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DOE OSTI2024

Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗

DOE OSTI2019

An a posteriori residual-based spatial discretization error estimator for S N neutron transport

The “residual source estimator”, an implicit residual-based spatial discretization error estimator for S N neutron transport methods, is introduced. The estimator uses an approximation of the residual as a fixed source for an analogous transport problem whose solution is the error estimate, using the same transport operator as the original numerical solution. The complete derivation of the residual source estimator, the approximation of the residual, and higher-order derivatives is included. The performance of the residual source estimator for 0-order DGFEM is tested against reference solutions. For problems with true solutions discontinuous in the first derivative across the singular characteristics, the residual source estimator is generally accurate, precise, and computationally affordable compared to similar estimators. It suffers in problems where solutions are discontinuous, particularly when the discontinuity inflicts significant inaccuracies on the discrete solution; however, compared to other estimators, which suffer similarly, it remains a competitive option.

42 ENGINEERING↗

DOE OSTI2017

Effects of scale of movement, detection probability, and true population density on common methods of estimating population density

Knowledge of population density is necessary for effective management and conservation of wildlife, yet rarely are estimators compared in their robustness to effects of ecological and observational processes, which can greatly influence accuracy and precision of density estimates. For this study, we simulate biological and observational processes using empirical data to assess effects of animal scale of movement, true population density, and probability of detection on common density estimators. We also apply common data collection and analytical techniques in the field and evaluate their ability to estimate density of a globally widespread species. We find that animal scale of movement had the greatest impact on accuracy of estimators, although all estimators suffered reduced performance when detection probability was low, and we provide recommendations as to when each field and analytical technique is most appropriately employed. The large influence of scale of movement on estimator accuracy emphasizes the importance of effective post-hoc calculation of area sampled or use of methods that implicitly account for spatial variation. In particular, scale of movement impacted estimators substantially, such that area covered and spacing of detectors (e.g. cameras, traps, etc.) must reflect movement characteristics of the focal species to reduce bias in estimates of movement and thus density.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Two-Stage Optimization Framework for Detecting and Correcting Parameter Cyber-Attacks in Power System State Estimation

One major tool of Energy Management Systems for monitoring the status of the power grid is State Estimation. Since the results of state estimation are used within the energy management system, the security of the state estimation process is most important. The focus research in this area is on detecting False Data Injection attacks on measurements. While this is important, State Estimation also rely on database that are used to describe the relationship between measurements and systems' states. This paper presents a two-stage programming framework to detect and correct attacks in the parameters of the measurement model used by the state estimation process in the Energy Management System. In the first stage, an estimate of the line parameters ratios are obtained. In the second stage, the estimated ratios from stage I are used in a Bi-Level model for obtaining a final estimate of the measurements' model parameters. Hence, the presented framework does not only unify the detection and correction in a single optimization run, but also provide a monitoring scheme for the SE database that is typically considered static. In addition, in the two stages, linear programming framework is preserved. For validation, the IEEE 118 bus system is used for implementation. The results of this paper illustrate the effectiveness of the proposed model for detecting attacks in the database used in the state estimation process.

state estimation, two-stage optimization, cyber-ph↗

DOE OSTI2020

Robust Matrix Completion State Estimation in Distribution Systems

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2012

Reliability Value of Fast State Estimation on Power Systems

Monitoring the state of a power system under stress is key to achieving reliable operation. State estimation and timely measurements become more important when applying and designing corrective control actions (manual and automatic) to arrest or mitigate cascading blackouts. The execution time of each process, including state estimation, should be as short as possible to allow for timely action. In this paper, we provide a methodology for estimating one of the components of value of faster and more frequent state estimation: the reliability value of state estimation to assist corrective control actions for arresting or mitigating cascading blackouts. We present a new algorithm for estimating the time between successive line trips in a cascading failure. The algorithm combines power flow calculations with characteristics of the protection system to estimate the time between successive equipment trips. Using this algorithm, we illustrate the value of fast state estimation by calculating the time remaining for automatic or manual corrective actions after state estimation is finalized.

