Mathematical Modeling in Experimental Nutrition

Carroll, R J, Freedman, L S, Kipnis, V, Carroll, Raymond J., Freedman, Laurence S., Kipnis, Victor

This chapter reviews work of Carroll, Freedman, Kipnis, and Li (1998) on the statistical analysis of the relationship between dietary intake and health outcomes. In the area of nutritional epidemiology, there is some evidence from biomarker studies that the usual statistical model for dietary measurements may break down due to two causes: (a) systematic biases depending on a person's body mass index; and (b) an additional random component of bias, so that the error structure is the same as a one-way random effects model. We investigate this problem, in the context of (1) the estimation of the distribution of usual nutrient intake; (2) estimating the correlation between a nutrient instrument and usual nutrient intake; and (3) estimating the true relative risk from an estimated relative risk using the error-prone covariate. While systematic bias due to body mass index appears to have little effect, the additional random effect in the variance structure is shown to have a potentially important impact on overall results, both on corrections for relative risk estimates and in estimating the distribution usual of nutrient intake. Our results point to a need for new experiments aimed at estimation of a crucial parameter.