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Journal articles on the topic 'Dose-Response modeling'

Author: Grafiati

Published: 15 February 2025

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1

May, Susanne, and Carol Bigelow. "Modeling Nonlinear Dose-Response Relationships in Epidemiologic Studies: Statistical Approaches and Practical Challenges." Dose-Response 3, no. 4 (October 1, 2005): dose—response.0. http://dx.doi.org/10.2203/dose-response.003.04.004.

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Non-linear dose response relationships pose statistical challenges for their discovery. Even when an initial linear approximation is followed by other approaches, the results may be misleading and, possibly, preclude altogether the discovery of the nonlinear relationship under investigation. We review a variety of straightforward statistical approaches for detecting nonlinear relationships and discuss several factors that hinder their detection. Our specific context is that of epidemiologic studies of exposure-outcome associations and we focus on threshold and J-effect dose response relationships. The examples presented reveal that no single approach is universally appropriate; rather, these (and possibly other) nonlinearities require for their discovery a variety of both graphical and numeric techniques.

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2

Hunt, Daniel L., Shesh N. Rai, and Chin-Shang Li. "Summary of Dose-Response Modeling for Developmental Toxicity Studies." Dose-Response 6, no. 4 (October 1, 2008): dose—response.0. http://dx.doi.org/10.2203/dose-response.08-007.hunt.

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Developmental toxicity studies are an important area in the field of toxicology. Endpoints measured on fetuses include weight and indicators of death and malformation. Binary indicator measures are typically summed over the litter and a discrete distribution is assumed to model the number of adversely affected fetuses. Additionally, there is noticeable variation in the litter responses within dose groups that should be taken into account when modeling. Finally, the dose-response pattern in these studies exhibits a threshold effect. The threshold dose-response model is the default model for non-carcinogenic risk assessment, according to the USEPA, and is encouraged by the agency for the use in the risk assessment process. Two statistical models are proposed to estimate dose-response pattern of data from the developmental toxicity study: the threshold model and the spline model. The models were applied to two data sets. The advantages and disadvantages of these models, potential other models, and future research possibilities will be summarized.

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3

COLEMAN, MARGARET, and HARRY MARKS. "Topics in Dose-Response Modeling." Journal of Food Protection 61, no. 11 (November 1, 1998): 1550–59. http://dx.doi.org/10.4315/0362-028x-61.11.1550.

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Great uncertainty exists in conducting dose-response assessment for microbial pathogens. The data to support quantitative modeling of dose-response relationships are meager. Our philosophy in developing methodology to conduct microbial risk assessments has been to rely on data analysis and formal inferencing from the available data in constructing dose-response and exposure models. The probability of illness is a complex function of factors associated with the disease triangle: the host, the pathogen, and the environment including the food vehicle and indigenous microbial competitors. The epidemiological triangle and interactions between the components of the triangle are used to illustrate key issues in dose-response modeling that impact the estimation of risk and attendant uncertainty. Distinguishing between uncertainty (what is unknown) and variability (heterogeneity) is crucial in risk assessment. Uncertainty includes components that are associated with (i) parameter estimation for a given assumed model, and (ii) the unknown “true” model form among many plausible alterative such as the exponential, Beta-Poisson, profit, logistic, and Gompertz. Uncertainty may be grossly understated if plausible alterative models are not tested in the analysis. Examples are presented of the impact of variability and uncertainty on species, strain, or serotype of microbial pathogens; variability in human response to administered doses of pathogens; and effects of threshold and nonthreshold models. Some discussion of the usefulness and limitations of epidemiological data is presented. Criteria for development of surrogate dose-response models are proposed for pathogens for which human data are lacking. Alterative dose-response models which consider biological plausibility are presented for predicting the probability of illness.

