Functional Data Analysis in Aging Research

Abstract

Due to the advancement of modern technology, more and more data are Being recorded at a high frequency overtime. The resulting longitudinal data are a sample of curves (or functionals). For example, in a study of medflies the reproduction history (in terms of the number of eggs laid per day) of 1,000 female medflies was observed. This yields a sample of 1,000 egg laying curves. In another study, the lifetimes of medflies held in 66 cages (with about 6,000 flies per cage) under different treatment were observed. This gives a survival or hazard function for each cohort. A sample of 66 survival functions or 66 hazard functions is thus observed. When a sample of curves or functionals is observed as in the aforementioned examples, one is then faced with the problem of analyzing a sample of curve data. Such data analysis is termed Functional Data Analysis (FDA) and is often nonparametric in nature. It provides an alternative approach to longitudinal data analysis and has been of keen interest recently to many researchers. Methods for analyzing functional data will be discussed. We'll first discuss some graphical methods to display the functional data and its covariates. Then we'll present several regression models for functional data including a functional random effect model and a multiplicative effects model. Methods to estimate the components of the models will be discussed and illustrated through the egg-laying data. These data originated in studies in the area of aging research where functional data are often observed. The proposed models provide new tools to analyze such data and help to resolve several issues in aging research.