TY - JOUR AU - Neill, Daniel PY - 2017/05/02 Y2 - 2024/03/28 TI - Multidimensional Tensor Scan for Drug Overdose Surveillance JF - Online Journal of Public Health Informatics JA - OJPHI VL - 9 IS - 1 SE - Novel algorithms, statistical or mathematical methods DO - 10.5210/ojphi.v9i1.7598 UR - https://ojphi.org/ojs/index.php/ojphi/article/view/7598 SP - AB - <div style="left: 90px; top: 280.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08129);" data-canvas-width="63.778333333333336">Objective</div><div style="left: 105px; top: 295.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.998616);" data-canvas-width="381.00541666666646">We present the multidimensional tensor scan (MDTS), a new</div><div style="left: 90px; top: 312.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04936);" data-canvas-width="397.63566666666674">method for identifying emerging patterns in multidimensional</div><div style="left: 90px; top: 329.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.97722);" data-canvas-width="395.44833333333315">spatio-temporal data, and demonstrate the utility of this approach</div><div style="left: 90px; top: 345.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02557);" data-canvas-width="394.48499999999933">for discovering emerging geographic, demographic, and behavioral</div><div style="left: 90px; top: 362.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00077);" data-canvas-width="171.14749999999998">trends in fatal drug overdoses.</div><div style="left: 90px; top: 390.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.11768);" data-canvas-width="82.63416666666666">Introduction</div><div style="left: 105px; top: 405.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01012);" data-canvas-width="378.88041666666675">Drug overdoses are an increasingly serious problem in the United</div><div style="left: 90px; top: 422.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.996605);" data-canvas-width="393.3601666666666">States and worldwide. The CDC estimates that 47,055 drug overdose</div><div style="left: 90px; top: 439.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.999759);" data-canvas-width="393.5216666666667">deaths occurred in the United States in 2014, 61% of which involved</div><div style="left: 90px; top: 455.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.988683);" data-canvas-width="395.8520833333332">opioids (including heroin, pain relievers such as oxycodone, and</div><div style="left: 90px; top: 472.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03551);" data-canvas-width="67.13583333333332">synthetics).</div><div style="left: 157.097px; top: 472.751px; font-size: 8.5px; font-family: serif;">1</div><div style="left: 161.456px; top: 472.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00196);" data-canvas-width="324.6858333333335">Overdose deaths involving opioids increased 3-fold</div><div style="left: 90px; top: 489.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.985155);" data-canvas-width="107.74316666666665">from 2000 to 2014.</div><div style="left: 197.689px; top: 489.417px; font-size: 8.5px; font-family: serif;">1</div><div style="left: 201.936px; top: 489.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.98481);" data-canvas-width="281.1304166666665">These statistics motivate public health to identify</div><div style="left: 90px; top: 505.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.972027);" data-canvas-width="394.6266666666666">emerging trends in overdoses, including geographic, demographic,</div><div style="left: 90px; top: 522.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01988);" data-canvas-width="396.66525">and behavioral patterns (e.g., which combinations of drugs are</div><div style="left: 90px; top: 539.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.979746);" data-canvas-width="392.97625">involved). Early detection can inform prevention and response efforts,</div><div style="left: 90px; top: 555.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00373);" data-canvas-width="393.6619166666667">as well as quantifying the effects of drug legislation and other policy</div><div style="left: 90px; top: 572.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00148);" data-canvas-width="49.1725">changes.</div><div style="left: 105px; top: 589.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00734);" data-canvas-width="114.41708333333332">The fast subset scan</div><div style="left: 219.406px; top: 589.417px; font-size: 8.5px; font-family: serif;">2</div><div style="left: 223.656px; top: 589.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01013);" data-canvas-width="260.14250000000004">detects significant spatial patterns of disease</div><div style="left: 90px; top: 605.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00177);" data-canvas-width="393.5103333333333">by efficiently maximizing a log-likelihood ratio statistic over subsets</div><div style="left: 90px; top: 622.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03362);" data-canvas-width="394.5827500000002">of data points, and has recently been extended to multidimensional</div><div style="left: 90px; top: 639.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.992808);" data-canvas-width="94.44916666666663">data (MD-Scan).</div><div style="left: 184.4px; top: 639.417px; font-size: 8.5px; font-family: serif;">3</div><div style="left: 188.639px; top: 639.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.980185);" data-canvas-width="294.49666666666644">While MD-Scan is a potentially useful tool for drug</div><div style="left: 90px; top: 655.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.977273);" data-canvas-width="393.10799999999995">overdose surveillance, the high dimensionality and sparsity of the data</div><div style="left: 90px; top: 672.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.98252);" data-canvas-width="393.13916666666677">requires a new approach to estimate and represent baselines (expected</div><div style="left: 90px; top: 689.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02531);" data-canvas-width="394.57283333333316">counts), maintaining both accuracy and efficient computation when</div><div style="left: 90px; top: 705.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00087);" data-canvas-width="131.01333333333332">searching over subsets.