The researchers are using a quasi-experimental research design. The study is quasi-experimental because the researchers are not able to randomly assign communities to either a treatment group (those that lost their hospitals) or a control group (those that did not lose their hospitals). Instead, the researchers are using a natural experiment, where they are taking advantage of a situation that occurred naturally (the hospital closures) to compare outcomes between the two groups. While the researchers cannot control the independent variable (hospital closure), they can control for other variables that might affect life expectancy, such as age, sex, race, and socioeconomic status, by matching the communities on several variables. This type of design allows the researchers to make comparisons between the two groups and infer causality, although there may be other factors that could have affected the results that were not accounted for in the study.