PAPERBACK
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### THE PROBABILITY APPROACH

The probability approach to estimating the prevalence of nutrient inadequacy was proposed by the National Research Council (NRC, 1986). The idea is simple. For a given a distribution of requirements in the population, the first step is to compute a risk curve that associates intake levels with risk levels under the assumed requirement distribution.

Formally, the risk curve1 is obtained from the cumulative distribution function (cdƒ) of requirements. If we let FR(.) denote the cdƒ of the requirements of a dietary component in the population, then

FR(a) = Pr(requirements ≤ a)

for any positive value a. Thus, the cdƒ FR takes on values between 0 and 1. The risk curve ρ (.) is defined as

ρ(a)=l − FR(a)=l − Pr(requirements ≤ a)

A simulated example of a risk curve is given in Figure 4-3. This risk curve is easy to read. On the x-axis the values correspond to intake levels. On the y-axis the values correspond to the risk of nutrient inadequacy given a certain intake level. Rougher assessments are also possible. For a given range of intake values, the associated risk can be estimated as the risk value that corresponds to the midpoint of the range.

For assumed requirement distributions with usual intake distributions estimated from dietary survey data, how should the risk curves be combined?

It seems intuitively appealing to argue as follows. Consider again the simulated risk curve in Figure 4-3 and suppose the usual intake distribution for this simulated nutrient in a population has been estimated. If that estimated usual intake distribution places a very high probability on intake values less than 90, then one would con-

 1 When the distribution of requirements is approximately normal, the cdƒ can be easily evaluated in the usual way for any intake level a. Let z represent the standardized intake, computed as z = (a − mean requirement) / SD, where SD denotes the standard deviation of requirement. Values of FR(z) can be found in most statistical textbooks, or more importantly, are given by most, if not all, statistical software packages. For example, in SAS, the function probnorm (b) evaluates the standard normal cdƒ at a value b. Thus, the “drawing the risk curve” is a conceptualization rather than a practical necessity.

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