Beware the Jaccard: the choice of similarity measure is important and non-trivial in genomic colocalisation analysis.

The generation and systematic collection of genome-wide data is ever-increasing. This vast amount of data has enabled researchers to study relations between a variety of genomic and epigenomic features, including genetic variation, gene regulation and phenotypic traits. Such relations are typically investigated by comparatively assessing genomic co-occurrence. Technically, this corresponds to assessing the similarity of pairs of genome-wide binary vectors. A variety of similarity measures have been proposed for this problem in other fields like ecology. However, while several of these measures have been employed for assessing genomic co-occurrence, their appropriateness for the genomic setting has never been investigated. We show that the choice of similarity measure may strongly influence results and propose two alternative modelling assumptions that can be used to guide this choice. On both simulated and real genomic data, the Jaccard index is strongly altered by dataset size and should be used with caution. The Forbes coefficient (fold change) and tetrachoric correlation are less influenced by dataset size, but one should be aware of increased variance for small datasets. All results on simulated and real data can be inspected and reproduced at https://hyperbrowser.uio.no/sim-measure.

The rainfall plot: its motivation, characteristics and pitfalls.

BACKGROUND: A visualization referred to as rainfall plot has recently gained popularity in genome data analysis. The plot is mostly used for illustrating the distribution of somatic cancer mutations along a reference genome, typically aiming to identify mutation hotspots. In general terms, the rainfall plot can be seen as a scatter plot showing the location of events on the x-axis versus the distance between consecutive events on the y-axis. Despite its frequent use, the motivation for applying this particular visualization and the appropriateness of its usage have never been critically addressed in detail. RESULTS: We show that the rainfall plot allows visual detection even for events occurring at high frequency over very short distances. In addition, event clustering at multiple scales may be detected as distinct horizontal bands in rainfall plots. At the same time, due to the limited size of standard figures, rainfall plots might suffer from inability to distinguish overlapping events, especially when multiple datasets are plotted in the same figure. We demonstrate the consequences of plot congestion, which results in obscured visual data interpretations. CONCLUSIONS: This work provides the first comprehensive survey of the characteristics and proper usage of rainfall plots. We find that the rainfall plot is able to convey a large amount of information without any need for parameterization or tuning. However, we also demonstrate how plot congestion and the use of a logarithmic y-axis may result in obscured visual data interpretations. To aid the productive utilization of rainfall plots, we demonstrate their characteristics and potential pitfalls using both simulated and real data, and provide a set of practical guidelines for their proper interpretation and usage.

Assessing prescription drug abuse using functional principal component analysis (FPCA) of wastewater data.

BACKGROUND: Wastewater-based epidemiology is an alternative method for estimating the collective drug use in a community. We applied functional data analysis, a statistical framework developed for analysing curve data, to investigate weekly temporal patterns in wastewater measurements of three prescription drugs with known abuse potential: methadone, oxazepam and methylphenidate, comparing them to positive and negative control drugs. METHODS: Sewage samples were collected in February 2014 from a wastewater treatment plant in Oslo, Norway. The weekly pattern of each drug was extracted by fitting of generalized additive models, using trigonometric functions to model the cyclic behaviour. From the weekly component, the main temporal features were then extracted using functional principal component analysis. Results are presented through the functional principal components (FPCs) and corresponding FPC scores. RESULTS: Clinically, the most important weekly feature of the wastewater-based epidemiology data was the second FPC, representing the difference between average midweek level and a peak during the weekend, representing possible recreational use of a drug in the weekend. Estimated scores on this FPC indicated recreational use of methylphenidate, with a high weekend peak, but not for methadone and oxazepam. CONCLUSION: The functional principal component analysis uncovered clinically important temporal features of the weekly patterns of the use of prescription drugs detected from wastewater analysis. This may be used as a post-marketing surveillance method to monitor prescription drugs with abuse potential. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Comparison of pharmaceutical, illicit drug, alcohol, nicotine and caffeine levels in wastewater with sale, seizure and consumption data for 8 European cities.

BACKGROUND: Monitoring the scale of pharmaceuticals, illicit and licit drugs consumption is important to assess the needs of law enforcement and public health, and provides more information about the different trends within different countries. Community drug use patterns are usually described by national surveys, sales and seizure data. Wastewater-based epidemiology (WBE) has been shown to be a reliable approach complementing such surveys. METHOD: This study aims to compare and correlate the consumption estimates of pharmaceuticals, illicit drugs, alcohol, nicotine and caffeine from wastewater analysis and other sources of information. Wastewater samples were collected in 2015 from 8 different European cities over a one week period, representing a population of approximately 5 million people. Published pharmaceutical sale, illicit drug seizure and alcohol, tobacco and caffeine use data were used for the comparison. RESULTS: High agreement was found between wastewater and other data sources for pharmaceuticals and cocaine, whereas amphetamines, alcohol and caffeine showed a moderate correlation. methamphetamine and 3,4-methylenedioxymethamphetamine (MDMA) and nicotine did not correlate with other sources of data. Most of the poor correlations were explained as part of the uncertainties related with the use estimates and were improved with other complementary sources of data. CONCLUSIONS: This work confirms the promising future of WBE as a complementary approach to obtain a more accurate picture of substance use situation within different communities. Our findings suggest further improvements to reduce the uncertainties associated with both sources of information in order to make the data more comparable.

Complex patterns of concomitant medication use: A study among Norwegian women using paracetamol during pregnancy.

BACKGROUND: Studies on medication safety in pregnancy often rely on an oversimplification of medication use into exposed or non-exposed, without considering intensity and timing of use in pregnancy, or concomitant medication use. This study uses paracetamol in pregnancy as the motivating example to introduce a method of clustering medication exposures longitudinally throughout pregnancy. The aim of this study was to use hierarchical cluster analysis (HCA) to better identify clusters of medication exposure throughout pregnancy. METHODS: Data from the Norwegian Mother and Child Cohort Study was used to identify subclasses of women using paracetamol during pregnancy. HCA with customized distance measure was used to identify clusters of medication exposures in pregnancy among children at 18 months. RESULTS: The pregnancies in the study (N = 9 778) were grouped in 5 different clusters depending on their medication exposure profile throughout pregnancy. CONCLUSION: Using HCA, we identified and described profiles of women exposed to different medications in combination with paracetamol during pregnancy. Identifying these clusters allows researchers to define exposure in ways that better reflects real-world medication usage patterns. This method could be extended to other medications and used as pre-analysis for identifying risks associated with different profiles of exposure.

Wastewater-Based Epidemiology of Stimulant Drugs: Functional Data Analysis Compared to Traditional Statistical Methods.

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. CONCLUSION: 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.