The term dilution assay is generally used to designate a special type of bioassay in which one or more preparations (e.g. a drug) are administered to experimental units at different dose levels inducing a measurable biological response.
The dose levels are prepared by dilution in a diluent that is inert in respect of the response.
The experimental units can for example be cell-cultures, tissues, organs or living animals.
The biological response may be quantal (e.g. positive/negative) or quantitative (e.g. growth).
The goal is to relate the response to the dose, usually by interpolation techniques, and in many cases to express the potency/activity of the test preparation(s) relative to a standard of known potency/activity.
In a direct dilution assay the amount of dose needed to produce a specific (fixed) response is measured, so that the dose is a stochastic variable defining the tolerance distribution.
Conversely, in an indirect dilution assay the dose levels are administered at fixed dose levels, so that the response is a stochastic variable.
In some assays, there may be strong reasons for believing that all the constituents of the test preparation except one, are without any effect on the studied response of the subjects.
An assay of the preparation against a standard preparation of the effective constituent, is then equivalent to an analysis for determining the content of the constituent.
For a mathematical definition of a dilution assay an observation space
This is the fundamental assumption of similarity of dose-response curves which is necessary for a meaningful and unambiguous definition of the relative potency.
In many cases it is convenient to apply a power transformation
is written for the log transformation the above equation can be redefined as Estimates
are usually restricted to be member of a well-defined parametric family of functions, for example the family of linear functions characterized by an intercept and a slope.
Statistical techniques such as optimization by Maximum Likelihood can be used to calculate estimates of the parameters.
Of notable importance in this respect is the theory of Generalized Linear Models with which a wide range of dilution assays can be modelled.
satisfactorily over the range of doses tested, but they do not necessarily have to describe
However, this does not mean that dissimilar curves can be restricted to an interval where they happen to be similar.
or an estimate of the dose that induces a specific response.
Fieller's theorem can be used to compute confidence intervals of these ratios.
Some special cases deserve particular mention because of their widespread use: If
An antibiotic standard (shown in red) and test preparation (shown in blue) are applied at three dose levels to sensitive microorganisms on a layer of agar in petri dishes.
The stronger the dose the larger the zone of inhibition of growth of the microorganisms.
and the method of least squares is used to fit two parallel lines to the data.
between the two lines (shown in green) serves as an estimate of the potency
The major statistical software packages do not cover dilution assays although a statistician should not have difficulties to write suitable scripts or macros to that end.
Several special purpose software packages for dilution assays exist.