</div><div style="left: 90px; top: 737.425px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.07287);" data-canvas-width="58.23916666666666">Methods</div><div style="left: 105px; top: 752.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03383);" data-canvas-width="379.6241666666667">The multidimensional tensor scan (MDTS) is a new approach to</div><div style="left: 90px; top: 769.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.967761);" data-canvas-width="394.7173333333333">subset scanning in multidimensional data. In addition to detecting</div><div style="left: 90px; top: 785.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.953435);" data-canvas-width="394.9921666666665">the spatial area (subset of locations) and time window affected by</div><div style="left: 90px; top: 802.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04199);" data-canvas-width="394.8108333333331">an emerging outbreak, MDTS can also identify the affected subset</div><div style="left: 90px; top: 819.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.948662);" data-canvas-width="394.75416666666666">of values for each observed attribute. For example, given the drug</div><div style="left: 90px; top: 835.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01942);" data-canvas-width="394.26116666666667">overdose surveillance data described below, MDTS can identify the</div><div style="left: 90px; top: 852.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01562);" data-canvas-width="394.1095833333333">affected genders, races, age ranges, and which drugs were involved.</div><div style="left: 90px; top: 869.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00864);" data-canvas-width="393.7724166666666">MDTS finds subsets of the attribute space with higher than expected</div><div style="left: 90px; top: 885.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01983);" data-canvas-width="396.59441666666646">case counts, first using a novel tensor decomposition approach</div><div style="left: 90px; top: 902.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.977533);" data-canvas-width="395.55883333333315">to estimate the expected counts. MDTS then iteratively applies a</div><div style="left: 90px; top: 919.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0293);" data-canvas-width="394.22149999999993">conditional optimization step, optimizing over all subsets of values</div><div style="left: 90px; top: 935.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01865);" data-canvas-width="394.09966666666674">for each attribute conditional on the current subsets of values for all</div><div style="left: 90px; top: 952.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00595);" data-canvas-width="85.8075">other attributes</div><div style="left: 175.795px; top: 952.751px; font-size: 8.5px; font-family: serif;">3</div><div style="left: 180.045px; top: 952.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01195);" data-canvas-width="295.7079166666667">, and using the linear-time subset scanning property</div><div style="left: 475.75px; top: 952.751px; font-size: 8.5px; font-family: serif;">2</div><div style="left: 90px; top: 969.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.992972);" data-canvas-width="393.1009166666666">to make each conditional optimization step computationally efficient.</div><div style="left: 90px; top: 985.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.970298);" data-canvas-width="395.2669999999999">The resulting approach has high power to detect and characterize</div><div style="left: 90px; top: 1002.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.961706);" data-canvas-width="395.16499999999996">emerging trends which may only affect a subset of the monitored</div><div style="left: 90px; top: 1019.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03599);" data-canvas-width="394.6762499999999">population (e.g., specific ages, genders, neighborhoods, or users of</div><div style="left: 90px; top: 1035.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00075);" data-canvas-width="192.79416666666665">particular combinations of drugs).</div><div style="left: 90px; top: 1067.42px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08488);" data-canvas-width="51.17">Results</div><div style="left: 105px; top: 1082.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01808);" data-canvas-width="381.67691666666656">We used MDTS to analyze publicly available data from the</div><div style="left: 90px; top: 1099.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02);" data-canvas-width="396.5575833333331">Allegheny County, PA medical examiner’s office and to detect</div><div style="left: 90px; top: 1115.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01839);" data-canvas-width="396.59441666666646">emerging overdose patterns and trends. The dataset consists of</div><div style="left: 90px; top: 1132.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00917);" data-canvas-width="396.2671666666663">~2000 fatal accidental drug overdoses between 2008 and 2015.</div><div style="left: 90px; top: 1149.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.971495);" data-canvas-width="395.44691666666654">For each overdose victim, we have date, location (zip code), age</div><div style="left: 90px; top: 1165.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00966);" data-canvas-width="396.05749999999995">decile, gender, race, and the presence/absence of 27 commonly</div><div style="left: 90px; top: 1182.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.992179);" data-canvas-width="393.16749999999973">abused drugs in their system. The highest-scoring clusters discovered</div><div style="left: 90px; top: 1199.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.966837);" data-canvas-width="395.06583333333333">by MDTS were shared with Allegheny County’s Dept. of Human</div><div style="left: 90px; top: 1215.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00085);" data-canvas-width="212.04666666666674">Services and their feedback obtained.</div><div style="left: 525px; top: 279.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.06787);" data-canvas-width="383.06383333333326">One set of potentially relevant findings from our analysis</div><div style="left: 510px; top: 295.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03384);" data-canvas-width="394.23708333333326">involved fentanyl, a dangerous and potent opioid which has been a</div><div style="left: 510px; top: 312.