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4

Zhao, Yuchao, and Paolo F. Ricci. "Modeling dose-Response at Low dose: A Systems Biology Approach for Ionization Radiation." Dose-Response 8, no. 4 (March 19, 2010): dose—response.0. http://dx.doi.org/10.2203/dose-response.09-054.zhao.

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5

Slob, W. "Dose-Response Modeling of Continuous Endpoints." Toxicological Sciences 66, no. 2 (April 1, 2002): 298–312. http://dx.doi.org/10.1093/toxsci/66.2.298.

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6

Feinendegen, Ludwig E., Myron Pollycove, and Ronald D. Neumann. "Low-Dose Cancer Risk Modeling Must Recognize Up-Regulation of Protection." Dose-Response 8, no. 2 (December 10, 2009): dose—response.0. http://dx.doi.org/10.2203/dose-response.09-035.feinendegen.

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7

Cox, Louis Anthony (Tony). "A Model of Cytotoxic Dose-Response Nonlinearities Arising from Adaptive Cell Inventory Management in Tissues." Dose-Response 3, no. 4 (October 1, 2005): dose—response.0. http://dx.doi.org/10.2203/dose-response.003.04.005.

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Why do low-level exposures to environmental toxins often elicit over-compensating responses that reduce risk to an organism? Conversely, if these responses improve health, why wait for an environmental challenge to trigger them? This paper presents a mathematical modeling framework that addresses both questions using the principle that evolution favors tissues that hedge their bets against uncertain environmental challenges. We consider a tissue composed of differentiated cells performing essential functions (e.g., lung tissue, bone marrow, etc.). The tissue seeks to maintain adequate supplies of these cells, but many of them may occasionally be killed relatively quickly by cytotoxic challenges. The tissue can “order replacements” (e.g., via cytokine network signaling) from a deeper compartment of proliferative stem cells, but there is a delivery lag because these cells must undergo maturation, amplification via successive divisions, and terminal differentiation before they can replace the killed functional cells. Therefore, a “rational” tissue maintains an inventory of relatively mature cells (e.g., the bone marrow reserve for blood cells) for quick release when needed. This reservoir is replenished by stimulating proliferation in the stem cell compartment. Normally, stem cells have a very low risk of unrepaired carcinogenic (or other) damage, due to extensive checking and repair. But when production is rushed to meet extreme demands, error rates increase. We use a mathematical model of cell inventory management to show that decision rules that effectively manage the inventory of mature cells to maintain tissue function across a wide range of unpredictable cytotoxic challenges imply that increases in average levels of cytotoxic challenges can increase average inventory levels and reduce the average error rate in stem cell production. Thus, hormesis and related nonlinearities can emerge as a natural result of cell-inventory risk management by tissues.

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8

Li, Zhenhong, Bin Sun, Rebecca A. Clewell, Yeyejide Adeleye, Melvin E. Andersen, and Qiang Zhang. "Dose-Response Modeling of Etoposide-Induced DNA Damage Response." Toxicological Sciences 137, no. 2 (November 16, 2013): 371–84. http://dx.doi.org/10.1093/toxsci/kft259.

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9

Cox, Louis Anthony (Tony). "Universality of J-Shaped and U-Shaped Dose-Response Relations as Emergent Properties of Stochastic Transition Systems." Dose-Response 3, no. 3 (May 1, 2005): dose—response.0. http://dx.doi.org/10.2203/dose-response.0003.03.006.

