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posed an algorithm—called the unmixing algorithm—for adjusting vitamin A intake distributions. Nusser and colleagues (1996), Stefanski and Bay (1996), Eckert and coworkers (1997), and more recently Chen (1999) started from the method proposed by the NRC (1986) and suggested methods for estimating usual intake distributions that address different sets of characteristics of dietary intake data. Brief descriptions of two approaches, the NRC (1986) method and the method developed at Iowa State University (ISU method, Nusser et al., 1996) are provided because they are most used today (Beaton, 1994; Carriquiry et al., 1997).

Suppose that daily intake data for a group of individuals are available. These data may have been collected via 24-hour recall methods or perhaps from multiple-day diet records. For each of the individuals, multiple days of dietary intake data were recorded. Even though it is assumed here that each individual in the group has the same number of independent daily intake observations, neither of the methods described below require that each individual in the group have the same number of observations. It is possible to adjust intake distributions as long as some individuals in the group have two or more daily intake observations, even if for many of the individuals only one observation is available.

For multiple daily intake observations for each individual in the sample, it is possible to obtain, for each individual, the mean intake over the multiple days of recording. As is discussed in Chapter 3, observed mean intakes can be used as estimates of individual usual intake, albeit imprecise ones. Estimating the usual intake distribution in the group as the distribution of the observed mean intakes, however intuitively appealing, is incorrect. The individual daily intakes must be used, rather than the mean intake, in order to adjust the usual intake distribution.

The National Research Council Method to Adjust Intake Distributions

In recognizing that daily intakes for an individual vary from day to day, and that daily intake data are not normally distributed, the NRC (1986) proposed that day-to-day variability in intakes be partially removed by fitting a measurement error model to daily intake data which had been power transformed. Power transformation refers to a family of mathematical conversions that includes, for example, the square root, the cube root, and log transformations (Fuller, 1987). The power transformation reduces the skewness typically observed in the distribution of daily intakes. The measure-

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