Understanding how the 7-day and 30-day average AHI's are computed

The PR System One machine's have particularly bad on-board LCD data. Not only is the AHI not broken down into the indices for each type of event (AI, OAI, CAI, HI), but also those dang AHI numbers are 7  and 30 day rolling averages. In other words, when you look at the AHI on your machine's LCD, you're seeing the overall (average) AHI for the last 7 (or 30) nights of data. These numbers are remarkably stable once you have a full set of data: A single night with a somewhat larger or somewhat smaller AHI will not affect them at all.  A single night with a much larger or much smaller AHI may affect them, but no where near as much as you might think.

Unfortunately, there is no good way to tell what goes on during any individual night based on those seven and thirty day averages.

Here's an example to help you make sense of what those 7 day averages actually are. Suppose the last seven nights, your machine has recorded the following information where Night #1 represents last night and Night #2 is the night before last night and so on.  So Night #7 is the oldest data:

NIGHT   RUN TIME    Number of events
       (in hours)    recorded
#1       7.5             50
#2       6.0             48
#3       8.2             58
#4       7.5             49
#5       8.0             65
#6       7.8             51
#7       6.9             43

When you check the LCD after 12 noon GMT, the 7-day average AHI that is shown will be computed as follows:

7-day AHI
= (total number of events)/(total run time)
= (50 + 48 + 58 + 49 + 65 + 51 + 43)/(7.5 + 6.0 + 8.2 + 7.5 + 8.0 + 7.8 + 6.9)
= 364/49.9
= 7.3

Now the next night the oldest data (the data for Night#7) is dropped from the numbers used to compute the seven day average; all the other data gets moved down one slot and the new data goes into Night #1.  So let's suppose the next night you ran the machine for 8.4 hours and the machine recorded 61 events.  The new 7-day AHI is computed based on this data:

NIGHT   RUN TIME    Number of events
       (in hours)    recorded
#1       8.4             61
#2       7.5             50
#3       6.0             48
#4       8.2             58
#5       7.5             49
#6       8.0             65
#7       7.8             51

And when you check the LCD's AHI after noon GMT, the number it shows is computed as follows:

7-day AHI
= (total number of events)/(total run time)
= (61+50 + 48 + 58 + 49 + 65 + 51)/(8.4+7.5 + 6.0 + 8.2 + 7.5 + 8.0 + 7.8)
= 382/51.4
= 7.4

Note that the 7-day AHI went up by 0.1.   But also note that the overnight AHI for the new Night#1 is equal to 61/8.4 = 7.3.  The overall average went up because we dropped a day with a relatively low AHI (as compared to the 7-day rolling average) and replaced it with a day with a relatively higher AHI (as compared to the 7-day rolling average:

The old Night#7 had an overnight AHI = 43/6.9 = 6.2.
The new Night#1 has an overnight AHI = 61/8.4 =7.3.

The new Night#1 is not pulling the overall average down as much as the old Night#7 did.  And that's why the 7-day rolling average goes UP even though the new Night#1's AHI is right at the (old) seven day average.

Thirty day rolling averages are computed in the same fashion---except they use thirty days' worth of data.  Again, each night the oldest data is dropped from the average and replaced with the new night's data.   Because of the size of the data set, it is very, very rare for a given day's data to make a noticeable change in the 30-day average.  When that 30-day average changes, it usually indicates a trend in the data rather than a particularly good or bad night for the over night AHI.


So remember that with a PR System One machine, the only way you can tell the nightly overnight AHI numbers is to look at the data on a computer---either in Encore Viewer or SleepyHead.