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Dose-response data for many chemical carcinogens exhibit multiple apparent concentration thresholds. A relatively small increase in exposure concentration near such a threshold disproportionately increases incidence of a specific tumor type. Yet, many common mathematical models of carcinogenesis do not predict such threshold-like behavior when model parameters (e.g., describing cell transition rates) increase smoothly with dose, as often seems biologically plausible. For example, commonly used forms of both the traditional Armitage-Doll and multistage (MS) models of carcinogenesis and the Moolgavkar-Venzon-Knudson (MVK) two-stage stochastic model of carcinogenesis typically yield smooth dose-response curves without sudden jumps or thresholds when exposure is assumed to increase cell transition rates in proportion to exposure concentration. This paper introduces a general mathematical modeling framework that includes the MVK and MS model families as special cases, but that shows how abrupt transitions in cancer hazard rates, considered as functions of exposure concentrations and durations, can emerge naturally in large cell populations even when the rates of cell-level events increase smoothly (e.g., proportionally) with concentration. In this framework, stochastic transitions of stem cells among successive events represent exposure-related damage. Cell proliferation, cell killing and apoptosis can occur at different stages. Key components include: An effective number of stem cells undergoing active cycling and hence vulnerable to stochastic transitions representing somatically heritable transformations. (These need not occur in any special linear order, as in the MS model.) A random time until the first malignant stem cell is formed. This is the first order-statistic, T = min{T1, T2, …, Tn} of n random variables, interpreted as the random times at which each of n initial stem cells or their progeny first become malignant. A random time for a normal stem cell to complete a full set of transformations converting it to a malignant one. This is interpreted very generally as the first passage time through a network of stochastic transitions, possibly with very many possible paths and unknown topology. In this very general family of models, threshold-like (J-shaped or multi-threshold) dose-response nonlinearities naturally emerge even without cytotoxicity, as consequences of stochastic phase transition laws for traversals of random transition networks. With cytotoxicity present, U-shaped as well as J-shaped dose-response curves can emerge. These results are universal, i.e., independent of specific biological details represented by the stochastic transition networks.

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10

Herbert, Donald E., and Colin G. Orton. "Dose/time/response modeling in radiation therapy." International Journal of Radiation Oncology*Biology*Physics 19 (January 1990): 114–15. http://dx.doi.org/10.1016/0360-3016(90)90636-x.

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11

Herbert, Donald E., and Colin G. Orton. "Dose/time/response modeling in radiation therapy." International Journal of Radiation Oncology*Biology*Physics 21 (January 1991): 102. http://dx.doi.org/10.1016/0360-3016(91)90416-2.

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12

Herbert, Donald E., and Colin G. Orton. "Dose/time/response modeling in radiation therapy." International Journal of Radiation Oncology*Biology*Physics 24 (January 1992): 108. http://dx.doi.org/10.1016/0360-3016(92)90110-4.

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13

Kerr, David R., and James P. Meador. "Modeling dose response using generalized linear models." Environmental Toxicology and Chemistry 15, no. 3 (March 1996): 395–401. http://dx.doi.org/10.1002/etc.5620150325.

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14

Begum, Munni, and Pranab K. Sen. "TK/TD dose–response modeling of toxicity." Environmetrics 18, no. 5 (2007): 515–25. http://dx.doi.org/10.1002/env.821.

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15

Sinkkonen, Aki. "Modeling the Effect of Density-Dependent Chemical Interference upon Seed Germination." Dose-Response 4, no. 3 (July 2006): dose—response.0. http://dx.doi.org/10.2203/dose-response.05-024.sinkkonen.

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16

Belyaeva, Z. D., S. V. Osovets, B. R. Scott, G. V. Zhuntova, and E. S. Grigoryeva. "Modeling of Respiratory System Dysfunction among Nuclear Workers: A Preliminary Study." Dose-Response 6, no. 4 (January 17, 2008): dose—response.0. http://dx.doi.org/10.2203/dose-response.06-117.belyaeva.

