Analysis of Dose Response Data

The two common approaches to analyzing dose-response data quantitatively is by the probit and log logistic models. Log normal curve (Figure 6) formed the basis for probit a) <n c o cp <n

Stressor intensity (X) Figure 6 Typical log normal curve for stressor-response data.

model and logistic model is linked to processes such as enzyme kinetics, autocatalysis, and adsorption phenomena. Both models predict a sigmoidal curve (Figure 5). During dose-response analysis, data may be used directly or transformed. In most cases, the objective behind the transformations is to make linear the relationship between dose and response. The most common transformation performed is the logarithm scale. The probit transformation is derived from the normal equivalent deviation (NED), that is, the proportion of response expressed in terms of standard deviations from the mean of a normal curve. For example, a proportion corresponding with the mean (50% of observed individuals) would have an NED of 0. A proportion below the mean by one standard deviation (16% of observed individuals) would have an NED of — 1. To get rid of negative values, the number 5 is added to NED values, probit (P) = NED (P) + 5, where P = proportion of observed individuals that responded to a treatment and NED = the normal equivalent deviation.

The log logistic model (logit) has the following form:

A transformed logit is more commonly employed than that calculated by equation above because values of this transformed logit are nearly the same as probit values -except for proportions at the extreme ends of the curves (Figure 7),

Transformed logit = [logit(P)/2] + 5 where logit (P) = logit value (estimated by logit (P) =

Slopes and intercepts of stressor-response lines provide valuable information about the relative sensitivity of biota to the same or different stressors. The slope quantifies the steepness of the line. It equals the change in response for each unit change in stressor intensity. It is expressed in the units of the response axis divided by the units of the stressor axis. If the slope is positive, response increases as stressor increases. If the slope is negative, response decreases as stressor increases. Imagine a second line with a much steeper slope intersecting the drawn line

Log stressor

Figure 7 Lines resulting from the probit and logit transformations. Reproduced by permission of Taylor & Francis.


e s




Slope = AY/AX


Stressor intensity (X)

Figure 8 Stressor-response relationship with intercept and slope.

at the LD50 (Figure 8). Although the LD50 would be the same for both lines, a small change in stressor intensity has much more of an effect with one stressor (steeper slope) than the other (shallow slope). The response intercept is the response value of the line when stressor intensity equals zero. It defines the elevation of the line and indicates the potential threshold exposure.

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