A SEMIPARAMETRIC TRANSFORMATION APPROACH TO ESTIMATING USUAL DAILY INTAKE DISTRIBUTIONS

The distribution of usual intakes of dietary components is important t o individuals formulating food policy and to persons designing nutriti on education programs. The usual intake of a dietary component for a p erson is the long-run average of daily intakes of that component for t hat person. Because it is impossible to directly observe usual intake for an individual, it is necessary to develop an estimator of the dist ribution of usual intakes based on a sample of individuals with a smal l number of daily observations on a subsample of the individuals. Dail y intake data for individuals are nonnegative and often very skewed. A lso, there is large day-to-day variation relative to the individual-to -individual variation, and the within-individual variance is correlate d with the individual means. We suggest a methodology for estimating u sual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with o ne-day dietary intakes. The estimation method contains four steps. Fir st, the original data are standardized by adjusting for nuisance effec ts, such as day-of-week and interview sequence. Second, the daily inta ke data are transformed to normality using a combination of power and grafted polynomial transformations. Third. using a normal components-o f-variance model, the distribution of usual intakes is constructed for the transformed data. Finally, a transformation of the normal usual i ntake distribution to the original scale is defined. The approach is a pplied to data from;he 1985 Continuing Survey of Food Intakes by Indiv iduals and works well for a set of dietary components that are consume d nearly daily and exhibit varying distributional shapes.