One action of aspirin (acetylsalicylic acid) is to decrease platelet aggregation (make platelets less likely to stick together and cause blood clots in the arteries). This action makes it valuable in preventing the blood clots that can lead to heart attack and stroke in at risk persons. On the down side this action of aspirin can also increase the risk of bleeding in people at risk. This bleeding can occur in many forms including gastrointestinal bleeding and bleeding in the brain (hemorrhagic stroke).
Over the last several years prescribing a daily low dose (65 mg) aspirin has become standard and even routine medical practice to prevent heart attack and stroke caused by blood clots in at risks populations. The study cited in the BMJ suggests that in the population over the age of 70 the use of aspirin may carry as many (or more) risks than not using it at all.
This study was a model (simulation of data) and indicates the need for a full clinical trial. More importantly it shows the need for physicians to individualize treatments for their patients.
If you are on prescribed daily low dose aspirin therapy talk with your doctor about the possible risks associated with that therapy and ways you can prevent those risks. If you notice any unusual bleeding while using aspirin report those events to your doctor. This includes excessive bruising or bleeding that takes a long time to stop or any gastrointestinal upset associated with taking these medications.