Power system state estimation, cascading failures,↗

DOE OSTI2025

Improved Gas Plume Identification Using Nearest Neighbor Methods for Background Estimation

Longwave infrared (LWIR) hyperspectral imaging (HSI) can be used for many tasks in remote sensing, including detecting and identifying effluent gases by LWIR sensors on airborne platforms. Identification is used after detection to increase confidence in weakly detected plumes, reduce false positives from detection, and distinguish between similar and confounding material signatures. Background estimation is an important step used to reveal the unique spectral characteristics of the detected gas, allowing the identification model to determine what the gas is specifically. The importance of proper background estimation increases when dealing with weak signals, large libraries of gases of interest, and uncommon or heterogeneous backgrounds. In this article, we propose two methods for background estimation: a novel k-nearest segments (KNS) algorithm and the standard k-nearest neighbors (KNN) algorithm. We test our methods and three existing background estimation methods for comparison against global background estimation to determine which performs best at estimating the true background radiance under a plume and for increasing identification confidence using a neural network classification model. We compare the different methods using 640 simulated weak plumes in an urban environment. For identification, our KNS algorithm improves median neural network identification confidence by 53.2%. For background radiance estimation, the KNN algorithm provides a median of 49 times less RMSE than global background estimation. Furthermore, KNN is the easiest method to tune for different plumes, making it an excellent “out of the box” background estimator.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

A life cycle and product type based estimator for quantifying the carbon stored in wood products

Background: Timber harvesting and industrial wood processing laterally transfer the carbon stored in forest sectors to wood products creating a wood products carbon pool. The carbon stored in wood products is allocated to end-use wood products (e.g., paper, furniture), landfill, and charcoal. Wood products can store substantial amounts of carbon and contribute to the mitigation of greenhouse effects. Therefore, accurate accounts for the size of wood products carbon pools for different regions are essential to estimating the land-atmosphere carbon exchange by using the bottom-up approach of carbon stock change. Results: To quantify the carbon stored in wood products, we developed a state-of-the-art estimator (Wood Products Carbon Storage Estimator, WPsCS Estimator) that includes the wood products disposal, recycling, and waste wood decomposition processes. The wood products carbon pool in this estimator has three subpools: (1) end-use wood products, (2) landfill, and (3) charcoal carbon. In addition, it has a user-friendly interface, which can be used to easily parameterize and calibrate an estimation. To evaluate its performance, we applied this estimator to account for the carbon stored in wood products made from the timber harvested in Maine, USA, and the carbon storage of wood products consumed in the United States. Conclusion: The WPsCS Estimator can efficiently and easily quantify the carbon stored in harvested wood products for a given region over a specific period, which was demonstrated with two illustrative examples. In addition, WPsCS Estimator has a user-friendly interface, and all parameters can be easily modified.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Robust Matrix Completion State Estimation in Distribution Systems: Preprint

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Prediction of Solar Irradiance and Photovoltaic Solar Energy Product Based on Cloud Coverage Estimation Using Machine Learning Methods

Cloud cover estimation from images taken by sky-facing cameras can be an important input for analyzing current weather conditions and estimating photovoltaic power generation. The constant change in position, shape, and density of clouds, however, makes the development of a robust computational method for cloud cover estimation challenging. Accurately determining the edge of clouds and hence the separation between clouds and clear sky is difficult and often impossible. Toward determining cloud cover for estimating photovoltaic output, we propose using machine learning methods for cloud segmentation. We compare several methods including a classical regression model, deep learning methods, and boosting methods that combine results from the other machine learning models. To train each of the machine learning models with various sky conditions, we supplemented the existing Singapore whole sky imaging segmentation database with hazy and overcast images collected by a camera-equipped Waggle sensor node. We found that the U-Net architecture, one of the deep neural networks we utilized, segmented cloud pixels most accurately. However, the accuracy of segmenting cloud pixels did not guarantee high accuracy of estimating solar irradiance. We confirmed that the cloud cover ratio is directly related to solar irradiance. Additionally, we confirmed that solar irradiance and solar power output are closely related; hence, by predicting solar irradiance, we can estimate solar power output. This study demonstrates that sky-facing cameras with machine learning methods can be used to estimate solar power output. This ground-based approach provides an inexpensive way to understand solar irradiance and estimate production from photovoltaic solar facilities.

