u/piscata2

https://preview.redd.it/inarx6zw5abh1.png?width=1502&format=png&auto=webp&s=86748d1c7dcce96970153ee2053f0b76307dec43

Some of my L3+ had glucose signal fluctuations as shown in the above screenshots captured by the iPhone’s Zukka app and by comparing an expiring sensor and a newly applied sensor. They overlapped one day without pre-soak. For the current sensor, the fluctuations have not stopped after 24 hours.

I have no idea what the origin of these fluctuations is. Because the fluctuations are often lower than the steady trace of the expiring sensor, I suspect they were caused by the body’s immune response to the applicator’s needle and the L3+’s filament insertion into the body. Also I don’t understand the dynamic nature of the fluctuations.

Below is a description of how the immune response affects the sensor’s operation:

“A layer of acute inflammatory tissue (containing damaged cells, connective tissue, edema fluid, and immune cells) may surround the working electrode to become a mechanical or physical barrier that significantly inhibits/slows the inward diffusion of glucose and oxygen. Metabolically active cells adjacent to the electrode (red blood cells, macrophages, and neutrophils) actively consume glucose, significantly decreasing the number of glucose molecules reaching the working electrode. Macrophages have been identified as the major cell type producing a “Cell-Based Metabolic Barrier” that limits the diffusion of glucose from the adjacent interstitial fluid to the sensor's electrodes, causing an artificially low sensor output signal. Thus, performance of an enzyme-based electrochemical glucose sensor may be significantly affected by the dynamically changing local tissue environment immediately adjacent to the working and reference electrodes.

The cellular, humoral, and chemical environment surrounding a CGM electrode will start to stabilize within several hours and become more stable within 12 h of implantation, depending upon the amount of initial tissue trauma, ongoing tissue trauma due to body movement, and the degree of immune response produced by the individual patient. Thrombus will undergo fibrinolysis, neutrophils and macrophages will continue to phagocytize debris, and capillary vessels will regain their vasomotor control and no longer release protein-rich fluid into the wound.^(”)

Depending on the individual and location of the sensor, this immune response could last hours to several days: “This delay of sensor functionality, which is also referred to as the run-in time of implantable biosensors and is defined as the time from implantation of the biosensor to the actual stabilization of the sensor baseline signal, can last a few hours to several days.”.

I hope the above references explain some of the complaints on this sub of initial poor performance or early failure of the sensor.

Obviously, these fluctuations cause unwanted errors. It will be interesting to find out if pre-soak could reduce or eliminate these fluctuations.

Beware: long post. Read only if you have nothing better to do!

1 -- Summary for readers who have no interest in math

For readers who have no interest in math, please just read “sweet spot” and then read no further, as the main result, to be given in later sections, is exactly what the title said: if we do 4 finger pricks on the same drop of blood and average the meter readings, the meter’s accuracy will improve by a factor of two.

1.1 -- Why is the average of 4 finger prick measurements a sweet spot for N (that is, N=4)?

From my experience, it is difficult to squeeze out a big drop of blood to do more than 5 measurements and to justify the increased cost of 5 strips. Thus, 4 measurements are a sweet spot because the accuracy will be improved by a factor of 2 and the cost is bearable. If the 4 measurement results scattered all over the place, then doing 5 measurements is recommended.

Because the accuracy is improved by the square root of N, when the number of measurements increases, the cost and effort also increase. This leads to “diminishing returns” as evident in the table below.

“The Math: The Law of Diminishing Returns

The reason 4 measurements is a sweet spot lies in the shape of the 1/sqrt(n) curve. When one counts how much precision one gains with each additional test strip, the benefit flattens out drastically after the first several measurements. (To calculate cost, I used 0.20 USD per strip, which is the cost at Costco.)

Number of Strips Used (N) & Cost	Reduction in Random Error 1/sqrt(N​)	Accuracy improvement compared to 1 measurement	Marginal Gain (What the next strip adds)
1 strip ($0.20)	1.00	Baseline	Baseline
2 strips ($0.40)	0.71	29% improvement	+29%
3 strips ($0.60)	0.58	42% improvement	+13%
4 strips ($0.80)	0.50	50% improvement (Exactly 2 times)	+8%
5 strips ($1.00)	0.45	55% improvement	+5%
6 strips ($1.20)	.41	59% improvement	+4%

The Drop-Off in Value: Moving from 1 strip to 4 strips buys a massive 50% reduction in random noise. But look at what happens when one burns a 5th strip: he only gains an extra 5% of precision. In practical terms, he is paying 25% more in cost (5 strips instead of 4) to get a measly 5% return in data quality.”

