Statistical Models in Toxicology

Mehdi Razzaghi

• Publisher: Chapman and Hall/CRC
• Year: 2020
• ISBN:
  9780429532351
• Edition: 1
• Topic: Mathématiques
• Subtopic: Mathématiques générales

Statistical Models in Toxicology presents an up-to-date and comprehensive account of mathematical statistics problems that occur in toxicology. This is as an exciting time in toxicology because of the attention given by statisticians to the problem of estimating the human health risk for environmental and occupational exposures. The development of modern statistical techniques with solid mathematical foundations in the 20th century and the advent of modern computers in the latter part of the century gave way to development of many statistical models and methods to describe toxicological processes and attempts to solve the associated problems. Not only have the models enjoyed a high level of elegance and sophistication mathematically, they are widely used by industry and government regulatory agencies.

Features:

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• Focuses on describing the statistical models in environmental toxicology that facilitate the assessment of risk mainly in humans. The properties and shortfalls of each model are discussed and its impact in the process of risk assessment is examined.

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• Discusses models that assess the risk of mixtures of chemicals.

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• Presents statistical models that are developed for risk estimation in different aspects of environmental toxicology including cancer and carcinogenic substances.

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• Includes models for developmental and reproductive toxicity risk assessment, risk assessment in continuous outcomes and developmental neurotoxicity.

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• Contains numerous examples and exercises.

Statistical Models in Toxicology introduces a wide variety of statistical models that are currently utilized for dose-response modeling and risk analysis. These models are often developed based on design and regulatory guidelines of toxicological experiments. The book is suitable for practitioners or as use as a textbook for advanced undergraduate or graduate students of mathematics and statistics.

1

Introduction

1.1 Background

The science of toxicology has a long and profound history. It has its roots in the ancient Greek and Roman empires where physicians made early attempts to classify plants and distinguish between toxic and therapeutic plants. In the late fifteenth century and early sixteenth century, a Swiss scientist known as Paracelsus pioneered the use of chemicals and minerals in medicine. He is credited with the well-known phrase “The dose makes the poison.” Although the original phrase was a little different, it emphasizes the fact that any substance can be harmful to living organisms if the dose or the concentration is high enough. Toxicologists believe that most chemicals, drugs, pollutants, and natural medicinal plants adhere to this principle. Paracelsus is often referred to as the father of toxicology. The development of modern toxicology is largely attributed to the Spanish scientist Orfila who is the father of modern toxicology and is considered to be the founder of the science of toxicology. Although different sources define toxicology a little differently, they all point to the fact that toxicology is the science that studies the adverse effects of chemical substances on living organisms including humans, animals, and the environment. It also involves the diagnosis and treatment of possible exposure to toxic substances and toxicants. Toxicologists use the power of science to predict how chemicals and damaging plants and minerals can be harmful. Not only is there individual variability in response, but other variables such as the exposure level, route of exposure, duration of exposure, age, gender, and the environment are used by toxicologists to determine the effect of toxicity.

1.2 Branches of Toxicology

Today, toxicology has grown into a multifaceted discipline. We provide here a list of these branches. The list is not exhaustive and there could be other branches as well, but it provides the most common branches with a brief description of each.

1. a. Aquatic Toxicology: Study of the effect of toxins such as chemical waste or natural material on aquatic organisms.
2. b. Chemical Toxicology: Involves the study of the structure and the mechanism of action of chemical toxicants.
3. c. Clinical Toxicology: Study concerning how much poison is present in the body as well as problems occurring due to overdose of drugs.
4. d. Developmental and Reproductive Toxicology: This branch of toxicology is concerned about the effect of toxins on the offspring when the parent, primarily the mother, is exposed to the toxicant during conception or pregnancy. It also concerns the multigenerational effects of toxic substances.
5. e. Ecotoxicology: Study of the effect of toxic substances in the ecosystem.
6. f. Environmental Toxicology: Study of the effects of pollutants naturally present in the environment, such as in air, water, and soil, on humans and other living organisms.
7. g. Forensic Toxicology: A topic within the general framework of forensic science that deals with the identification and quantification of poison, often leading to the determination of the cause of death.
8. h. Industrial Toxicology: Study of the effects of exposure to industrial waste and chemicals released from industries including, but not limited to, soot and other air pollutants.
9. i. Molecular Toxicology: This is concerned about the study of the ­cellular and molecular processes of toxicity.
10. j. Regulatory Toxicology: Study of toxicological processes based on the characteristics and guidelines of regulatory agencies.
11. k. Neurotoxicology: Study of the effects of toxicants on the brain and the nervous system.
12. l. Nutritional Toxicology: Concerned about food additives and nutritional habits, as well as the hazards posed by the way food is prepared, and so on.
13. m. Occupational Toxicology: Study of workplace-related health hazards, particularly in the chemical and mining industries.
14. n. Veterinary Toxicology: Study of the process of toxicity in animals.
15. o. Immunotoxicology: This is the study and analysis of how toxicity can damage the immune system.
16. p. Analytical Toxicology: Application of analytical chemistry methods in the quantitative and qualitative evaluation of toxic effects.
17. q. Mechanistic Toxicology: Similar to Chemical Toxicology, this study deals with the mechanism of action.

