The criterion of ≥ 1.86 ms to define a positive test is arbitrary. Using different cutoff points to define positivity, obtain the ROC curve for the FAIR test. What is the area under the ROC curve? What does it mean in this context? 

Orthopedics

A study was conducted of a diagnostic test (the FAIR test, i.e., hip flexion, adduction, and internal rotation) used to identify people with piriformis syndrome (PS), a pelvic condition that involves malfunction of the piriformis muscle (a deep buttock muscle), which often causes lumbar and buttock pain with sciatica (pain radiating down the leg) [7]. The FAIR test is based on nerve-conduction velocity and is expressed as a difference score (nerve-conduction velocity in an aggravating posture minus nerve-conduction velocity in a neutral posture). It is felt that the larger the FAIR test score, the more likely a participant will be to have PS. Data are given in the Data Set PIRIFORM.DAT for 142 participants without PS (piriform = 1) and 489 participants with PS (piriform = 2) for whom the diagnosis of PS was based on clinical criteria. The FAIR test value is called MAXCHG and is in milliseconds (ms). A cutoff point of ≥ 1.86 ms on the FAIR test is proposed to define a positive test.