Generally it's not possible for an individual, or their bed partner, to make an accurate assessment of the presence or severity of OSA.  [to come : papers to support this].

Most common test is "Overnight Sleep Study" in a hospital sleep centre.  Medical term is Polysomnography (PSG).  Provides a lot of hard data and is a very useful tool.  Some concerns that sleeping in a hospital with wires plugged in everywhere is so radically different from sleeping at home that the results may be unreliable.  However, on balance still seems to be the best tool we have.  Waiting lists in Australia are obscenely long, generally greater than 6 months.

[to come : list of Australian sleep centres performing PSG and approximate waiting times]

"Take home testing" is becoming popular.  Small pieces of equipment can be taken home, worn overnight, and brought back to the doctor for interpretation of the results. 

[to come : list of organisations providing take-home testing]

Urine analysis might become a useful screening tool one day.  OSA involves repeated episodes where the "fight or flight" response is activated (in response to the lack of oxygen) and left over chemicals from these responses circulate in the blood for some time afterward. 

Jun 2009
A study found that norepinephrine and epinephrine levels (not not dopamine levels) in morning urine were higher in children with OSA than those without, and that the levels were higher in children with worse OSA.  Levels were normalised against creatinine levels.     Snow AB, Khalyfa A, Serpero LD, Capdevila OS, Kim J, Buazza MO, et al. Catecholamine alterations in pediatric obstructive sleep apnea: effect of obesity. Pediatric pulmonology. 2009 Jun;44(6):559-67