Setting Model

May be long to compute.

For long-running tasks, the Advanced plan allows you to close the browser tab and receive an email notification when the task is completed.

Plot

            

What is a dose–response for continuous endpoints?

In many ecotoxicological tests, the measured endpoint is continuous (non-integer): body weight or length, biomass, specific growth rate, chlorophyll-a, enzyme activity, etc. A dose–response relationship is then fitted to quantify how a toxicant changes the mean response (or a derived rate/percent inhibition).

Statistically, such data are handled with models for continuous responses: nonlinear regression using log-logistic, Weibull, Hill or exponential families; generalized linear or additive models (e.g., Gamma or log-normal for positive, right-skewed data); and mixed-effects models when there are repeated measures or block/replicate structure. ECx/EDx values (EC10, EC20, EC50) and Benchmark Doses (BMD) are estimated with uncertainty, taking into account heteroscedasticity (e.g., variance increasing with the mean).

Depending on the test, the response can be: (i) a direct measurement (e.g., length, dry mass), (ii) a rate (e.g., specific growth rate), (iii) a percent inhibition (e.g., % inhibition of growth rate vs. control). Proper transformation (e.g., log-scale), variance modelling (weights/GLS), and analysis at the replicate level help avoid bias.

OECD frameworks and guidance documents for continuous data

OECD provides both statistical principles and test guidelines. For analysis, the Guidance Document on Statistical Analysis of Ecotoxicity Data (ENV/JM/MONO(2006)18) covers ECx estimation, model comparison and continuous-data modelling (including variance heterogeneity, transformations, and mixed models).

Benchmark Dose (BMD) approaches are recommended in several regulatory frameworks because they provide a continuous effect estimate with uncertainty. For continuous data, the Benchmark Response (BMR) is typically defined as a percentage change from the control mean (e.g., 5% or 10% decrease in growth rate), and BMD/BMDL are obtained from fitted continuous models.

Main OECD Test Guidelines with continuous endpoints

Aquatic primary producers:

• TG 201 — Freshwater Alga and Cyanobacteria, Growth Inhibition Test : continuous endpoints such as biomass, yield, and specific growth rate (µ).

• TG 221 — Lemna sp. Growth Inhibition Test : continuous endpoints include frond area/biomass and growth rate (alongside frond number).

Fish and other aquatic vertebrates:

• TG 215 — Fish, Juvenile Growth Test : continuous endpoints like specific growth rate, length and weight.

Terrestrial and aquatic plants:

• TG 208 — Seedling Emergence and Seedling Growth Test : growth measurements such as shoot/root length and (dry) biomass.

• TG 227 — Vegetative Vigour Test : continuous growth endpoints (height, growth rate, biomass).

Benthic/sediment-associated tests (examples):

• TG 218 / 219 — Chironomus sediment/water toxicity tests : may include continuous measures such as mean dry weight or time to emergence, in addition to emergence counts.

• TG 225 — Sediment-Water Lumbriculus variegatus Reproduction Test : biomass can be analysed as a continuous endpoint alongside reproduction.

Best practices for modelling continuous endpoints

• Check distributional assumptions → consider log-normal/Gamma models for positive, skewed data;

• Address heteroscedasticity → use variance functions or weighted/GLS regression;

• Prefer replicate-level analysis over pre-averaged data to preserve variance;

• Report ECx and BMD with confidence intervals (profile likelihood or bootstrap), and consider model averaging;

• For repeated measures or blocks, use mixed-effects models (random effects for tank/block/replicate);

• Clearly define the response scale (raw, log-transformed, percent inhibition) and keep units consistent.

Other regulatory frameworks referring to continuous endpoints

• ECHA/REACH : Guidance documents R.7 (R.7a/b/c) recommend ECx and BMD approaches for growth and other continuous endpoints, with attention to variance modelling and appropriate distributions.

• US EPA OCSPP 850 series : aquatic plant and growth-related guidelines (e.g., algal and macrophyte growth tests) report continuous endpoints such as specific growth rate, yield, length and biomass.

References

OECD — ENV/JM/MONO(2006)18, Guidance Document on Statistical Analysis of Ecotoxicity Data (methods for ECx, continuous-data modelling, transformations, variance functions, mixed models).

OECD TG 201, 221, 215, 208, 227, 218/219, 225 — Test Guidelines where primary or secondary endpoints include continuous measurements .

ECHA (REACH) — Guidance R.7 (R.7a/b/c) : choice of endpoints, ECx/BMD recommendations, analysis principles.

US EPA — OCSPP 850 series : aquatic plants and growth-related tests with continuous endpoints.