Statistical Approaches to Analyzing Energy Expenditure Data Among Zucker Diabetic Fatty Rats.

Obesity is widely becoming a worldwide epidemic and often results from a combination of a sedentary lifestyle, inadequate food intake, and genetic predisposition. It is often of interest to scientists studying this epidemic to assess how much physical activity the study participants partake in or the amount of energy expenditure expended within a given time period. Energy expenditure is often used for this purpose where the study participants are subjected to devices which measure the amount of energy expended frequently within a specified time period. For example, in studying obesity among Zucker diabetic fatty (ZDF) rats, an animal model often used for studying obesity and the onset of diabetes, energy expenditure can be assessed by the use of an Oxymas instrument (an open circuit calorimeter; Columbus Instruments, Ohio, USA), a device which measures various components of energy expenditure every five to ten minutes.

The resulting data are often of the functional longitudinal form and several statistical techniques can be employed to analyze such data. In this paper, we apply various statistical approaches to analyze the energy expenditure data from the ZDF rats; we compare statistical models based on linear mixed effects models and functional mixed effects models with smoothing splines. We find that in our current analyses, the use of the mixed effects models with a quadratic term for the time of observation following a summary of the data from minutes to hours and a log transformation to achieve approximate normality perform adequately well in assessing the effects of the treatment on the energy expenditure variables. We also find that the functional mixed effects model with a quadratic spline can be used as an effective option for analyzing the data after summarizing the data per hour without applying any transformation techniques. We therefore recommend first summarizing the energy expenditure per hour to reduce the noise associated with the frequency of the data collection and using either linear mixed effects models with polynomial terms for time or functional mixed effects model with smoothing splines to analyze the data collected repeatedly over a 24-hour period, when a curve linear relationship is suspected between time and the various energy expenditure variables.