Probably not. However, there are some important details that may change my answer:
- What type of arthritis runs in the family?
There are more than 100 types, some of which are at least partly genetic.
- How old were the family members when they developed arthritis?
The younger they were, the more likely that its a condition that may be inherited.
- Has the distance running been associated with injuries?
If so, this may increase the risk of arthritis (with or without a family history of arthritis).
Past research that examined whether running increases the risk of arthritis has been mixed, but some of the best studies have shown no increased risk. Such studies are difficult to perform because they may take decades of follow-up or they may rely on self-reported diagnosis of arthritis (which may be inaccurate).
Also, there are many variables that affect a persons risk of arthritis and the likelihood they would become a runner. For example, people who gain significant weight may be less likely to run regularly. And they are more likely to develop osteoarthritis of the knees and hips. As a result, non-runners might seem to be at higher risk of arthritis than runners even if the risk of arthritis is not directly related to running.
As far as I know, the impact of family history on long-term arthritis risk associated with competitive distance running has not been well studied. Research in the mid-1990s, however, did find that older runners had less disability related to arthritis than non-runners, even after accounting for a family history of arthritis.
In my view, a family history of arthritis is not a reason to avoid distance running. But, the details matter.