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Numerous studies have reported on cancers among Mayak Production Association (PA) nuclear workers. Other studies have reported on serious deterministic effects of large radiation doses for the same population. This study relates to deterministic effects (respiratory system dysfunction) in Mayak workers after relatively small chronic radiation doses (alpha plus gamma). Because cigarette smoke is a confounding factor, we also account for smoking effects. Here we present a new empirical mathematical model that was introduced for simultaneous assessment of radiation and cigarette-smoking-related damage to the respiratory system. The model incorporates absolute thresholds for smoking- and radiation-induced respiratory system dysfunction. As the alpha radiation dose to the lung increased from 0 to 4.36 Gy, respiratory function indices studied decreased, although remaining in the normal range. The data were consistent with the view that alpha radiation doses to the lung above a relatively small threshold (0.15 to 0.39 Gy) cause some respiratory system dysfunction. Respiratory function indices were not found to be influenced by total-body gamma radiation doses in the range 0–3.8 Gy when delivered at low rates over years. However, significant decreases in airway conductance were found to be associated with cigarette smoking. Whether the indicated cigarette smoking and alpha radiation associated dysfunction is debilitating is unclear.

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17

Liu, Yinghu, Xiaoqiu Chen, Shunshan Duan, Yuanjiao Feng, and Min An. "Mathematical Modeling of Plant Allelopathic Hormesis Based on Ecological-Limiting-Factor Models." Dose-Response 9, no. 1 (May 28, 2010): dose—response.0. http://dx.doi.org/10.2203/dose-response.09-050.liu.

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18

Chen, James J., and David W. Gaylor. "Dose-response modeling of quantitative response data for risk assessment." Communications in Statistics - Theory and Methods 21, no. 8 (January 1992): 2367–81. http://dx.doi.org/10.1080/03610929208830918.

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19

Huang, Yimei, Michael Joiner, Bo Zhao, Yixiang Liao, and Jay Burmeister. "Dose convolution filter: Incorporating spatial dose information into tissue response modeling." Medical Physics 37, no. 3 (February 11, 2010): 1068–74. http://dx.doi.org/10.1118/1.3309440.

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20

Hsu, Chyi-Hung. "Evaluating potential benefits of dose-exposure-response modeling for dose finding." Pharmaceutical Statistics 8, no. 3 (July 2009): 203–15. http://dx.doi.org/10.1002/pst.392.

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21

Roy, Munmun, Kanak Choudhury, M. M. Islam, and M. A. Matin. "Dose-Time-Response Modeling Using Negative Binomial Distribution." Journal of Biopharmaceutical Statistics 23, no. 6 (October 18, 2013): 1249–60. http://dx.doi.org/10.1080/10543406.2013.834916.

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22

Handler, F. A. "Modeling ultraviolet dose–response ofBacillusspore clusters in air." Aerosol Science and Technology 50, no. 2 (January 8, 2016): 148–59. http://dx.doi.org/10.1080/02786826.2015.1137556.

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23

Parham, Fred, Chris Austin, Noel Southall, Ruili Huang, Raymond Tice, and Christopher Portier. "Dose-Response Modeling of High-Throughput Screening Data." Journal of Biomolecular Screening 14, no. 10 (October 14, 2009): 1216–27. http://dx.doi.org/10.1177/1087057109349355.

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The National Toxicology Program is developing a high-throughput screening (HTS) program to set testing priorities for compounds of interest, to identify mechanisms of action, and potentially to develop predictive models for human toxicity. This program will generate extensive data on the activity of large numbers of chemicals in a wide variety of biochemical- and cell-based assays. The first step in relating patterns of response among batteries of HTS assays to in vivo toxicity is to distinguish between positive and negative compounds in individual assays. Here, the authors report on a statistical approach developed to identify compounds positive or negative in an HTS cytotoxicity assay based on data collected from screening 1353 compounds for concentration-response effects in 9 human and 4 rodent cell types. In this approach, the authors develop methods to normalize the data (removing bias due to the location of the compound on the 1536-well plates used in the assay) and to analyze for concentration-response relationships. Various statistical tests for identifying significant concentration-response relationships and for addressing reproducibility are developed and presented.

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24

Teunis, Peter F. M., Fumiko Kasuga, Aamir Fazil, Iain D. Ogden, Ovidiu Rotariu, and Norval J. C. Strachan. "Dose–response modeling of Salmonella using outbreak data." International Journal of Food Microbiology 144, no. 2 (December 2010): 243–49. http://dx.doi.org/10.1016/j.ijfoodmicro.2010.09.026.

