Functional data arise in many fields of medical research, with examples from studies of growth patterns, gait, melanoma incidence rates, CD4 counts and many others. Indeed, any set of measurements gathered over time (or space), including time dependent covariates in survival analysis, may be thought of as functional data. There are many advantages to viewing such data as functions rather than disconnected points, perhaps the most important being the ability to routinely include derivative information into the analysis. Historically, functional data has been analyzed using multivariate or time series methods, but these methods are weak for irregularly spaced data or data measured at different times for different subjects. Recent advances make it possible to analyze such data as functions. Here we propose to implement an S-Plus module for functional data analysis. The module will be a commercial implementation of the exploratory methods developed by Ramsay and Silverman (1997), with extensions to adaptive regression splines and local polynomial kernel based smoothers. We also plan to extend the methodology to include generalized linear models and survival analysis models. The new module will seamlessly integrate functional data analysis methods into the S-Plus.
As computers become integrated into daily life, the ability of researchers to collect functional data is becoming more common. There are currently no commercial products available for handling functional data. The proposed methods have significant advantages over existing techniques. A well designed and comprehensive module for implementing these models will find a ready market.
