There are actually 2 types of sleep apnea, but for purposes of this thread, and not to go on a tangent, I will focus on obstructive sleep apnea. That is the actual obstruction of the opening of the trachea, usually caused by the collapsing of the soft palate in the back of the throat.
The only connection that a layman like myself could draw that Gout and sleep apnea would be connected would be that people who tend to be overweight usually have sleep apnea. SOME gout sufferers tend to be overweight, linking diet, lifestyle, and health issues as contributing factors. Notice I said some, because what these doctors who use these contributing factors are failing to say is that for the majority of Gout sufferers, it was inherited through family DNA. In my OPINION, this could be a link. I don’t really understand how sleep apnea itself could lead to higher Uric Acid in your blood stream, in and of itself. But then again, I don’t tend to read JAMA or other medical journals for light reading.
The only connection that I could link all this together is that being overweight has significant health risks. One of those issues is kidney problems, which can be linked to Uric Acid filtration and Gout. So in a roundabout way, there may be a connection, but several other factors would have to come into play. Again, I’m not a doctor and this is just my opinion, FWIW.