The apnea–hypopnea index, or AHI, is the number of apneas and hypopneas divided by the number of hours of sleep. In a laboratory sleep study, sleep is identified using signals that include brain activity, so time spent awake can be separated from time asleep.
For example, 30 scored events during 6 hours of sleep gives an AHI of 5 events per hour. The same 30 events divided by 8 hours would give 3.75. This is why the denominator matters as much as the count.
Home tests may report a different index
Many home sleep apnea tests do not directly measure sleep with EEG. They report a respiratory event index, or REI, using monitored time as defined by the test and its analysis. That is not necessarily every minute between turning the recorder on and off; unusable data or identified wakefulness may be handled differently. Some systems estimate sleep time using other signals.
Including wake time in the denominator can lower the apparent event rate compared with an index based on actual sleep. This is one reason a negative home test may need follow-up when clinical suspicion remains.
The scoring rule changes the numerator
An event must satisfy the rule used by the scorer. Adult hypopnea rules differ in whether they count a smaller oxygen drop or a brain arousal, versus requiring a larger oxygen drop. Therefore two analyses of the same recording can produce different counts without either calculation being arithmetically wrong.
Ask which rule and sensors were used before comparing reports. There is no fixed percentage that converts one rule's AHI into another.
Your PAP device reports treated breathing
A PAP machine usually estimates events per hour of recorded treatment, using its own signals and algorithms. It does not ordinarily know exactly when you were asleep. Its residual AHI describes breathing while receiving treatment, unlike the untreated diagnostic study.
A much lower device estimate after starting therapy can be encouraging, but the size of that reduction is not an exact like-for-like measurement. Usage, leak, symptoms and any relevant oxygen or ventilation measurements still matter.
When comparing two reports, first match the treatment state, date range, index label, denominator and scoring method. Only then ask what the change may mean clinically.
Related reading: Apnea and hypopnea: how adult sleep studies score events