelling evidence-based justification for a general low-exposure linearity; rather, case-specific mechanistic arguments are needed.
Lung, 1997
To determine whether the slope of a maximal bronchial challenge test (in which FEV 1 falls by over 50%) could be extrapolated from a standard bronchial challenge test (in which FEV 1 falls up to 20%), 14 asthmatic children performed a single maximal bronchial challenge test with methacholine (dose range: 0.097-30.08 mol) by the dosimeter method. Maximal dose-response curves were included according to the following criteria: (1) at least one more dose beyond a ⌬FEV 1 ജ 20%; and (2) a MFEV 1 ജ 50%. PD 20 FEV 1 was calculated, and the slopes of the early part of the dose-response curve (standard dose-response slopes) and of the entire curve (maximal dose-response slopes) were calculated by two methods: the two-point slope (DRR) and the least squares method (LSS) in % ⌬FEV 1 × mol −1. Maximal dose-response slopes were compared with the corresponding standard dose-response slopes by a paired Student's t test after logarithmic transformation of the data; the goodness of fit of the LSS was also determined. Maximal dose-response slopes were significantly different (p < 0.0001) from those calculated on the early part of the curve: DRR 20% (91.2 ± 2.7 ⌬FEV 1 % ⅐ mol −1) was 2.88 times higher than DRR 50% (31.6 ± 3.4 ⌬FEV 1 % ⅐ mol −1), and the LSS 20% (89.1 ± 2.8% ⌬FEV 1 ⅐ mol −1) was 3.10 times higher than LSS 50% (28.8 ± 1.5% ⌬FEV 1 ⅐ mol −1). The goodness of fit of LSS 50% was significant in all cases, whereas LSS 20% failed to be significant in one. These results suggest that maximal dose-response slopes cannot be predicted from the data of standard bronchial challenge tests.
Theoretical Biology and Medical Modelling, 2020
Background: To employ the benchmark dose (BMD) method in toxicological risk assessment, it is critical to understand how the BMD lower bound for reference dose calculation is selected following statistical fitting procedures of multiple mathematical models. The purpose of this study was to compare the performances of various combinations of model exclusion and selection criteria for quantal response data. Methods: Simulation-based evaluation of model exclusion and selection processes was conducted by comparing validity, reliability, and other model performance parameters. Three different empirical datasets for different chemical substances were analyzed for the assessment, each having different characteristics of the dose-response pattern (i.e. datasets with rich information in high or low response rates, or approximately linear dose-response patterns). Results: The best performing criteria of model exclusion and selection were different across the different datasets. Model averaging over the three models with the lowest three AIC (Akaike information criteria) values (MA-3) did not produce the worst performance, and MA-3 without model exclusion produced the best results among the model averaging. Model exclusion including the use of the Kolmogorov-Smirnov test in advance of model selection did not necessarily improve the validity and reliability of the models. Conclusions: If a uniform methodological suggestion for the guideline is required to choose the best performing model for exclusion and selection, our results indicate that using MA-3 is the recommended option whenever applicable.
Dose-Effect Modeling of Experimental Data.
This paper proposes a mathematical model for estimation of the dose-response relationship of experimental data. А modified logistic function is used as analytical model for determining the dose-effect. Parameters of the model are identified with the optimization procedure based on the cyclic coordinate descent method. Formulas are derived to calculate the effective dose level and the standard deviation of doses. The approach is implemented in the computer program KORELIA-Dynamics.
Comparing Experimental Designs for Benchmark Dose Calculations for Continuous Endpoints
Risk Analysis, 2006
The BMD (benchmark dose) method that is used in risk assessment of chemical compounds was introduced by Crump (1984) and is based on dose-response modeling. To take uncertainty in the data and model fitting into account, the lower confidence bound of the BMD estimate (BMDL) is suggested to be used as a point of departure in health risk assessments. In this article, we study how to design optimum experiments for applying the BMD method for continuous data. We exemplify our approach by considering the class of Hill models. The main aim is to study whether an increased number of dose groups and at the same time a decreased number of animals in each dose group improves conditions for estimating the benchmark dose. Since Hill models are nonlinear, the optimum design depends on the values of the unknown parameters. That is why we consider Bayesian designs and assume that the parameter vector has a prior distribution. A natural design criterion is to minimize the expected variance of the BMD estimator. We present an example where we calculate the value of the design criterion for several designs and try to find out how the number of dose groups, the number of animals in the dose groups, and the choice of doses affects this value for different Hill curves. It follows from our calculations that to avoid the risk of unfavorable dose placements, it is good to use designs with more than four dose groups. We can also conclude that any additional information about the expected dose-response curve, e.g., information obtained from studies made in the past, should be taken into account when planning a study because it can improve the design.