14 SOLAR ENERGY↗

DOE OSTI2016

Pre-commercial Demonstration of Direct Non-iterative State Estimator for Operational Use of Synchrophasor Management Systems

The objective of this project was to demonstrate functionality and performance of a Direct Non-iterative State Estimator (DNSE) integrated with NYPA’s Energy Management System (EMS) and with enhanced Real Time Dynamics Monitoring System (RTDMS) synchrophasor platform from Electric Power Group (EPG). DNSE is designed to overcome a major obstacle to operational use of Synchro-Phasor Management Systems (SPMS) by providing to synchrophasor management systems (SPMS) applications a consistent and a complete synchrophasor data foundation in the same way that a traditional EMS State Estimator (SE) provides to EMS applications. Specifically, DNSE is designed to use synchrophasor measurements collected by a central PDC, Supervisory Control and Data Acquisition (SCADA) measurements, and Energy Management System (EMS) network model, to obtain the complete state of the utility’s operating model at rates that are close to the synchrophasor data rates. In this way, the system is comprehensive in that it does not only cover the part of the network that is “visible” via synchrophasors, but also the part that is only “visible” through the SCADA measurements. Visualization needs associated with the use of DNSE results are fulfilled through suitably enhanced Real Time Dynamics Monitoring System (RTDMS), with the enhancements implemented by EPG. This project had the following goals in mind: To advance the deployment of commercial grade DNSE software application that relies on synchrophasor and SCADA data ; Apply DNSE at other utilities, to address a generic and fundamental need for “clean” operational data for synchrophasor applications; Provide means for “live” estimated data access by control system operators; Enhance potential for situational awareness through full system operational model coverage; Sub-second execution rate of the Direct Non-iterative State Estimator, eventually at a near-phasor data rate execution speed, i.e. < 0.1 sec. Anticipated benefits from this projects are: Enhanced reliability and improvements in the economic efficiency of bulk power system planning and operations; Providing “clean” data to other synchrophasor applications; Enhancement of situational awareness by providing the full operational model updated at near synchrophasor rate; A production-grade software tool that incorporate synchrophasor and SCADA data; Provides a basis for development of next generation monitoring and control applications, based on both SCADA and PMU data. Quanta Technology (QT) team worked in collaboration with Electric Power Group (EPG) whose team has enhanced its commercial Real Time Dynamics Monitoring System (RTDMS) to accommodate the requirements posed by DNSE application. EPG also provided its ePDC and Model-less Data Conditioning (PDVC) software for integration with DNSE+. QT developed the system requirements for DNSE; developed system architecture and defined interfaces between internal DNSE components. The core DNSE algorithm with all surrounding interfaces was named DNSE+. Since the DNSE development was done in a simulated system environment, QT used its PMU simulator that was enhanced during this project for development and factory acceptance testing (FAT). SCADA data in this stage was simulated by commercial PSS/e software. The output of DNSE are estimates of System states in C37.118-2 format, sent to RTDMS for further processing and display. As the number of these states is large, it was necessary to expand the C37.111-2 standard to accommodate large data sets. This enhancement was implemented in RTDMS. The demonstration of pre-production DNSE technology was done at NYPA using streaming field data from NYPA PMUs and from its RTUs through their SCADA system. NYPA provided ICCP interface as well as Common Information Model (CIM). The relevance of the DNSE+ application is that it provides state estimation of the power system based on hybrid set of data, consisting of both available PMU data and SCADA measurements. As this is a direct, non-iterative method of calculation of the system states, if does not suffer from convergence issues which is potential problem for conventional state estimators. Also, it can take any available PMU measurements, so it does not need to have a high percentage of PMU coverage needed in the case of Linear State Estimator. As the DNSE calculates synchrophasors of the system states (both phase and absolute value) as sub-second rate, this application can provide a basis for development of next generation of applications based both on SCADA and PMU data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Improving Abundance Estimates of Spring–Summer Snake River Chinook Salmon for Fisheries Management

