There's a fair amount of imprecision around each number. The NEJM figure is an extrapolation from a household survey. As such, it comes with a fairly wide margin of error: the researchers are confident that the true number of fatalities is somewhere between 793 and 8,498. They report 4,645 as the top line figure because it falls exactly within the middle of the range.
The government figures, on the other hand, are not an estimate but actual data derived from death certificates and other official sources. They show that about 1,400 more people died between September and December 2017 than during the same period in 2016.
The problem here, however, is that we don't have a precise baseline: had the hurricane not hit, in other words, would deaths at the end of the year have been higher or lower than previous years?
At any rate, it's clear that the true toll of Maria is considerably higher than the 64 previously reported by Puerto Rican authorities.
Beyond that, there are a number of different ways to define a “disaster.” Some tallies include disease outbreaks such as the 1918 flu, while others include man-made catastrophes such as the Sept. 11, 2001, terrorist attacks (about 3,000 deaths, per FEMA) and the 1865 Sultana steamboat explosion (roughly 2,000).
For the purposes of the chart above, we've excluded both diseases and human-caused events to focus on what are typically considered “natural” disasters.
Hurricanes are well-represented on the list, taking up six out of 13 slots (if you consider that Maria is represented twice). The NEJM estimate would make Maria the fourth-deadliest natural disaster ever to hit the United States, following the 1900 Galveston hurricane and a pair of widespread heat waves in the 1980s.
According to the official government figures released yesterday, on the other hand, Maria would rate the 12th deadliest natural disaster, just behind Hurricane Katrina. As in Puerto Rico, the federal response to Katrina received widespread criticism for being sluggish and inadequate to the challenges posed by the storm.
According to the NEJM study, most of the post-Maria deaths resulted from “unsafe or unhealthy conditions resulting in injury, illness, or loss of necessary medical services” in the aftermath of a storm. “Interruption of medical care was the primary cause of sustained high mortality rates in the months after the hurricane,” the authors write.
The study only looked at the period up to Dec. 31, but challenging conditions have persisted long afterward. By the end of January, for instance, nearly one third of the country was still without power. That makes it possible that more hurricane-attributable fatalities have occurred well into this year.
Note: This story was updated to include newly released mortality figures from the government of Puerto Rico for the months following Hurricane Maria's landfall.