Inference on Ratios of Correlated Variables with Applications to Dietary Quality Assessment

• Activity Number: 478
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
• Sponsor: SPAIG Committee
• Author(s): Aiyi Liu* and Xiaoyu Cai and Zhaohai Li
• Companies: Eunice Kennedy Shriver National Institute of Child Health and Human Development and The George Washington University and The George Washington University
• Keywords: Ratio of variables ; Transformation models ; Bivariate distributions

Abstract

Ratios of correlated variables and their inferences are frequently encountered in biomedical research. For example, dietary quality measures are usually derived from ratios of the amount of food intake to the amount of energy intake per 1000 cal. Research on the exact inference of ratios of correlated variables, however, is quite limited in the literature. A few papers discuss the issues for correlated normal or gamma variates, but in reality the exact distributions of ratios of correlated variables are far more complex because the divisors and the dividends may follow quite complicated distributions. We investigate the exact distribution of the ratio under the assumption that the divisor and dividend variables follow a bivariate normal distribution after monotone transformations. We conducted numerical studies to examine the efficiency of the methods, and exemplify the methods using dietary quality data from a dietary behavior intervention trial among children with type I diabetes to promote more healthful eating. This research work was done by a graduate student under joint mentoring of NIH intramural investigator and George Washington University statistics faculty.