| Food Composition Data: A User's Perspective (1987) |
|Consideration of food composition variability: What is the variance of the estimate of one-day intakes? Implications for setting priorities|
Additional impact of a random error in intake estimation
Given the above construct of the impact of food composition variation, in order to offer informational perspective it is possible to extend the model to include the impact of another source of variation - an error in the estimation of portion size when obtaining the record of intake. In this case the two variances (composition and intake estimate) would be multiplicative. Assuming that they are not correlated, the following equation would serve to predict the variance of the estimated nutrient content of a single food item. The equation is based on one presented in the FAO/WHO/UNU report on Energy and Protein Requirements .
V(food 1) = I2*V(C) + C2*V(I) + V(c)*V(I)
- I2 is the square of reported (mean) intake of units of food;
- C2 is the square of reported (mean) concentration of nutrient per unit of food;
- V (food 1) is the variance of content of food 1 where content is I*C;
- V(I) is the variance of the intake measurement;
- V(c) is the variance of the composition measurement.
(The equation presented assumes no correlation between values of I and C; approximations are available for situations in which correlation exists.)
This equation derives the combined variance for a single food. To obtain the variance (and then SD and CV) for a one-day intake, the variances of the individual foods must be summed. The exercise was carried out first in a simulation exercise with 1,000 iterations and then by the statistical formula. The results were in very close agreement. For simplicity, table 6 presents the results of application of the above equation only for diets HW1 and HW2. The assumed error term in food-intake estimation had a CV of 10 per cent of the reported intake of the food item.
As was done above, this model can be generalized to illustrate the principles involved (table 7). To extend this to a one-day intake, it was assumed that all foods made an equal contribution to the one-day intake and that the diet contained 15 foods. Table 8 then presents the estimate of the variability that would be associated with the estimate of one-day intake.
If the data in table 8 are compared with the line in table 5 portraying the impact of food composition variation in a diet containing 15 foods, the impact of the additional source of error in the estimation of food intake can be seen. Thus, for example, if the composition variability is taken as 20 per cent and the intake error as 0 (table 5), the variation term in the one-day intake is 5.2 per cent. If an error term of 10 per cent CV in the intake estimation is now added (table 8), the one-day intake estimate has a variability of 5.8 per cent. The addition of the second errot term has only relatively small impact!