SUMMARY OF DOSE-RESPONSE MODELING FOR DEVELOPMENTAL
Daniel L. Hunt h Department of Biostatistics, St. Jude Children’s Research
Hospital, Memphis, TN
Shesh N. Rai h Biostatistics Shared Facility, JG Brown Cancer Center, and
Department of Bioinformatics and Biostatistics, School of Public Health and
Information Sciences, University of Louisville, Louisville, KY
Chin-Shang Li h Division of Biostatistics, MS1C, Room 145, Department of
Public Health Sciences, University of California, Davis, CA h 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.
Keywords: Developmental toxicity study, Dose-group variation, Estimation, Spline, Threshold
Developmental toxicity studies involve the investigation of the responses of fetal litters to maternal exposure to a potentially toxic agent, which while it may cause negative effects, is considered to be a non-carcinogen for humans. The U.S. Environmental Protection Agency (USEPA) is the primary federal protection agency that uses the results of these studies to develop guidelines for safe levels of human exposure to these toxic agents, which can manifest themselves naturally in the air, but also in common man-made products and structures that humans are exposed to in the home, workplace, and the general public. Therefore,
USEPA works in collaboration with other regulatory agencies such as the
Dose-Response, 6:352–368, 2008
Formerly Nonlinearity in Biology, Toxicology, and Medicine
Copyright © 2008 University of Massachusetts
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Address correspondence to Daniel L. Hunt, Department of Biostatistics, St. Jude
Children’s Research Hospital, Memphis, TN, USA 38105-2794, USA; Tel: (901) 495-5501; Fax: (901) 544-8843; Email: email@example.com
Food and Drug Administration (FDA) and Occupational Safety and
Health Administration (OSHA) to establish guidelines. Additionally, one or more of the most recent USEPA guidelines for areas of risk assessment associated with developmental toxicity, may be combined with (or may supersede) the USEPA developmental toxicity guidelines when exposure is under suspicion of resulting in additional toxicity not accounted for in the developmental guidelines (USEPA, 1986; 1992;1996; 1998; 2005).
In the developmental toxicity study, each impregnated animal is randomly assigned to a dose group corresponding to an exposure level of the toxic agent under study. The agent is usually administered orally to the animals during fetal development. Endpoints are then measured and recorded on both the animals and their fetal litters. A dose-response relationship that relates agent dose level to these endpoints is assumed to exist. Some method for determining tolerable level of exposure is used.
This should primarily involve estimating the dose-response pattern. At the conclusion of the risk assessment process when a dose-response relationship has been estimated, the results are then extrapolated to determine safe exposure levels of the toxic agent in humans during fetal development (USEPA, 1991). USEPA considers statistical modeling to be an important step in the risk assessment process (Ryan, 2000).
The major endpoints that are measured on fetuses are deaths, structural malformations, growth aberrations, and functional deficiencies.
Also, endpoints relating to fetal weight and length are measured and modeled using some continuous distribution. Data relating to endpoints such as indicators of death and malformation are categorical and these are the endpoints that we investigate in this paper. An endpoint of death or malformation is categorized as an ‘adverse event’, with death superseding malformation for a given fetus. Since each litter is a natural cluster, individual litter measures are typically accumulated into a sum or average and that quantity is seen as a data value to represent the entire litter, e.g., number of deaths or malformations in the litter, or average litter weight. Thus, the study sample size equates to the total number of litters.
Even after the grouping, the sample size is still adequately large enough for the study to have appreciable power and for the estimates to be meaningful. This is not always the case as data can be left as individual-level and modeled accordingly. Typically, individual-level data is used in cases of jointly modeling bivariate outcomes, such as fetal weight and malformation (Catalano and Ryan, 1992).
Developmental toxicity studies typically involve investigation of environmentally unsafe agents, which, when exposed to an unacceptable level, results in non-carcinogenic toxic effects. Since carcinogenic risk assessment studies are restricted to use of the linear dose-response model, i.e., the linear-no-threshold (LNT) model, as the default model (USEPA, 2005), the developmental toxicity study is not tied down by such limitaSummary of dose-response modeling 353 tions. In general, the default model in the assessment of non-carcinogenic risk is the threshold dose-response model (USEPA, 1991). In the context of the typical single-agent and endpoint dose-response study, the threshold is defined as the maximum dose level at which the toxic response equates to the background control level response. Threshold is assumed to exist for developmentally toxic agents due to biological ability of organism to defend itself against tolerable level of toxic threat.