Multidimensional Tensor Scan for Drug Overdose Surveillance

Introduction Drug overdoses are an increasingly serious problem in the United States and worldwide. The CDC estimates that 47,055 drug overdose deaths occurred in the United States in 2014, 61% of which involved opioids (including heroin, pain relievers such as oxycodone, and synthetics).1 Overdose deaths involving opioids increased 3-fold from 2000 to 2014.1 These statistics motivate public health to identify emerging trends in overdoses, including geographic, demographic, and behavioral patterns (e.g., which combinations of drugs are involved). Early detection can inform prevention and response efforts, as well as quantifying the effects of drug legislation and other policy changes. The fast subset scan2 detects significant spatial patterns of disease by efficiently maximizing a log-likelihood ratio statistic over subsets of data points, and has recently been extended to multidimensional data (MD-Scan).3 While MD-Scan is a potentially useful tool for drug overdose surveillance, the high dimensionality and sparsity of the data requires a new approach to estimate and represent baselines (expected counts), maintaining both accuracy and efficient computation when searching over subsets.