Abstract The Columbia River basin is home to a run of spring–summer Chinook Salmon Oncorhynchus tshawytscha that returns to the Snake River drainage of Idaho, Oregon, and Washington in the Pacific Northwest. Historically, the run was one of the more productive throughout the Columbia River basin. However, Snake River spring–summer Chinook Salmon have experienced declines in abundance due to overfishing, habitat degradation, and dams. Several stocks are listed as threatened under the U.S. Endangered Species Act and are supported by mitigation hatcheries funded by Idaho Power Company, the Lower Snake River Compensation Plan, and the Bonneville Power Administration. To maximize tribal and state harvest of returning hatchery adults, minimize impacts on wild fish, and ensure that enough hatchery fish return to meet broodstock needs, careful fisheries management is required. Since 2008, managers have used hatchery adults, PIT-tagged as juveniles and detected at Lower Granite Dam, to generate adult abundance estimates. In season, these estimates inform state and tribal harvest shares and ensure that broodstock needs are met. Postseason, they provide smolt-to-adult survival and return rates. Since 2012, parentage-based tagging (PBT) has provided an alternative method to estimate stock- and age-specific returns at Lower Granite Dam, since returning hatchery adults sampled at Lower Granite Dam can be assigned to their parents. We compared stock-specific abundance estimates between PIT- and PBT-derived methodologies for return years 2016–2019. Across all years, PIT tag estimates accounted for 65% of the PBT-based estimates at Lower Granite Dam across all age-groups and release sites combined. This underrepresentation across all groups equated to 49,833 fish that were not accounted for in PIT tag abundance estimates. It is clear that PBT-based estimates should aide in-season harvest management and postseason run reconstruction to avoid the known bias of estimates from PIT tags, especially during years of low returns when increased accuracy is critical.

Coykendall, D. Katharine (ORCID:0000000211482397)↗

DOE OSTI2021

Calibration approach and range of observed sap flow influences transpiration estimates from thermal dissipation sensors

Calibrating thermal dissipation (TD) sap flow sensors has become increasingly important to accurately estimate whole-tree transpiration, but it is unclear how the calibration approach itself influences the resulting coefficients and estimates. Here, we compare the two most common calibration approaches, gravimetric and potometric, using TD sensors inserted into Eucalyptus benthamii tree stems. The gravimetric approach uses an excised stem segment devoid of branches and leaves and pushes water through the stem using gravity, a positive force. The potometric approach uses a severed stem containing an intact canopy placed upright in a reservoir where water is pulled through the stem via transpiration, a negative force. We hypothesized that the positive pressure associated with gravimetric calibration would overestimate conductive sapwood area relative to that estimated from potometric calibration and that coefficients from these different approaches would result in different estimates of transpiration when applied to intact trees. We also predicted that calibrations could improve transpiration estimates by targeting the range of observed sap flow rates (i.e., K values) in intact trees. Conductive sapwood area was higher under gravimetric calibrations and resulting estimates of transpiration were lower compared to potometric calibrations. Segmented calibration curves, which fit two separate curves for the relationship between sap flux density (Fd) and sap flux index (K) based on the range of sap flow rates observed in intact trees, increased transpiration estimates from both gravimetric and potometric coefficients and diminished the magnitude of difference in transpiration estimates between approaches. Researchers should be aware that calibration approach and range of observed sap flow profoundly influences transpiration estimates from TD sensors and this likely applies to calibrations of other heat-based sap flow sensors.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Comparing cropland net primary production estimates from inventory, a satellite-based model, and a process-based model in the Midwest of the United States

