This study used adjusted risk of death as a measure. This measure refers to the probability of a person dying, so a lower number means decreased risk.
From the graph, you can see that for both males and females increased amounts of coffee per day resulted in a decreased risk of death. But, once the number of cups reached 6 or more, that risk started increasing again.
The study also noted that the observed effects were true for caffeinated and decaffeinated coffee, so caffeine was not the cause of the effect.
This is not the only study to find such an outcome.
A more recent study also looked at this connection.
This study also used an observational approach and used data from more than 200,000 people.