New Exponential Scoring Functions for Diet Quality Indexes Solve Problems Caused by Truncation

Abstract

Abstract Background Diet quality indexes, including the Healthy Eating Index (HEI), assess diets based on usual dietary intakes and a scoring function. Nearly all diet quality indexes use scoring functions that have floors and ceilings, thereby truncating the scores and losing information about intakes outside the scoring range. This score truncation has two important impacts: 1) the index does not reflect all intakes; and 2) the assumption that measurement error in intake reporting has a neutral impact on the diet quality score cannot be upheld. Objective The main objective was to devise new diet quality scoring functions that eliminate truncation and its attendant problems. Methods Seven desirable properties of a new scoring function were identified: 1) avoid truncations in component scoring to prevent information loss and to provide scoring sensitivity in the currently truncated regions; 2) reduce dependency on the accuracy of dietary standards; 3) minimize measurement error bias and subsequent misclassification; 4) relate plausibly to biological processes; 5) possess desirable mathematical and statistical properties; 6) have simple representations which are easy to calculate and add minimum artifacts of their own; and 7) otherwise closely mimic existing scoring functions. Results The recommended replacement for piecewise-linear scoring is a family of scoring functions based on exponentials. For components where higher intakes are better, the function is a single exponential. For components where lower intakes are better, the function is a concave-convex mirrored pair of exponentials. The proposed exponential scoring functions have all seven desired properties. Conclusions The proposed exponential scoring functions will improve the usefulness of dietary scoring indexes by eliminating truncations. Compared to existing scoring functions, the use of exponentials makes the scores more inclusive of very high and very low intakes, reduces measurement error bias, and is less sensitive to the exact placement of the scoring standards.