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I think your interpretation is correct, no conclusion can be drawn from the results of this study.
If a similar study were repeated and adequately powered, I wouldn't consider it p-hacking. The larger sample should only decrease the uncertainty in the primary outcome. P-hacking would be like if they set out to measure like 20 different outcomes to see if some turn out to be statistically significant by pure chance.
As an aside, I think it might be hard to gather enough participants for an adequately powered study given how close the outcomes were in this study. I'm no cardiac surgeon, but I think mechanical heart valves are generally less favored compared with bioprosthetics. Furthermore, the addition of aspirin to warfarin may cut down the number of participants as well, as aspirin is not routinely recommended.
Happily it seems they did do more.
Follow up study
They took the same control group and did a second set of experimental participants. They did find a difference between the groups, quite a significant one to be honest.
Now to see if it replicates, maybe we can aim for a lower INR. It would be ideal to not have quite so much bleed risk but also to not clot.
Edit: also, I am on warfarin and asparin with a mechanical valve, I was recommended a mechanical valve as it should outlast me and if I had a biovalve it would need replacement in 15 years max at which point it would be mechanical anyway. I'm in my mid thirties so if I have a second major surgery at 50 I will have to repair bone and muscle again and have rehab again, all at a lower likelihood of recovery. Going full mechanical means one surgery, lifelong warfarin, and one set of recovery from that surgery.
Also, based in Australia so our recommendations may differ from yours, but here we get aspirin as a recommendation as standard for most mechanical valve replacements, along with many other people.
The link to the follow up study seems to be split, but I was able to pick together the link There are two major differences between the two studies: 1. The first one looked at mitral valves, and this one studied aortic valves; 2. The target INRs were different, although given the difference between aortic and mitral valves, both correspond to an INR 0.5 points lower than standard targets.
In your case, given the risks involved, a mechanical valve sounds like the best choice. I mostly see valve replacements in the elderly, so there's my personal observational bias. I'm from the US. From what I can tell about our warfarin recommendations, On-X aortic valves do get warfarin and aspirin at lower INR targets. In contrast, there is no such recommendation for On-X valves in the mitral position (yet).