Dose-Response Models for Pesticides
Researchers: Eckhard Limpert, work done at
Institut für Pflanzenwissenschaften, ETHZ,
Dr. Werner Stahel,
Christian Sangiorgio.
Roman Lutz.
Abstract:
Nature of Data and Routine Analysis.
Fungicide sensitivity is analyzed by a standard routine:
Fungi are grown on plant leaves in small boxes. The leaves within the
small box are pretreated with a certain dose of fungicide.
A standard series of 10 such small boxes consists of one without
fungicide, and nine with a geometric sequence of doses from, e.g.,
0.001 to 10.
Each series thus gives rise to 10 outcome variables measuring the growth
for the 10 doses.
The outcome variable for our data is a score between 0 and 100 with 12
possible values 0, 5, 10, 20, ..., 90, 100.
The values should generally decline. Due to random variability
and possibly a stimulating effect of very low doses (hormesis effect)
this is not always the case.
Routine analysis performs, for each series, a probit analysis with a
logarithmic scale for the dose. The analysis yields a sensitivity value
log(ED50), which we call a for short, and a slope value b.
Model.
Probit analysis is based on the binomial (or Bernoulli) distribution.
It attributes maximal random variation for doses around ED50.
In data of the type described, random variation is maximum for low doses.
We use a suitably adjusted model and estimate parameters by maximum
likelihood.
Common slope.
The parameters may be expected to depend on
-
host type (wheat vs. barley), with respective pathogens;
and within this:
genotype of pathogen (fungus), and
host (eg., different locations).
- fungicide type and application mode; and within type: individual
substance (and within this: production lot)
These factors clearly affect the sensitivity a.
The slope b is essentially constant over genotypes.
This has considerable implications for data analysis:
While b cannot be reliably estimated from an individual series,
the parameter of interest a, or ED50, can be estimated more
precisely if b is assumed to be known from (many) related
series.
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