We conducted a randomized survey of 3299 households from January 17 through February 24, 2018. The target sample of approximately 3000 households was calculated to detect a 50% increase in the annual mortality rate from a historic (September 20 through December 31) baseline rate of 8 per 1000,21 with 80% power at a significance level of 0.05. To ensure sampling of households across geographic regions, we stratified the population according to remoteness, defined according to the travel time to the nearest city with a population of at least 50,000 persons.22,23 We determined an average remoteness index for each of the 900 barrios (administrative units) by using population and road-network data from official government sources.24 Barrios were grouped into eight categories according to percentile from least remote (category 1) to most remote (category 8), and 13 barrios were randomly sampled from each category (Fig. S1 in the Supplementary Appendix, available with the full text of this article at NEJM.org). We randomly sampled an additional barrio from each of the two inhabited island municipalities off the northeast coast, Vieques and Culebra, and excluded largely uninhabited barrios such as nature reserves.

We randomly selected 35 households from each barrio using OpenStreetMap (OSM) layers to identify buildings.25 When data collectors encountered an abandoned home or nonhome structure, they sampled a house from all surrounding visible houses using a random number generator. The same process was followed if consent was declined, if the house was empty at the time of the interview, or when sparsely populated barrios had fewer than 35 points sampled because of incomplete data structures on OSM. Our survey logistics did not allow for the data collectors to revisit an empty house (see the Supplementary Appendix for details).

Data collectors did not record any personal identifiers; global positioning system (GPS) coordinates were aggregated after data collection. To avoid coercion and reduce bias, no compensation was provided. The participants were informed that their responses would not result in direct benefits to them or their families. If respondents requested health services, data collectors provided information on accessible resources identified by local partners. Consent for participation was acquired before administration of the survey. This study was granted a human subjects research exemption (45CFR46) by the institutional review board of the Harvard T.H. Chan School of Public Health.

We used a hybrid census method, collecting information about each household member, including all persons who had moved in, moved out, been born, or died in 2017.26 Persons who were reported to be missing from households, but not known to be deceased, were considered to be alive for our calculations. Households were defined as a person or a group of persons, related or unrelated, who live together. The survey was administered to one adult respondent per household and took less than 10 minutes to complete. The survey instrument is provided in the Supplementary Appendix. The survey included questions on age, sex, cause of death if after the hurricane, hurricane-related migration, neighborhood deaths, and access to electricity, water, and cellular network coverage on an ordinal scale for each month (0 days, 1 to 7 days, 8 to 14, 15 to 30 days, or all month).

Survey weights (w) were constructed by calculating the inverse probability of selection of a household and were defined as

and

We used the following formulas to calculate the general population estimate:

and

where i is the household. Weights and estimates of excess deaths were constructed with the use of the most recent official population estimate in 2016.27

To estimate excess deaths, we estimated the mortality rate after the hurricane (from September 20 through December 31, 2017) and compared it with the official mortality rate for the same period in 2016, since mortality rates showed seasonal but stable trends from 2010 through 2016 (Fig. S2 in the Supplementary Appendix). Official monthly mortality data for 2016 were obtained from the Department of Health 2016 mortality data provided by the Institute of Statistics of Puerto Rico.28 We computed our rate without applying survey weights, since we observed no remoteness category–specific clustering of deaths (see the Supplementary Appendix for further discussion). The post-hurricane unweighted crude mortality rate (Rafter), estimated from our survey, was therefore defined as

where 102 is the number of days between September 20 and December 31, and Rbefore is the unweighted crude mortality rate in 2017 before September 20. The standard error for Rafter was estimated from our survey:

We assumed deaths were Poisson distributed, and we calculated the corresponding 95% confidence interval assuming the rate would be large enough that we could assume the normal approximation for the Poisson distribution:

All rates were reported as deaths per 1000 persons. To estimate excess deaths from September 20 through December 31, 2017, we calculated the difference between the estimated Rafter and the rate for the same period in 2016. Excess deaths were estimated by the application of this rate difference to the 2016 baseline population estimates for Puerto Rico obtained from the American Community Survey (ACS) (conducted annually by the Census Bureau), as follows: excess deaths=Rdiff×(population×102/365). By definition, the calculations include a mortality rate of 0 for single-person households (because of survivor bias; see the Supplementary Appendix for details). Therefore, we also calculated a per-household-size annualized mortality rate for before and after the hurricane, and we made a simple adjustment to our estimated mortality rate assuming that persons in one-person households had the same annualized death rate as in 2016 and to reflect household size distributions (see the Supplementary Appendix). We have made all the anonymized data, analysis, and code for generating our figures, as well as a version of this article in Spanish, available at https://github.com/c2-d2/pr_mort_official.