Multidimensional Tensor Scan for Drug Overdose Surveillance
Authors: Neill Daniel 
Published: May 2017

ObjectiveWe present the multidimensional tensor scan (MDTS), a newmethod for identifying emerging patterns in multidimensionalspatio-temporal data, and demonstrate the utility of this approachfor discovering emerging geographic, demographic, and behavioraltrends in fatal drug overdoses.IntroductionDrug overdoses are an increasingly serious problem in the UnitedStates and worldwide. The CDC estimates that 47,055 drug overdosedeaths occurred in the United States in 2014, 61% of which involvedopioids (including heroin, pain relievers such as oxycodone, andsynthetics).1Overdose deaths involving opioids increased 3-foldfrom 2000 to 2014.1These statistics motivate public health to identifyemerging trends in overdoses, including geographic, demographic,and behavioral patterns (e.g., which combinations of drugs areinvolved). Early detection can inform prevention and response efforts,as well as quantifying the effects of drug legislation and other policychanges.The fast subset scan2detects significant spatial patterns of diseaseby efficiently maximizing a log-likelihood ratio statistic over subsetsof data points, and has recently been extended to multidimensionaldata (MD-Scan).3While MD-Scan is a potentially useful tool for drugoverdose surveillance, the high dimensionality and sparsity of the datarequires a new approach to estimate and represent baselines (expectedcounts), maintaining both accuracy and efficient computation whensearching over subsets.MethodsThe multidimensional tensor scan (MDTS) is a new approach tosubset scanning in multidimensional data. In addition to detectingthe spatial area (subset of locations) and time window affected byan emerging outbreak, MDTS can also identify the affected subsetof values for each observed attribute. For example, given the drugoverdose surveillance data described below, MDTS can identify theaffected genders, races, age ranges, and which drugs were involved.MDTS finds subsets of the attribute space with higher than expectedcase counts, first using a novel tensor decomposition approachto estimate the expected counts. MDTS then iteratively applies aconditional optimization step, optimizing over all subsets of valuesfor each attribute conditional on the current subsets of values for allother attributes3, and using the linear-time subset scanning property2to make each conditional optimization step computationally efficient.The resulting approach has high power to detect and characterizeemerging trends which may only affect a subset of the monitoredpopulation (e.g., specific ages, genders, neighborhoods, or users ofparticular combinations of drugs).ResultsWe used MDTS to analyze publicly available data from theAllegheny County, PA medical examiner’s office and to detectemerging overdose patterns and trends. The dataset consists of~2000 fatal accidental drug overdoses between 2008 and 2015.For each overdose victim, we have date, location (zip code), agedecile, gender, race, and the presence/absence of 27 commonlyabused drugs in their system. The highest-scoring clusters discoveredby MDTS were shared with Allegheny County’s Dept. of HumanServices and their feedback obtained.One set of potentially relevant findings from our analysisinvolved fentanyl, a dangerous and potent opioid which has been aserious problem in western PA. In addition to identifying two well-known, large clusters of overdoses—14 deaths in January 2014 and26 deaths in March-April 2015—MDTS was able to provide additionalinformation about each cluster. For example, the first cluster waslikely due to fentanyl-laced heroin, while the second was more likelydue to fentanyl disguised as heroin (only 11 victims had heroin intheir system). Moreover, the second cluster was initially confinedto the Pittsburgh suburb of McKeesport and a typical demographic(white males ages 20-49), before spreading across the county. Ouranalysis demonstrated that prospective surveillance using MDTSwould have identified the cluster as early as March 29th, enablingtargeted prevention efforts. MDTS also discovered a previouslyunidentified, highly localized cluster of fentanyl-related overdosesaffecting an unusual and underserved demographic (elderly blackmales near downtown Pittsburgh). This cluster occurred in January-February 2015, and may have been related to the larger cluster offentanyl-related overdoses that occurred two months later. Finally,we identified multiple overdose clusters involving combinationsof methadone and Xanax between 2008 and 2012, and observeddramatic reductions in these clusters corresponding to the passageof the Methadone Death and Incident Review Act (October 2012),which increased state oversight of methadone clinics and prescribingphysicians.ConclusionsRetrospective analysis of Allegheny County overdose datasuggests high potential utility for a prospective overdose surveillancesystem, which would enable public health users to identify emergingpatterns of overdoses in their early stages and facilitate targeted andeffective health interventions. The MDTS approach can also be usedfor other multidimensional public health surveillance tasks, such asSTI surveillance, where the patterns or outbreaks of interest may havedemographic, geographic, and behavioral components.