represent individuals with intakes greater than the EAR, who still do not meet their requirements (they are to the right of the intake = EAR line in the shaded area above the 45° line where intake equals requirement). Next, note the number of data points in triangle B which represent individuals with intakes below the EAR but whose intakes are adequate. The EAR cut-point method works when intakes and requirements are independent (see Figure 4-8) and the number of points in triangles A and B are virtually identical. In Figure 4-9 there are more points in triangle B than in triangle A. Accordingly, when usual intake and requirement are correlated, using the EAR cut-point method (i.e., determining the number of individuals to the left of the intake = EAR line) would overestimate the number of people with inadequate intakes (those in the shaded area above the 45° line where intake = requirement).
This example is illustrative, but does not indicate what the expected bias resulting from using the cut-point method might be. The bias of the cut-point method will be severe for energy because the correlation between usual energy intakes and requirements (expenditure) is high. How severe a bias is expected if the association between intakes and requirements is not as extreme? This question is difficult to answer because usual intakes and requirements cannot be observed for a sufficiently large sample of individuals. However, limited empirical evidence suggests that the expected bias is likely to be low as long as the correlation between intakes and requirements is moderate—no larger than 0.25 or 0.30 (Carriquiry, 1999). Furthermore, when the mean intake of a group and the EAR are approximately the same, the effect of the correlation on the bias of the cut-point method is likely to be very low even at correlations greater than 0.30. An exception to this rule is the extreme case in which the correlation between intakes and requirements of the nutrient is equal to 1. In this unlikely event, the prevalence estimates obtained from the EAR cut-point method will be severely biased, even if mean intake and the EAR are identical. This purely hypothetical case is used in an illustrative example in the next section.
Do the probability approach and the EAR cut-point method work for food energy?
No, because empirical evidence indicates a strong correlation between energy intake and energy requirements. This correlation most likely reflects either the regulation of energy intake to meet needs or the adjustment of energy expenditures to be consistent with intakes (FAO/WHO/UNU, 1985). Because of this strong correlation, neither the EAR cut-point method nor the probability approach can be used to assess the probability of inadequacy of food energy intake.