# Parametric and Semiparametric Approaches to Analyzing Device-Based Measures of Energy Expenditure in Zucker Diabetic Fatty Rats

## TL;DR

This paper compares statistical methods to analyze energy expenditure data in diabetic rats and finds that flexible models work best.

## Contribution

The study introduces a recommended approach using semiparametric models and data summarization for analyzing frequent energy expenditure measurements.

## Key findings

- No effect of interferon tau on energy expenditure was observed in the study.
- A B-spline semiparametric model performed best for modeling nonlinear energy expenditure patterns.
- Summarizing data into 30-60 minute epochs is recommended to reduce noise in high-dimensional energy expenditure data.

## Abstract

Obesity results from a chronic imbalance between energy intake and energy expenditure. Total energy expenditure for all physiological functions combined can be measured approximately by calorimeters. These devices assess energy expenditure frequently (e.g., in 60-second epochs), resulting in massive complex data that are nonlinear functions of time. To reduce the prevalence of obesity, researchers often design targeted therapeutic interventions to increase daily energy expenditure.

We analyzed previously collected data on the effects of oral interferon tau supplementation on energy expenditure, as assessed with indirect calorimeters, in an animal model for obesity and type 2 diabetes (Zucker diabetic fatty rats). In our statistical analyses, we compared parametric polynomial mixed effects models and more flexible semiparametric models involving spline regression.

We found no effect of interferon tau dose (0 vs. 4μg/kg body weight/day) on energy expenditure. The B-spline semiparametric model of untransformed energy expenditure with a quadratic term for time performed best in terms of the Akaike information criterion value.

To analyze the effects of interventions on energy expenditure assessed with devices that collect data at frequent intervals, we recommend first summarizing the high dimensional data into epochs of 30 to 60 minutes to reduce noise. We also recommend flexible modeling approaches to account for the nonlinear patterns in such high dimensional functional data. We provide freely available R codes in GitHub.