Sulindac is a generic NSAID. TNF-A is regulatory chemical in the body that has been implicated in many inflammatory diseases (rheumatoid arthritis, ankylosing spondylitis) - more TNF-A causes greater inflammation. Interestingly, taking Sulindac can actually increase TNF-A, at least in special circumstances. According to a 2009 study in rats (Sulindac metabolism and synergy with tumor necrosis factor-alpha in a drug-inflammation interaction model of idiosyncratic liver injury), sulindac, when administered with a another inflammatory agent, can significantly increase the amount of TNF-A in the blood as compared to the inflammatory agent alone.
This reduction may be specific to the inflammatory agent (lipopolysaccharide), but it may also occur for any cause of inflammation (ie rheumatoid arthritis, or ankylosing spondylitis, though these are chronic, and the lipopolysaccharide injection was not). It's important to note that the same study found no TNF-A increase when the rats were only injected with sulindac. Something has to cause the TNF-A to be present before sulindac can make it worse.
Other interactions between sulindac and TNF-A have been documented. One paper found that sulindac made TNF-A more effective at killing cancerous cells. Great, but if TNF-A is instead causing needless inflammation then perhaps here too sulindac is increasing it's efficacy. Another paper also suggests that Sulidac can make TNF-A a more effective cancer cell killer.
While it's too early to conclude anything, there are lots of NSAIDs on the market, so it might be prudent to take something else if Sulindac has no special appeal for you. Which is to say, it's not going to cause extra damage, but it might not be as effective.
Two papers have compared sulindac to other common NSAID treatments for AS. A 1979 double-blind cross-over study found that patients preferred taking Indomethacin to Sulindac, though the effect was small, and there was no clinically assessable difference (I prefer indomethacin, myself)in pain. Another study compared diclofenac and sulindac, and found mild evidence that diclofenac was slightly more effective (I also prefer diclofenac).