Comparing four methods to estimate usual intake distributions

The aim of this paper was to compare methods to estimate usual intake distributions of nutrients and foods. As 'true' usual intake distributions are not known in practice, the comparison was carried out through a simulation study, as well as empirically, by application to data from the European Food Consumption Validation (EFCOVAL) Study in which two 24-h dietary recalls (24-HDRs) and food frequency data were collected. The methods being compared were the Iowa State University Method (ISU), National Cancer Institute Method (NCI), Multiple Source Method (MSM) and Statistical Program for Age-adjusted Dietary Assessment (SPADE).

Simulation data were constructed with varying numbers of subjects (n), different values for the Box-Cox transformation parameter (λ(BC)) and different values for the ratio of the within- and between-person variance (r(var)). All data were analyzed with the four different methods and the estimated usual mean intake and selected percentiles were obtained. Moreover, the 2-day within-person mean was estimated as an additional 'method'. These five methods were compared in terms of the mean bias, which was calculated as the mean of the differences between the estimated value and the known true value. The application of data from the EFCOVAL Project included calculations of nutrients (that is, protein, potassium, protein density) and foods (that is, vegetables, fruit and fish).

Overall, the mean bias of the ISU, NCI, MSM and SPADE Methods was small. However, for all methods, the mean bias and the variation of the bias increased with smaller sample size, higher variance ratios and with more pronounced departures from normality. Serious mean bias (especially in the 95th percentile) was seen using the NCI Method when r(var) = 9, λ(BC) = 0 and n = 1000. The ISU Method and MSM showed a somewhat higher s.d. of the bias compared with NCI and SPADE Methods, indicating a larger method uncertainty. Furthermore, whereas the ISU, NCI and SPADE Methods produced unimodal density functions by definition, MSM produced distributions with 'peaks', when sample size was small, because of the fact that the population's usual intake distribution was based on estimated individual usual intakes. The application to the EFCOVAL data showed that all estimates of the percentiles and mean were within 5% of each other for the three nutrients analyzed. For vegetables, fruit and fish, the differences were larger than that for nutrients, but overall the sample mean was estimated reasonably.

The four methods that were compared seem to provide good estimates of the usual intake distribution of nutrients. Nevertheless, care needs to be taken when a nutrient has a high within-person variation or has a highly skewed distribution, and when the sample size is small. As the methods offer different features, practical reasons may exist to prefer one method over the other.