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25

Haas, Charles N. "Microbial Dose Response Modeling: Past, Present, and Future." Environmental Science & Technology 49, no. 3 (January 12, 2015): 1245–59. http://dx.doi.org/10.1021/es504422q.

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26

Belz, Regina G., and Hans-Peter Piepho. "Modeling Effective Dosages in Hormetic Dose-Response Studies." PLoS ONE 7, no. 3 (March 16, 2012): e33432. http://dx.doi.org/10.1371/journal.pone.0033432.

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27

Messner, Michael J., and Philip Berger. "CryptosporidiumInfection Risk: Results of New Dose-Response Modeling." Risk Analysis 36, no. 10 (January 15, 2016): 1969–82. http://dx.doi.org/10.1111/risa.12541.

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28

Isaksson, Christine, Johan Gabrielsson, Kristina Wallenius, Lambertus A. Peletier, and Helena Toreson. "Turnover Modeling of Non-Esterified Fatty Acids in Rats after Multiple Intravenous Infusions of Nicotinic Acid." Dose-Response 7, no. 3 (April 8, 2009): dose—response.0. http://dx.doi.org/10.2203/dose-response.08-028.isaksson.

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29

Vaughn, Aaron B., Nathan B. Cruze, Matthew Boucher, and William Doebler. "Dose error correction using simulation extrapolation for community noise dose-response modeling." Journal of the Acoustical Society of America 155, no. 3_Supplement (March 1, 2024): A256. http://dx.doi.org/10.1121/10.0027412.

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The objective of this work is to provide a framework to account and correct for dose error in dose-response modeling due to measurement uncertainty. Error in noise measurements, especially in the case of limited monitoring locations in a community, can lead to an attenuation or misestimation of parameters in dose-response models. This error can result in overpredicted annoyance at lower doses and underpredicted annoyance at higher doses. Simulated data in the present work are based on previous NASA community studies and incorporate a notional design for future studies with the X-59 aircraft. Several populations of different annoyance response sensitivities are included. Simulation extrapolation (SIMEX) is used to correct for the dose error in a simple, fully pooled logistic regression. Results indicate the negative impact of attenuation is greatly diminished for all amounts of dose error considered, regardless of a population’s annoyance sensitivity. Therefore, SIMEX can help produce a more accurate dose-response relationship.

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30

Bhandare, N., W. Song, V. Moiseenko, R. Malyapa, C. G. Morris, and W. Mendenhall. "Radiation-induced Optic Neuropathy: Dose Response and Modeling Total Dose and Fractionation." International Journal of Radiation Oncology*Biology*Physics 72, no. 1 (September 2008): S396. http://dx.doi.org/10.1016/j.ijrobp.2008.06.1274.

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31

Ebert, Martin A., and Sergei F. Zavgorodni. "Modeling dose response in the presence of spatial variations in dose rate." Medical Physics 27, no. 2 (February 2000): 393–400. http://dx.doi.org/10.1118/1.598843.

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32

Scott, Bobby R. "Modeling DNA Double-Strand Break Repair Kinetics as an Epiregulated Cell-Community-Wide (Epicellcom) Response to Radiation Stress." Dose-Response 9, no. 4 (February 10, 2011): dose—response.1. http://dx.doi.org/10.2203/dose-response.10-039.scott.

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33

Tavares, Adriana Alexandre S., and João Manuel R. S. Tavares. "Computational Modeling of Cellular Effects Post-Irradiation with Low- and High-Let Particles and Different Absorbed Doses." Dose-Response 11, no. 2 (March 19, 2012): dose—response.1. http://dx.doi.org/10.2203/dose-response.11-049.tavares.

