Application of functional data analysis (FDA) to weekly wastewater data

Abstract

Wastewater-based epidemiology (WBE) is a novel approach in drug use epidemiology, which may provide more objective estimates of illicit drug use in a community. Simple summary statistics and specification tests have typically been used to analyse WBE data. Such standard statistical methods may, however, overlook important nuances in the data. Functional data analysis (FDA) is a statistical framework specifically developed for analysing curves, while wavelet principal component analysis (WPCA) is a more flexible methodology for temporal data. The overall aim of this thesis was to explore the possibility and usefulness of using advanced statistical methods to WBE data, to extract more information on the weekly temporal pattern of weekly drug loads in Europe. We also compared several advanced statistical methods and investigated the possibility of using FDA to distinguish between what could be considered the proper medical use and the recreational use of prescription drugs. In all studies, the main temporal features of the selected illicit and prescription drugs were extracted using functional principal component (FPC) analysis, where the first three FPCs represented the most important temporal components. The first component (FPC1) represented the level of the drug load in wastewater, while the second and third temporal components represented the level and the timing of the weekend peak/peaks. The area under the curve (AUC) was highly correlated with FPC1, but other temporal characteristic were not captured by the simple summary measures. Among all the advanced statistical methods explored, using FPCA with Fourier basis and common-optimal smoothing was the most stable and least sensible method to missing data. Overall, these findings show that FDA of WBE data extracts more detailed information about drug load patterns during the week which are not identified by more traditional statistical methods.