Generalized exposure-reponse description

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Generalised exposure-response (GER) is such a description of the relationship between exposure (or dose) and response (or health effect) that is generalisable enough to be applicable to all kinds of exposures and responses in both humans and animals. The purpose of such description is to facilitate combinations of data from different species or exposure ranges.

Description

The GER is a multi-dimensional variable describing responses of individuals to a given exposure. Thus, it is NOT a population-level phenomenon, because this would create generalisability problems from one population to another. In addition, dose-response IS an individual-level phenomenon, because individuals, not populations, respond to exposures. (in the case of herd immunity or mob responses, which are truly population-level phenomena, they must be described as individual populations. However, I do not know how to deal with that in practice.)

It has at least the following dimensions. The first two are obvious, but also the next three are necessary for a generalised description (although in some cases they may cancel out).

1) Description of response in some quantifiable units, preferably on a continuous scale.

2) Description of exposure (or dose) in mass per time units (possibly scaled to the body weight). If exposure is a signle bolus or a constant rate exposure, it can be expressed in a one-dimensional scale. However, the exposure may also vary in an irregular fashion. In this case, it is not possible to describe the exposure with a single value, but a more thorough understanding is needed about the pharmacokinetics of the compound and time dynamics of the patophysiological effects. It may then be possible to describe the exposure with a simple model such as area under the curve.

An exposure-response curve is a function that describes how a particular individual would respond if the individual were exposed to a particular amount of exposure for the first time. It is of course impossible to expose someone more than once for the first time, and therefore an exposure-response curve can never be really measured, but we don't worry about that for the moment. Now we have Response R given exposure E, or R|E.

3) The response of a given exposure of course changes in time. The physiological processes mediating the response take time, and feedback mechanisms and metabolism will probably reduce the response after some peak period. It is therefore necessary to describe the response as a function of observation time. However, often it is enough to observe the most relevant (usually the response peak) period, and other time points can be cancelled out as long as the actual observation time point is reported. This is R|E,t.

4) Description of sensitivity of the individual in the population measured on a continuous scale. The best way (so far known) is to define it as the exposure that causes a 5% change from the individual background level (where exposure=0). This exposure can be called as RE₀₅ (responsive exposure 5%). Each individual ER curve is thus located at the point of RE₀₅ on the sensitivity dimension. This is R|E,t,RE₀₅.

The advantage of this approach (compared with e.g. a fractile in a population variability scale) is that it is not population-dependent and thus the same individual always locates at the same point in the sensitivity axis irrespective of the population the individual comes from.

5) Probability of the response given all the constraints. This is P(R|E,t,RE₀₅).

Definition

• R:= Response
• E:= Exposure
• RE₀₅:= Responsive exposure 05
• t:= Effect window

Unit

• absolute or relative change from individual background per mg/kg/g

Result

P(R|E,t,RE₀₅)