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34

Zhao, Yuchao, In Chio Lou, and Rory B. Conolly. "Computational Modeling of Signaling Pathways Mediating Cell Cycle Checkpoint Control and Apoptotic Responses to Ionizing Radiation-Induced DNA Damage." Dose-Response 10, no. 2 (October 25, 2011): dose—response.1. http://dx.doi.org/10.2203/dose-response.11-021.zhao.

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35

Jafari, H., H. s. Bazargani, Y. Khaki, and T. Jafari. "Dose-response Modeling Applications In Field Of Environmental Health." Journal of Mathematics and Computer Science 09, no. 04 (April 30, 2014): 401–7. http://dx.doi.org/10.22436/jmcs.09.04.16.

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36

Carnes, Bruce A., Peter G. Groer, and Thomas J. Kotek. "Radium Dial Workers: Issues concerning Dose Response and Modeling." Radiation Research 147, no. 6 (June 1997): 707. http://dx.doi.org/10.2307/3579484.

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37

Doerge, Daniel R., and Frederick A. Beland. "Toxicokinetic and dose response modeling in chemical risk assessment." Toxicology Letters 211 (June 2012): S27. http://dx.doi.org/10.1016/j.toxlet.2012.03.121.

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38

Sielken, Robert L. "Driving Cancer Dose-Response Modeling with Data, Not Assumptions." Risk Analysis 10, no. 2 (June 1990): 207–8. http://dx.doi.org/10.1111/j.1539-6924.1990.tb01040.x.

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39

Nyman, Elin, Isa Lindgren, William Lövfors, Karin Lundengård, Ida Cervin, Theresia Arbring Sjöström, Jordi Altimiras, and Gunnar Cedersund. "Mathematical modeling improves EC50estimations from classical dose-response curves." FEBS Journal 282, no. 5 (February 6, 2015): 951–62. http://dx.doi.org/10.1111/febs.13194.

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40

Smith, Daniel L., Bisrat G. Debeb, Howard D. Thames, and Wendy A. Woodward. "Computational Modeling of Micrometastatic Breast Cancer Radiation Dose Response." International Journal of Radiation Oncology*Biology*Physics 96, no. 1 (September 2016): 179–87. http://dx.doi.org/10.1016/j.ijrobp.2016.04.014.

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41

Blessinger, Todd D., Susan Y. Euling, Lily Wang, Karen A. Hogan, Christine Cai, Gary Klinefelter, and Anne-Marie Saillenfait. "Ordinal dose-response modeling approach for the phthalate syndrome." Environment International 134 (January 2020): 105287. http://dx.doi.org/10.1016/j.envint.2019.105287.

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42

Castillo, E., N. K. Myziuk, J. Zhang, Y. Vinogradskiy, R. Castillo, and T. M. Guerrero. "Radiation Dose Response Modeling Using CT-Derived Ventilation Imaging." International Journal of Radiation Oncology*Biology*Physics 99, no. 2 (October 2017): E644. http://dx.doi.org/10.1016/j.ijrobp.2017.06.2156.

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43

Zarn, Jürg A., Ursina A. Zürcher, and H. Christoph Geiser. "Toxic Responses Induced at High Doses May Affect Benchmark Doses." Dose-Response 18, no. 2 (April 1, 2020): 155932582091960. http://dx.doi.org/10.1177/1559325820919605.

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To derive reference points (RPs) for health-based guidance values, the benchmark dose (BMD) approach increasingly replaces the no-observed-adverse-effect level approach. In the BMD approach, the RP corresponds to the benchmark dose lower confidence bounds (BMDLs) of a mathematical dose–response model derived from responses of animals over the entire dose range applied. The use of the entire dose range is seen as an important advantage of the BMD approach. This assumes that responses over the entire dose range are relevant for modeling low-dose responses, the basis for the RP. However, if part of the high-dose response was unnoticed triggered by a mechanism of action (MOA) that does not work at low doses, the high-dose response distorts the modeling of low-dose responses. Hence, we investigated the effect of high-dose specific responses on BMDLs by assuming a low- and a high-dose MOA. The BMDLs resulting from modeling fictitious quantal data were scattered over a broad dose range overlapping with the toxic range. Hence, BMDLs are sensitive to high-dose responses even though they might be irrelevant to low-dose response modeling. When applying the BMD approach, care should be taken that high-dose specific responses do not unduly affect the BMDL that derives from low doses.