Accurately quantifying the spatial and temporal variability of net primary production (NPP) for croplands is essential to understand regional cropland carbon dynamics. We compared three NPP estimates for croplands in the Midwestern United States: inventory-based estimates using crop yield data from the U.S. Department of Agriculture (USDA) National Agricultural Statistics Service (NASS); estimates from the satellite-based Moderate Resolution Imaging Spectroradiometer (MODIS) NPP product; and estimates from the General Ensemble biogeochemical Modeling System (GEMS) process-based model. The three methods estimated mean NPP in the range of 469–687 g C m -2 yr -1 and total NPP in the range of 318–490 Tg C yr -1 for croplands in the Midwest in 2007 and 2008. The NPP estimates from crop yield data and the GEMS model showed the mean NPP for croplands was over 650 g C m -2 yr -1 while the MODIS NPP product estimated the mean NPP was less than 500 g C m -2 yr -1 . MODIS NPP also showed very different spatial variability of the cropland NPP from the other two methods. We found these differences were mainly caused by the difference in the land cover data and the crop specific information used in the methods. Our study demonstrated that the detailed mapping of the temporal and spatial change of crop species is critical for estimating the spatial and temporal variability of cropland NPP. Finally, we suggest that high resolution land cover data with species–specific crop information should be used in satellite-based and process-based models to improve carbon estimates for croplands.

Biogeochemical model↗

DOE OSTI2012

Evaluating Bounds and Estimators for Constants of Random Polycrystals Composed of Orthotropic Elastic Materials

While the well-known Voigt and Reuss (VR) bounds, and the Voigt-Reuss-Hill (VRH) elastic constant estimators for random polycrystals are all straightforwardly calculated once the elastic constants of anisotropic crystals are known, the Hashin-Shtrikman (HS) bounds and related self-consistent (SC) estimators for the same constants are, by comparison, more difficult to compute. Recent work has shown how to simplify (to some extent) these harder to compute HS bounds and SC estimators. An overview and analysis of a subsampling of these results is presented here with the main point being to show whether or not this extra work (i.e., in calculating both the HS bounds and the SC estimates) does provide added value since, in particular, the VRH estimators often do not fall within the HS bounds, while the SC estimators (for good reasons) have always been found to do so. The quantitative differences between the SC and the VRH estimators in the eight cases considered are often quite small however, being on the order of ±1%. These quantitative results hold true even though these polycrystal Voigt-Reuss-Hill estimators more typically (but not always) fall outside the Hashin-Shtrikman bounds, while the self-consistent estimators always fall inside (or on the boundaries of) these same bounds.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches to RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

Is the assumption of normality or log-normality for continuous response data critical for benchmark dose estimation?

Continuous responses (e.g. body weight) are widely used in risk assessment for determining the benchmark dose (BMD) which is used to derive a U.S. EPA reference dose. One critical question that is not often addressed in dose–response assessments is whether to model the continuous data as normally or log-normally distributed. Additionally, if lognormality is assumed, and only summarized response data (i.e., mean ± standard deviation) are available as is usual in the peer-reviewed literature, the BMD can only be approximated. In this study, using the “hybrid” method and relative deviation approach, we first evaluate six representative continuous dose–response datasets reporting individual animal responses to investigate the impact on BMD/BMDL estimates of (1) the distribution assumption and (2) the use of summarized versus individual animal data when a log-normal distribution is assumed. We also conduct simulation studies evaluating model fits to various known distributions to investigate whether the distribution assumption has influence on BMD/BMDL estimates. Our results indicate that BMDs estimated using the hybrid method are more sensitive to the distribution assumption than counterpart BMDs estimated using the relative deviation approach. The choice of distribution assumption has limited impact on the BMD/BMDL estimates when the within dose-group variance is small, while the lognormality assumption is a better choice for relative deviation method when data are more skewed because of its appropriateness in describing the relationship between mean and standard deviation. Additionally, the results suggest that the use of summarized data versus individual response data to characterize log-normal distributions has minimal impact on BMD estimates. - Highlights: • We investigate to what extent the distribution assumption can affect BMD estimates. • Both real data analysis and simulation study are conducted. • BMDs estimated using hybrid method are more sensitive to distribution assumption. • Summarized continuous data are adequate for BMD estimation.

60 APPLIED LIFE SCIENCES↗