Exploring functional data analysis and wavelet principal component analysis on ecstasy (MDMA) wastewater data

Background: Wastewater-based epidemiology (WBE) is a novel approach in drug use epidemiology which aims to monitor the extent of use of various drugs in a community. In this study, we investigate functional principal component analysis (FPCA) as a tool for analysing WBE data and compare it to traditional principal component analysis (PCA) and to wavelet principal component analysis (WPCA) which is more flexible temporally. Methods: We analysed temporal wastewater data from 42 European cities collected daily over one week in March 2013. The main temporal features of ecstasy (MDMA) were extracted using FPCA using both Fourier and B-spline basis functions with three different smoothing parameters, along with PCA and WPCA with different mother wavelets and shrinkage rules. The stability of FPCA was explored through bootstrapping and analysis of sensitivity to missing data. Results: The first three principal components (PCs), functional principal components (FPCs) and wavelet principal components (WPCs) explained 87.5-99.6 % of the temporal variation between cities, depending on the choice of basis and smoothing. The extracted temporal features from PCA, FPCA and WPCA were consistent. FPCA using Fourier basis and common-optimal smoothing was the most stable and least sensitive to missing data. Conclusion: FPCA is a flexible and analytically tractable method for analysing temporal changes in wastewater data, and is robust to missing data. WPCA did not reveal any rapid temporal changes in the data not captured by FPCA. Overall the results suggest FPCA with Fourier basis functions and common-optimal smoothing parameter as the most accurate approach when analysing WBE data.