ecxsys {stressaddition}

ECx-SyS

Description

ECx-SyS is a model for tri-phasic concentration-response relationships where hormetic and subhormetic effects are observed at low concentrations. It expands the Stress Addition Model (SAM) by introducing system stress (SyS) which is negatively correlated with toxicant stress. A constant environmental stress can be included. See the publication for details.

Usage

ecxsys(
  concentration,
  hormesis_concentration,
  survival_tox_observed,
  survival_tox_env_observed = NULL,
  survival_max = 100,
  curves_concentration_max = NULL,
  p = 3.2,
  q = 3.2
)

Arguments

concentration

A vector of concentrations. Must be sorted in ascending order and the first element must be 0 to indicate the control.

hormesis_concentration

The concentration where the hormesis occurs. This is usually the concentration of the highest survival after the control.

survival_tox_observed

A vector of survival values observed at the given concentrations and in absence of environmental stress. Values must be between 0 and survival_max.

survival_tox_env_observed

Survival values observed in the presence of environmental stress. Must be between 0 and survival_max.

survival_max

The maximum value the survival could possibly reach. For survival data in percent this should be 100 (the default).

curves_concentration_max

The maximum concentration of the predicted curves. This might be useful if for example your highest observed concentration is 30 but you would like to know the predicted values on a scale between 0 and 100.

p, q

The shape parameters of the beta distribution. Default is p = q = 3.2.

Details

It is advised to complete the curve down to zero for optimal prediction. Therefore survival_tox_observed in the highest concentration should be at or close to zero. If the model does not fit properly try adding a survival of 0 at ten times the maximum observed concentration.

The vectors concentration, survival_tox_observed and survival_tox_env_observed (if provided) must be of equal length and sorted by increasing concentration.

Value

A list (of class ecxsys) containing many different objects of which the most important are listed below. The survival and stress vectors correspond to the provided concentrations.

survival_tox

Modeled survival resulting from toxicant stress.

survival_tox_sys

Modeled survival resulting from toxicant and system stress.

survival_tox_env

Modeled survival resulting from toxicant and environmental stress.

survival_tox_env_sys

Modeled survival resulting from toxicant, environmental and system stress.

survival_tox_LL5

The survival predicted by the five-parameter log-logistic model derived from the observations under toxicant stress but without environmental stress.

survival_tox_env_LL5

The survival predicted by the five-parameter log-logistic model derived from the observations under toxicant stress with environmental stress.

curves

A data frame containing survival and stress values as returned by predict_ecxsys. The concentrations are regularly spaced on a logarithmic scale in the given concentration range. The control is approximated by the lowest non-control concentration times 1e-7. The additional column concentration_for_plots is used by the plotting functions of this package to approximate the control and generate a nice concentration axis.

References

Liess, M., Henz, S. & Knillmann, S. Predicting low-concentration effects of pesticides. Sci Rep 9, 15248 (2019).

Examples

model <- ecxsys(
    concentration = c(0, 0.05, 0.5, 5, 30),
    hormesis_concentration = 0.5,
    survival_tox_observed = c(90, 81, 92, 28, 0),
    survival_tox_env_observed = c(29, 27, 33, 5, 0)
)

# Use survival_max if for example the survival is given as the average number
# of surviving animals and the initial number of animals is 21:
model <- ecxsys(
    concentration = c(0, 0.03, 0.3, 3, 30),
    hormesis_concentration = 0.3,
    survival_tox_observed = c(17, 15.2, 18.8, 7, 0),
    survival_tox_env_observed = c(4.8, 4.6, 6.4, 0, 0),
    survival_max = 21
)