## 4.3.2. Concentration-response relationships

Author: Kees van Gestel

Reviewers: Michiel Kraak, Thomas Backhaus

Learning goals:

You should be able to

- understand the concept of the concentration-response relationship
- define measures of toxicity
- distinguish quantal and continuous data
- mention the reasons for preferring ECx values above NOEC values

Keywords: concentration-related effects, measure of lethal effect, measure of sublethal effect, regression-based analysis

Key paradigm in human and environmental toxicology is that the dose determines the effect. This paradigm goes back to Paracelsus, stating that any chemical is toxic, but that the dose determines the severity of the effect. In practice, this paradigm is used to quantify the toxicity of chemicals. For that purpose, toxicity tests are performed in which organisms (microbes, plants, invertebrates, vertebrates) or cells are exposed to a range of concentrations of a chemical. Such tests also include incubations in non-treated control medium. The response of the test organisms is determined by monitoring selected endpoints, like survival, growth, reproduction or other parameters (see section on Endpoints). Endpoints can increase (e.g. mortality) or decrease with increasing exposure concentration (e.g. survival, reproduction, growth). The response of the endpoints is plotted against the exposure concentration, and so-called concentration-response curves (Figure 1) are fitted, from which measures of the toxicity of the chemical can be calculated.

Figure 1: Concentration-response relationships. Left: response of the endpoint (e.g., survival, reproduction, growth) decreases with increasing concentration. Right: response of the endpoint (e.g., mortality, induction of enzyme activity) increases with increasing exposure concentration.

The unit of exposure, the concentration or dose, may be expressed differently depending on the exposed subject. Dose is expressed as mg/kg body weight in human toxicology and following single (oral or dermal) exposure events in mammals or birds. For other orally or dermally exposed (invertebrate) organisms, like honey bees, the dose may be expressed per animal, e.g. µg/bee. Environmental exposures generally express exposure as the concentration in mg/kg food, mg/kg soil, mg/l surface, drinking or ground water, or mg/m3 air.

Ultimately, it is the concentration (number of molecules of the chemical) at the target site that determines the effect. Consequently, expressing exposure concentrations on a molar basis (mol/L, mol/kg) is preferred, but less frequently applied.

At low concentrations or doses, the endpoint measured is not affected by exposure. At increasing concentration, the endpoint shows a concentration-related decrease or increase. From this decrease or increase, different measures of toxicity can be calculated:

ECx/EDx: the "effective concentration" resp. "effective dose"; "x" denotes the percentage effect relative to an untreated control. This should always be followed by giving the selected endpoint.

LCx/LDx: same, but specified for a specific endpoint: lethality.

EC50/ED50: the median effect concentration or dose, with “x” set to 50%. This is the most common estimate used in environmental toxicology. This should always be followed by giving the selected endpoint.

LC50/LD50: same, but specified for a specific endpoint: lethality.

The terms LCx and LDx refer to the fraction of animals responding (dying), while the ECx and EDx indicate the degree of reduction of the measured parameter. The ECx/EDx describe the overall average performance of the test organisms in terms of the parameter measured (e.g., growth, reproduction). The meaning of an LCx/LDx seems obvious: it refers to lethality of the test chemical. The use of ECx/EDx, however, always requires explicit mentioning of the endpoint it concerns.

Concentration-response models usually distinguish quantal and continuous data. Quantal data refer to constrained (“yes/no”) responses and include, for instance, survival data, but may also be applicable to avoidance responses. Continuous data refer to parameters like growth, reproduction (number of juveniles or eggs produced) or biochemical and physiological measurements. A crucial difference between quantal and continuous responses is that quantal responses are population-level responses, while continuous responses can also be observed on the level of individuals. An organism cannot be half-dead, but it can certainly grow at only half the control rate.

Concentration-response models are usually sigmoidal on a log-scale and are characterized by four parameters: minimum, maximum, slope and position. The minimum response is often set to the control level or to zero. The maximum response is often set to 100%, in relation to the control or the biologically plausible maximum (e.g. 100% survival). The slope identifies the steepness of the curve, and determines the distance between the EC50 and EC10. The position parameter indicates where on the x-axis the curve is placed. The position may equal the EC50 and in that case it is named the turning point. But this in fact holds only for a small fraction of models and not for models that are not symmetrical to the EC50.

In environmental toxicology, the parameter values are usually presented with 95% confidence intervals indicating the margins of uncertainty. Statistical software packages are used to calculate these corresponding 95% confidence intervals.

Regression-based test designs require several test concentrations, and the results are dependent on the used statistical model, especially in the low-effect region. Sometimes it is simply impossible to use a regression-based design because the endpoint does not cover a sufficiently high effect range (>50% effect is typically needed for an accurate fit).

In case of quantal responses, especially survival, the slope of the concentration-response curve is an indication of the sensitivity distribution of the individuals within the population of test organisms. For a very homogenous population of laboratory test animals having the same age and body size, a steeper concentration-response curve is expected than when using field-collected animals representing a wider range of ages and body sizes (Figure 2).

Figure 2: The steepness of the concentration-response curve for effects on survival (top) may provide insight into the sensitivity distribution of the individuals within the population of test animals (bottom). The steeper the curve the smaller the variation in sensitivity among the test organisms.

In addition to ECx values, toxicity tests may also be used to derive other measures of toxicity:

NOEC/NOEL: No-Observed Effect Concentration or Effect Level

LOEC/LOEL: Lowest Observed Effect Concentration or Effect Level

NOAEL: No-Observed Adverse Effect Level. Same as NOEL, but focusing on effects that are negative (adverse) compared to the control.

LOAEL: Lowest Observed Adverse Effect Level. Same as LOEL, but focusing on effects that are negative (adverse) compared to the control.

Where the ECx are derived by curve fitting, the NOEC and LOEC are derived by a statistical test comparing the response at each test concentration with that of the controls. The NOEC is defined as the highest test concentration where the response does not significantly differ from the control. The LOEC is the next higher concentration, so the lowest concentration tested at which the response significantly differs from the control. Figure 3 shows NOEC and LOEC values derived from a hypothetical test. Usually an Analysis of Variance (ANOVA) is used combined with a post-hoc test, e.g. Tukey, Bonferroni or Dunnett, to determine the NOEC and LOEC.

Figure 3: Derivation of NOEC and LOEC values from a toxicity test.

Most available toxicity data are NOECs, hence they are the most common values found in databases and therefore used for regulatory purposes. From a scientific point of view, however, there are quite some disadvantages related to the use of NOECs:

- Obtained by statistical test (hypothesis testing) (compared to regression analysis);
- Equal to one of the test concentrations, so not using all data from the toxicity test;
- Sensitive to the number of replicates used per exposure concentration and control;
- Sensitive to variation in response, so for differences between replicates;
- Depends on the statistical test chosen, and on the variance (σ);
- Does not have confidence intervals;
- Makes it hard to compare toxicity data between laboratories and between species.

The NOEC may, due to its sensitivity to variation and test design, sometimes be equal to or even higher than the EC50.

Because of the disadvantages of the NOEC, it is recommended to use measures of toxicity derived by fitting a concentration-response curve to the data obtained from a toxicity test. As an alternative to the NOEC, usually an EC10 or EC20 is used, which has the advantages that it is obtained using all data from the test and that it has a 95% confidence interval indicating its reliability. Having a 95% confidence interval also allows a statistical comparison of ECx values, which is not possible for NOEC values.