In the United States 52,404 people died a of drug overdose in 2015. By some estimates, the number of deaths may have increased by up to 19% in 2016, implying just over 59,000 drug overdose deaths.To put these numbers in perspective, something like 32,000 people were killed by guns, and about 38,000 were killed in auto accidents in 2015. The majority of these drug overdose deaths are being blamed on opiates - specifically heroin, prescription painkillers, and synthetic opiates. Synthetic opiates especially are causing consternation among public health officials. For instance, use of the fentanyl analog drug carfentanil (which has been used as an elephant tranquilizer) is responsible for a string of deaths in Detroit.

While I'm not a fan of the term "epidemic", many people are beginning to realize that this is a bona fide public health crisis. What shocks me about this crisis isn't necessarily the raw numbers, but the concentration of deaths, and the rapidity of the increase. To explore where this crisis has affected the nation most heavily, I utilized the CDC-WONDER Multiple Cause of Death data set. This data represents a compilation of the causes of deaths reported on individual death certificates. When we aggregate these by year and state, and filter by death type, we can observe trends in types of death over time.

### A Handful of States

Opiate Drug Overdose Deaths per 100,000 (1999 - 2015)

### Bayesian Structural Time Series

It's clear from looking at the state-by-state charts that the overall trend of opiate drug overdoses is increasing across the United States. However, much of this increase is clustered in a few states. Places like Connecticut, Kentucky, Main, Massachusetts, Ohio, Rhode Island, and West Virginia all saw double-digit increases from 2010 to 2015. Other places saw pretty stable or deceasing trends during the same time. While there's a number of ways we can approach the analysis, an interesting method is using **Bayesian Structural Time Series **models.

Bayesian structural time series models represent a general family of models which can be used to predict future values (forecasting), estimate current values (nowcasting), or provide estimates of coefficients (such as the impact of an advertising campaign). In many cases, Bayesian structural time series models operate similar to traditional time-series models (like exponential smoothing, ARMA and ARIMA models, etc...). However, they are a great deal more flexible and have fewer assumptions than their classical counterparts.In short, these models are constructed of two components: an *observation* *equation*** **which links the observed data to an unobserved latent state, and a *transition* equation which defines how the latent state evolves over time (Scott & Varian, 2013). I wont get too much into the complexities of these models, but I will elaborate a bit on how I fit this one.

Using the 'bsts' package in R I fit individual models to each state, with each year as a time point. For the state space portion of the model I fit a local linear trend. This assumes that both the mean and slope of the trend follow a random walk. The value of the both the mean and the linear trend component are estimated directly from the data. After I was satisfied with the fit to the observed data, I created predictions based on these models for what the change in opiate overdose deaths might look like in 2016.Below are the results from each of the predictions (note: some states are missing because of insufficient data).

### Predicted Percent Increase Percent Change (2015 - 2016)

The first table shows the estimated percent change in opiate drug overdose deaths from 2015 to 2016. The points represent the average estimate, while the lines represent 80% prediction intervals. The second set of tables display the actual number of deaths as points, with the 80 and 95% prediction intervals from the model as dark blue and light blue respectively. The purple points and shaded area represent the predicted number of deaths for 2016 and 2017.

### The Takeaway

The models suggest a few things about the predicted change in deaths from 2015 to 2016. First, it appears that the number of deaths in most states are predicted to increase - however this varies a lot within and between states.A lot of the states are hovering around zero, which means they might be expected to increase a bit, or decrease a bit. On the other hand, several states are predicted to increase quite a lot. While Maine, New Hampshire, Massachusetts, Connecticut, Ohio, and Kansas are expected to see double-digit increases in 2016, some of the predictions are quite wide. Indeed - looking at Kansas, the 80% prediction intervals suggest the number of deaths could be as high as 33% or as low as -10%. Some of the more well-behaved like Ohio have much smaller prediction intervals.

Overall, the models suggest that drugs deaths may have increased by as much as 16% overall in the United States. There are a few caveats here - first, my models are missing about 10 states where I couldn't get reliable information. Second, the model I fit is very naive - it doesn't account for time-varying variables which might be expected to be predictive of drug overdose deaths (like the number of drug sold, prevalence of chronic pain conditions, etc...). However, this model seems to square up with a New York Times investigation that suggests a 19% increase.

In practical terms, what does this all mean? At the very least, it suggests that the worst of the opiate drug overdose crisis is not yet behind us. With the number of people dying from these dangerous drugs increasing every year, public health officials should begin looking at evidence-based practices to help stem this tide.