Dietary assessment and estimation of intake densities

The U.S. government has conducted nationwide food consumption surveys since 1936. Information obtained from these surveys is used to design food assistance programs, guide food and nutrition policy, and monitor the dietary status of the population. The distribution of usual intakes of a nutrient in the population is of interest to policy makers. Here, usual intake is deened as the long-run average intake of a nutrient by an individual. Usual intakes are not observable in practice. Instead, we observe daily intakes for a sample of individuals and a small number of days, and assume that observed intakes measure usual intakes with error. The distributions of observed intakes, however, are typically very skewed, and the day-today variability in intakes tends to be large relative to the between-individual variance, and can be heterogeneous across individuals (Nusser, Carriquiry, Dodd, and Fuller, 1996). In this paper, we present a Bayesian approach to estimating the distribution of usual intakes of a nutrient in a population. Starting with a sample of dietary intakes, we model a function to map the intakes into the normal scale. This function combines a power transformation and a cubic spline (constrained to be monotonic) with unknown number and location of knots, and is estimated using reversible jump Markov chain Monte Carlo methods (Green, 1995). From each \draw" of the transformation function we obtain a transformed set of intakes which are approximately normally distributed. We then remove the day-today variability in daily intakes by tting a measurement error model to each set of transformed observations. Each set of estimated individual usual intakes is then mapped back to the original scale using the inverse of the transformation function. Posterior distributions of percentiles and other attributes of the density for each nutrient are estimated accounting for all major sources of uncertainty. We apply these methods to a subset of the 1994-1996 Continuing Survey of Food Intakes by Individuals (CSFII) collected by the USDA (USDA, 1997).