title: Wastewater-Based Epidemiology of Stimulant Drugs: Functional Data Analysis Compared to Traditional Statistical Methods.
abstract: BACKGROUND
  Wastewater-based epidemiology (WBE) is a new methodology for estimating the drug load in a population. Simple summary statistics and specification tests have typically been used to analyze WBE data, comparing differences between weekday and weekend loads. Such standard statistical methods may, however, overlook important nuanced information in the data. In this study, we apply functional data analysis (FDA) to WBE data and compare the results to those obtained from more traditional summary measures.
  
  
  METHODS
  We analysed temporal WBE data from 42 European cities, using sewage samples collected daily for one week in March 2013. For each city, the main temporal features of two selected drugs were extracted using functional principal component (FPC) analysis, along with simpler measures such as the area under the curve (AUC). The individual cities' scores on each of the temporal FPCs were then used as outcome variables in multiple linear regression analysis with various city and country characteristics as predictors. The results were compared to those of functional analysis of variance (FANOVA).
  
  
  RESULTS
  The three first FPCs explained more than 99% of the temporal variation. The first component (FPC1) represented the level of the drug load, while the second and third temporal components represented the level and the timing of a weekend peak. AUC was highly correlated with FPC1, but other temporal characteristic were not captured by the simple summary measures. FANOVA was less flexible than the FPCA-based regression, and even showed concordance results. Geographical location was the main predictor for the general level of the drug load.
  
  
  CONCLUSIONS
  FDA of WBE data extracts more detailed information about drug load patterns during the week which are not identified by more traditional statistical methods. Results also suggest that regression based on FPC results is a valuable addition to FANOVA for estimating associations between temporal patterns and covariate information.
authors.affiliation: Norwegian Centre for Addiction Research, University of Oslo, Oslo, Norway.
authors.forename: Stefania
authors.initials: S
authors.lastname: Salvatore
authors.affiliation: Norwegian Centre for Addiction Research, University of Oslo, Oslo, Norway.
authors.forename: Jørgen Gustav
authors.initials: JG
authors.lastname: Bramness
authors.affiliation: Norwegian Institute for Water Research, Oslo, Norway.
authors.forename: Malcolm J
authors.initials: MJ
authors.lastname: Reid
authors.affiliation: Norwegian Institute for Water Research, Oslo, Norway.
authors.forename: Kevin Victor
authors.initials: KV
authors.lastname: Thomas
authors.affiliation: Norwegian Institute for Water Research, Oslo, Norway.
authors.forename: Christopher
authors.initials: C
authors.lastname: Harman
authors.affiliation: Norwegian Centre for Addiction Research, University of Oslo, Oslo, Norway; Department of Biostatistics, Institute of Basic Medical Sciences, Oslo, Norway.
authors.forename: Jo
authors.initials: J
authors.lastname: Røislien
mesh_terms: D000661:Amphetamine / Q000032:analysis; D002947:Cities; D004784:Environmental Monitoring / Q000379:methods; D062665:Epidemiological Monitoring; D005060:Europe / Q000453:epidemiology; D006801:Humans; D013287:Illicit Drugs / Q000032:analysis*; D016014:Linear Models; D018817:N-Methyl-3,4-methylenedioxyamphetamine / Q000032:analysis; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012722:Sewage / Q000737:chemistry; D015813:Substance Abuse Detection / Q000379:methods*; D019966:Substance-Related Disorders / Q000453:epidemiology*; D062065:Wastewater / Q000737:chemistry*; D014874:Water Pollutants, Chemical / Q000032:analysis*
chemical_list: D000661:Amphetamine; D013287:Illicit Drugs; D018817:N-Methyl-3,4-methylenedioxyamphetamine; D012722:Sewage; D062065:Wastewater; D014874:Water Pollutants, Chemical