The CDC have just updated their annual report "Drug Overdose Deaths in the United States, 1999-2017". The average age-adjusted rate in 2017 is almost 22 per 100,000; up 10% on the 2016 figures. Some individual states are well above these numbers: the highest death rates are in West Virginia (58 per 100,000), Ohio (46), Pennsylvania (44) and District of Columbia (44).
What does this look like at the county level? The CDC make the Detailed Mortality Files—on which the above report is based—available through WONDER, the Wide-ranging OnLine Data for Epidemiologic Research. Unfortunately this has not been updated with the 2017 numbers, so a county-level analysis can only go through to 2016.
The counties with the highest death rates are shown below (click to enlarge).
As a New Mexico resident I am not surprised that Rio Arriba is at the top. Its largest town, Española, has been identified as a "drug capital of America" for a decade or more (for example, see this Forbes article from 2009). The West Virginia counties are not surprising either, given the state figures.
But the figures that really shock me are those for the counties in Maryland and Ohio. Yes, the rates are somewhat lower (though still north of 50 per 100,000) but the populations of these counties are much higher than you see in counties in NM and WV. The numbers of deaths in Baltimore, Montgomery, Butler, and Clermont Counties are—to my eyes—startlingly high.
This raises the question of how to measure "worst". Is it death rate (i.e. deaths per 100,000 population), deaths, or some combination? Although the use of rate has a mathematical appeal, I think it carries an inherent assumption that may not be correct. Specifically, that if county A has 10 times the population of county B, the threshold at which local services get overloaded is also 10 times higher in A than it is in B. I suspect (though I don't have evidence for this) that this is not the case and that the threshold in A would be substantially less than 10 times the threshold in B.
Note: The R code for the above plots and a discussion of assumptions is available here.