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44

Yuan, Zhigang, Marissa Frazer, Kamran A. Ahmed, Syeda Mahrukh Hussnain Naqvi, Michael J. Schell, Seth Felder, Julian Sanchez, et al. "Modeling precision genomic-based radiation dose response in rectal cancer." Future Oncology 16, no. 30 (October 2020): 2411–20. http://dx.doi.org/10.2217/fon-2020-0060.

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Aim: Genomic-based risk stratification to personalize radiation dose in rectal cancer. Patients & methods: We modeled genomic-based radiation dose response using the previously validated radiosensitivity index (RSI) and the clinically actionable genomic-adjusted radiation dose. Results: RSI of rectal cancer ranged from 0.19 to 0.81 in a bimodal distribution. A pathologic complete response rate of 21% was achieved in tumors with an RSI <0.31 at a minimal genomic-adjusted radiation dose of 29.76 when modeling RxRSI to the commonly prescribed physical dose of 50 Gy. RxRSI-based dose escalation to 55 Gy in tumors with an RSI of 0.31–0.34 could increase pathologic complete response by 10%. Conclusion: This study provides a theoretical platform for development of an RxRSI-based prospective trial in rectal cancer.

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45

Howell, Roger W., and Prasad V. S. V. Neti. "Modeling Multicellular Response to Nonuniform Distributions of Radioactivity: Differences in Cellular Response to Self-Dose and Cross-Dose." Radiation Research 163, no. 2 (February 2005): 216–21. http://dx.doi.org/10.1667/rr3290.

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46

Doebler, William, Aaron B. Vaughn, Kathryn Ballard, and Jonathan Rathsam. "The effect of modeling dose uncertainty on low-boom community noise dose-response curves." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A259. http://dx.doi.org/10.1121/10.0008216.

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47

Yuan, Z. M., K. A. Ahmed, S. M. Naqvi, M. Schell, S. Felder, J. Sanchez, S. Dessureault, et al. "Beyond Blind Dose-Escalation: Modeling Precision Genomic-Based Radiation Dose-Response In Rectal Cancer." International Journal of Radiation Oncology*Biology*Physics 105, no. 1 (September 2019): S159—S160. http://dx.doi.org/10.1016/j.ijrobp.2019.06.176.

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48

Regan, Meredith M., and Paul J. Catalano. "Bivariate Dose-Response Modeling and Risk Estimation in Developmental Toxicology." Journal of Agricultural, Biological, and Environmental Statistics 4, no. 3 (September 1999): 217. http://dx.doi.org/10.2307/1400383.

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49

Andersen, Melvin E., Rory B. Conolly, Elaine M. Faustman, Robert J. Kavlock, Christopher J. Portier, Daniel M. Sheehan, Patrick J. Wier, and Lauren Ziese. "Quantitative Mechanistically Based Dose-Response Modeling with Endocrine-Active Compounds." Environmental Health Perspectives 107 (August 1999): 631. http://dx.doi.org/10.2307/3434556.

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50

Andersen, M. E., R. B. Conolly, E. M. Faustman, R. J. Kavlock, C. J. Portier, D. M. Sheehan, P. J. Wier, and L. Ziese. "Quantitative mechanistically based dose-response modeling with endocrine-active compounds." Environmental Health Perspectives 107, suppl 4 (August 1999): 631–38. http://dx.doi.org/10.1289/ehp.99107s4631.

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