Some other branches of toxicology mentioned in the literature are Behavioral Toxicology, Comparative Toxicology, and Genetic Toxicology. Clearly many of these branches are interrelated and cannot be studied in isolation.

1.3 Basic Elements of Toxicology

Toxicity is defined as any undesirable or adverse effect of exogenous substances on humans, animals, and the environment. These substances include chemicals such as food additives, drugs and medicines, organic plants, or inorganic material such as mercury and lead. A specific undesirable outcome, such as carcinogenicity or neurotoxicity, is called a toxicological endpoint. Outcomes of toxicology testing experiments can be both continuous such as changes in brain weight and qualitative such as the presence or absence of a specific endpoint like cancer or can be evaluated on an ordinal scale such as low, moderate, or high. Toxicology tests have for a long time used laboratory animals in bioassay experiments to perform in vivo studies and to determine the effects of toxicants, although in recent years the use of in silico approaches (Computational Toxicology) has become popular. Experiments may consist of single exposure, as in case-control studies, or may have several exposure levels. The exposure level or the concentration level, that is, the amount of the chemical used in the experiment, is called the dose or the dosage level. Clearly, the dose is a crucial factor in the amount of toxicity, and determination of an efficient dose regimen is an important problem in the design of toxicological experiments. Several other factors play important roles in the extent of toxicity. One is the route of exposure, which could be by injection, oral (mixed in the diet), dermal, or by inhalation. Other factors are the frequency of exposure (how often the exposure occurs), duration of exposure, and the excretion rate of the chemical, often measured by half-life. Individuals respond differently to the same dosage, and other subject-specific variables such as age and gender add more variations to the outcome.

Toxicity is generally measured by the severity of the effect of the substance on the organism or the target tissue. The most fundamental method of measuring the toxicity of a substance is by using LD ₅₀, which is the dosage level of the substance that creates lethality in 50% of the subjects. In inhalation toxicity studies, air concentrations are usually used for exposure values and LD ₅₀ is utilized as a measure of toxicity. Another similar measure is ED ₅₀ or EC ₅₀, which is the effective dose or concentration of the chemical that makes an observable endpoint of interest in 50% of subjects. These measures have often been used to compare and classify chemicals. Clearly, 50% is a nominal and convenient value corresponding to the median, and other percentiles of interest may also be used. That is, in general, LD _{100 p} and LC _{100 p}, where 0 ≤ p ≤ 1 is the dosage or concentration level that results in lethality in 100% of the subjects. Thus, for example, if p = 0.01, then ED ₀₁ refers to the dosage of the chemical that affects 1% of the subjects. Because humans are generally exposed to low levels of chemicals, much of the interest among toxicologists is to study the behavior and toxicity in the low-dose region. In fact, there was a large-scale experiment in the 1970s conducted by the National Center for Toxicological Research (NCTR) of the Food and Drug Administration (FDA) and reported by Staffa and Mehlman (1979), also referred to as the ED ₀₁ study. In that experiment, over 24,000 mice in several strains were exposed to the known carcinogen 2-acetylaminofluorene (2-AAF) to study the lethality of the chemical in low doses (see also Brown and Hoel, 1983a, b). However, LD ₅₀ and LC ₅₀ have limited usage as they cannot be directly extrapolated across species and to low doses. In fact, their application as a measure of toxicity has been criticized by many toxicologists (see Zbinden and Flury-Roversi, 1981; LeBeau, 1983). Alternative measures of toxicity are listed below:

1. a. Acceptable Daily Intake (ADI): For food additives and drugs.
2. b. Benchmark Dose (BMD): A dose of the toxin that produces a predetermined level (e.g. 5%) of change of the adverse effect.
3. c. Lowest-Observed-Effect-Level (LOEL): Lowest dose that causes an observable effect.
4. d. Lowest-Observed-Adverse-Effect-Level (LOAEL): Lowest dose that causes an observable adverse effect.
5. e. Maximum Tolerated Dose (MTD): Used mostly in chronic toxicology and represents highest dose with no health effects.
6. f. Median Tolerated Dose (TD ₅₀): Median toxic dose causing toxicity in 50% of exposed individuals.
7. g. No Toxic Effect Level (NTEL): Largest dose with no observed effect.
8. h. No-Observed-Effect-Level (NOEL): Highest dose with no effect.
9. i. No-Observed-Adverse-Effect-Level (NOAEL): Largest experimental dose that produces no undesirable outcome.
10. j. Reference Dose (RfD): Daily acceptable dose that produces no risk of adverse effect.
11. k. Tolerable Daily (Weekly) Intakes: For contaminants and additives not consumed intentionally.
12. l. Reference Intake: Used mainly for nutrients.

There is a large body of literature in toxicology that describes the properties and applications of each of the abovementioned measures of toxicity. In addition, the measures are not independent and many of them are interrelated. Several publications discuss some of the relationships. For example, Gaylor and Gold (1995) and Razzaghi and Gaylor (1996) discuss the relation between TD ₅₀ and MTD.

1.4 Emergence of Statistical Models

Although statisticians have always played an important role in toxicological research and made contributions towards the development of many of the...