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02701);" data-canvas-width="390.0239166666667">serious problem in western PA. In addition to identifying two well-</div><div style="left: 510px; top: 329.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02321);" data-canvas-width="394.41274999999985">known, large clusters of overdoses—14 deaths in January 2014 and</div><div style="left: 510px; top: 345.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.96595);" data-canvas-width="392.75525000000005">26 deaths in March-April 2015—MDTS was able to provide additional</div><div style="left: 510px; top: 362.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.973802);" data-canvas-width="395.21741666666657">information about each cluster. For example, the first cluster was</div><div style="left: 510px; top: 379.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.996757);" data-canvas-width="393.4366666666667">likely due to fentanyl-laced heroin, while the second was more likely</div><div style="left: 510px; top: 395.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.945712);" data-canvas-width="394.59833333333313">due to fentanyl disguised as heroin (only 11 victims had heroin in</div><div style="left: 510px; top: 412.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.974976);" data-canvas-width="395.15791666666655">their system). Moreover, the second cluster was initially confined</div><div style="left: 510px; top: 429.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03429);" data-canvas-width="394.2555">to the Pittsburgh suburb of McKeesport and a typical demographic</div><div style="left: 510px; top: 445.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04447);" data-canvas-width="394.8108333333334">(white males ages 20-49), before spreading across the county. Our</div><div style="left: 510px; top: 462.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.997804);" data-canvas-width="395.4794999999998">analysis demonstrated that prospective surveillance using MDTS</div><div style="left: 510px; top: 479.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.951312);" data-canvas-width="394.6833333333331">would have identified the cluster as early as March 29th, enabling</div><div style="left: 510px; top: 495.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01018);" data-canvas-width="396.3266666666664">targeted prevention efforts. MDTS also discovered a previously</div><div style="left: 510px; top: 512.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.978293);" data-canvas-width="395.06724999999994">unidentified, highly localized cluster of fentanyl-related overdoses</div><div style="left: 510px; top: 529.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.982303);" data-canvas-width="395.3279166666666">affecting an unusual and underserved demographic (elderly black</div><div style="left: 510px; top: 545.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01585);" data-canvas-width="390.00266666666664">males near downtown Pittsburgh). This cluster occurred in January-</div><div style="left: 510px; top: 562.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.950556);" data-canvas-width="394.9241666666668">February 2015, and may have been related to the larger cluster of</div><div style="left: 510px; top: 579.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04226);" data-canvas-width="394.825">fentanyl-related overdoses that occurred two months later. Finally,</div><div style="left: 510px; top: 595.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01096);" data-canvas-width="395.9753333333333">we identified multiple overdose clusters involving combinations</div><div style="left: 510px; top: 612.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.984853);" data-canvas-width="395.45116666666667">of methadone and Xanax between 2008 and 2012, and observed</div><div style="left: 510px; top: 629.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.965608);" data-canvas-width="394.949666666667">dramatic reductions in these clusters corresponding to the passage</div><div style="left: 510px; top: 645.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0405);" data-canvas-width="394.7669166666665">of the Methadone Death and Incident Review Act (October 2012),</div><div style="left: 510px; top: 662.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.999879);" data-canvas-width="393.53583333333336">which increased state oversight of methadone clinics and prescribing</div><div style="left: 510px; top: 679.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00084);" data-canvas-width="63.35333333333332">physicians.</div><div style="left: 510px; top: 710.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.10336);" data-canvas-width="85.01416666666667">Conclusions</div><div style="left: 525px; top: 725.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.06291);" data-canvas-width="382.82299999999987">Retrospective analysis of Allegheny County overdose data</div><div style="left: 510px; top: 742.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.993264);" data-canvas-width="393.2496666666667">suggests high potential utility for a prospective overdose surveillance</div><div style="left: 510px; top: 759.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00276);" data-canvas-width="393.6165833333333">system, which would enable public health users to identify emerging</div><div style="left: 510px; top: 775.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01621);" data-canvas-width="394.05291666666653">patterns of overdoses in their early stages and facilitate targeted and</div><div style="left: 510px; top: 792.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00519);" data-canvas-width="393.69875">effective health interventions. The MDTS approach can also be used</div><div style="left: 510px; top: 809.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02637);" data-canvas-width="394.6564166666667">for other multidimensional public health surveillance tasks, such as</div><div style="left: 510px; top: 825.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.981276);" data-canvas-width="392.77225">STI surveillance, where the patterns or outbreaks of interest may have</div><div style="left: 510px; top: 842.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00082);" data-canvas-width="310.41999999999996">demographic, geographic, and behavioral components.</div> ER -