Number Crunchin'

Okay.

So last weekend I ate the better part of a half gallon of Breyer's Vanilla ice cream, had a slice of birthday cake, and a few Girl Scout cookies.

I think I've got that out of my system now (at least I hope so).

But the non-movement of my A1c still haunts me.
So when faced with a situation like this I decided to do what any self-respecting geek would do: turn to the data.

WARNING

This is going to get a little technical.
You might want to turn back now.

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So after explaining my dilemma here and to a few other friends or family, several have asked whether there's an issue with when I'm measuring my blood sugar: Could I be missing peaks? Could I be biasing my results with more frequent tests when I'm low? And I think these are valid questions.

Going into all of this, I have as my baseline a report in Diabetes Care titled "Defining the Relationship between Plasma Glucose and HbA1c." The result of the article is to estimate a reltionship between average meter readings and HbA1c readings (duh). And basically, the table below is what was found.

A1c (%)	Mean Plasma Glucose
	mg/dl	mmol/l
6	135	7.5
7	170	9.5
8	205	11.5
9	240	13.5
10	275	15.5
11	310	17.5
12	345	19.5
From Diabetes Care - 26 (Supplement 1): Table 1

This relationship was based on a sample of 1,439 type 1 diabetics producing 26,056 quarterly HbA1c readings (mean duration of participation in the study was 6.5 years), and blood glucose readings taken 7 times/day (before and after each of 3 meals and at bed time). The relationship was estimated using least-squares linear regression.

But first, in order to estimate the relationship, they needed to come up with a measure of "mean plasma glucose" that is appropriately weighted for time.

This is important.

Below is a simple example I created. Imagine you have 3 blood sugar readings over a period of 4 hours. At 1 PM you have a reading of 200 mg/dl, at 3 PM you have a reading of 150 mg/dl, and at 4 PM you have a reading of 100 mg/dl. If you were to take the simple average of these three readings, you'd have an average of 150 mg/dl over the 4-hour period.

But that's not likely to be what you're "True Average" blood sugar reading was over the 4-hour period. If we assume a straight drop in blood sugar between 1 PM and 3 PM, you could imply (or interpolate) a reading for 2 PM of 175 mg/dl. If you include this reading of 175 mg/dl, your average for the 4-hour period now goes up to 156 mg/dl -- 6 mg/dl higher.

Conversely, if you were to have the timing switched up a little (like Scenario 3), you could arrive at a lower average reading if you were to interpolate between readings (150 mg/dl vs. 144 mg/dl).

Meter Readings
Time	Scenario 1	Scenario 2	Scenario 3	Scenario 4
1:00 PM	200	200	200	200
2:00 PM		175	150	150
3:00 PM	150	150		125
4:00 PM	100	100	100	100
Average	150	156	150	144

To account for this timing effect of blood sugar readings, the authors "linearly interoplate" between the 7-points of actual data they collected. Or in their own words:

"For each profile, the seven time points were connected by straight lines over time for a 24-h period, and then the trapezoidal areas under each curve were determined, added together, and divided by time. A constant BG level between bedtime and the following morning was assumed."

Basically, you need a measure of the "area under the glucose curve." If you had a continuous function, you would simply take the integral of the function to calculate the area under the curve. To arrive at an approximation of this, however, you can chop up the area under the glucose curve into small units of time, create rectangular areas for each unit of time that go as high as the glucose curve, and add up the area of all these interpolated rectangles, and divide by time to come up with a properly weighted average blood sugar reading.

So... based on their table, my 7.1 HbA1c reading indicates that my average blood sugar has been around 170 mg/dl. This is been IMMENSELY puzzling to me as my average meter readings for the past 9 months(!) have been almost entirely below 150 mg/dl and as low as 130 mg/dl.

To (attempt to) get to the bottom of my dilemma, I exported the data from my OneTouch meters to comma separated values (*.csv) file going all the way back to November 2005. I read these data into SAS and wrote a program

Details

SAS is a statistical programming language used heavily in research and particularly in clinical trial research. I don't know exactly what time increment the authors used in the Diabetes Care paper, but I interpolated readings for each-and-every-one of the 1,440 minutes in a day. I also didn't assume that blood sugars remained constant over night like the authors did. I simply interpolated them to the next morning's blood sugar reading. I'm not sure whether these differences would bias my averages one way or the other relative to the methodolgy used in the other analysis.

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to interpolate the value of blood sugar in between all my meter readings and produce 7, 14, 30, 60, and 90 day averages. I also calculated these averages based solely on the meter readings for comparison.

First, below is a graph of the average readings from November 2006:



Clearly, the interpolated averages are higher than my simple averages of meter readings by about 8 mg/dl.

And then here is a similar graph of my average readings from February 2007:



While the interpolated average is still a bit higher than my simple averages that I've been relying on, the most remarkable thing about this graph is how much lower my readings are relative to my November averages (both interpolated and simple).

What I was hoping to get out of this exercise was to find that the interpolated values were indeed higher than my meter readings (which I did learn), but also that there would be little difference between the interpolated average in November and the interpolated average in February.

Unfortunately, that is not the case. My blood sugar averages dropped significantly over the 3-month period, but my A1c stayed rock solid at 7.1.

So.

All that, and I'm still puzzled as ever...