The surveyors used off-road vehicles because of the continuing threat of landslides in mountain areas. In part of Culebra, a small island off the main island of Puerto Rico, they arrived planning to interview 35 households. Only one person remained. “It was a bathroom and half a room,” said Domingo J. Marqués, an associate professor of psychology at Albizu University San Juan, who helped conduct the study with his students and who himself lacked power and running water for months after the hurricane. “All the other houses were gone.”

Those conditions, he said, made clearer why the government’s official death count was incomplete. “Even if they were really doing a good job, it was really hard unless you did something like we did — go talk to people on the ground,” he said. People, he added, “died alone in their houses. Nobody went there. Some of them were covered by a landslide, and months after they’ve not recovered the bodies.”

Notably, abnormally high death rates continued at least through the end of December. “They didn’t show any sign of coming down in the several months following the hurricane that we were looking at,” said Caroline Buckee, an associate professor of epidemiology at the Harvard School of Public Health and the study’s other senior author.

“There is clearly an excess mortality, and let’s not argue very specific numbers,” said Dr. Gilbert Burnham, a professor of international health and founder of the Center for Humanitarian Health at Johns Hopkins University, who was not involved in the research, but has performed similar studies assessing deaths, including in Mosul, Iraq.

Dr. Burnham said that despite the study’s limitations, including the difficulty of estimating Puerto Rico’s total population in light of migration, and the possible oversampling of smaller populations in more remote areas, such surveys “should become a standard activity in post-disaster situations,” because they help reveal vulnerabilities that can be addressed to save lives.

Dr. Burnham and another expert unaffiliated with the study agreed with the researchers that the toll could be even higher than estimated if adjusted for the fact that people who died alone could not be surveyed. “It just is stunning how poor our information was as to what was happening in Puerto Rico,” said Leslie Roberts, a professor and director of the program on forced migration and health at the Columbia University Mailman School of Public Health.

The use of surveys to assess the extent of deaths and suffering in disasters, and to guide improvements, extends back decades. Particularly important was a series of studies in Bangladesh in 1970 and 1971, which revealed that women died at a higher rate than men from a massive cyclone that the researchers estimated killed at least 224,000 people.