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2 -- Background

For CGM users, a blood glucose meter (BGM) is the only tool to check if the CGM levels are working according to spec. Thus, understanding how the accuracy of BGM could be improved is important to the use of the meter. Some users, like me, are not familiar with statistics. Intuitively, we know the accuracy of measurement improves if we average more measurements, but we are not sure just how much improvement there is.

In this post, I will quantify this accuracy improvement. Before this post, I had never learned statistics, so I did research and was surprised to find out that this problem had been solved in statistics. Not only that, but there is also a powerful theorem, the Central Limit Theorem, governing the results.  Below are the research results. I have a Contour Next (CN) meter, which I will use to show the improvement.  The CN spec is given in ±10mg/dL and MARD. What is interesting is that, through this research, I was able to link the two specs together, which may not have been done before. Since I don’t know statistics, I hope readers who know statistics could correct my mistakes.

Since the Central Limit Theorem’s result is given in terms of Gaussian (or call normal or bell) distribution, parameters that define the Gaussian distribution and its relationship to accuracy will be presented next.

3 – The Gaussian distribution and how I determine accuracy from the bell (Gaussian or normal) curve?

Gaussian Distribution and how I determine accuracy

A graph of the Gaussian curve is given in Fig. 1 (from this reference). Two parameters define the curve, mu (the mean) and sigma (the standard deviation). mu has two representations: it is the mean of all the meter measurements, or it is the mean of all the meter’s errors, which centered at zero. For the former, mu is a positive value and is measured from 0 mg/dL (called the biased mean) and represents the true blood glucose value, and for the latter, mu = 0, that is, the meter’s error is 0, and it occurs when the meter’s reading represents the true blood glucose value. Since this post concerns meter error, I will use mu= 0, but when dealing with MARD, I will use the biased mean.

For the Gaussian curve, it is well known that the probability of a measured meter error value that lies between two values A and B on the horizontal axis is the area under the curve enclosed by these two values. From Fig. 1, if the errors have a Gaussian distribution, then there is a 95.4% chance that the measurement error lies between m±2sigma, and there is a 99.7% chance that the measurement error lies between m±3sigma. For the current purpose, I will call them 95% and 100% probability, respectively. These two probabilities are the same as the accuracy definitions used by the BGM and by CGM. So, when m = 0, the 95% accuracy is within ±2sigma, and the 100% accuracy is within ±3sigma. Thus, I define:

Accurac_95% (95% of the time) = ±2sigma    EQ(1)

Accurac_100% (100% of the time) = ±3sigma EQ(2)

For the current analysis, I will use the 100% probability accuracy that is EQ(2) because one of the Contour Next specs is given as 100% of the time, the error is less than ±10 mg/dL.

4 -- Do the meter errors follow a Gaussian distribution?

Yes, they do because each error is the sum of the following factors:

• “Minute fluctuations in the meter's electrical current.
• Tiny variations in the thickness or consistency of the enzyme layer on each test strip.
• Micro-changes in ambient temperature or humidity during the reaction.
• Small differences in the hematocrit level or oxygenation within that specific sample.

Because these small factors pull the reading slightly higher or lower with equal probability, they cancel each other out on the average, creating a symmetrical bell curve centered around the meter’s mean (or biased mean).” About meter errors follow a Gaussian distribution; see, for example, this publication.

The meter’s errors following the Gaussian distribution are an important requirement to justify the use of the Central Limit Theorem; see section 5 below.

5 – The Central Limit Theorem in statistics predicts that the BGM’s accuracy will be improved by the square root of N if we average N consecutive meter measurement results.

When the BGM is used to do more than 1 measurement, there are two types of errors: one is the error of the 1 measurement, and the other one is the error for the average of N measurements (I assume the Contour Next’s  bias (~1%) is negligible).

______________________________________________

The Central Limit Theorem says that when N is greater than 30, the various averages are normally distributed. Also, the standard deviations and the mean errors of the averages and the single measurement are related through the following equations:

sigma(N) = sigma / sqrt(N) …... EQ(3),

mu(N) = mu   ………….    EQ(4).

Further, if the errors of 1 measurement are normally distributed, then the averages of N measurements are also normally distributed for any N. This is a great help because in practice, N is no larger than 5.

This is true because the strip-to-strip random errors across the entire manufacturing batch are already approximately Gaussian.

In EQ(3) and EQ(4), sigma and mu are the standard deviation and mean for the errors of 1 measurement, whereas the symbol (N) indicates the parameters are for the averages of N measurements. sigma(N) is called the standard error of the means. In the following analysis, mu = 0 except when analyzing MARD.

________________________________________________

The main result of the Central Limit Theorem, embodied in EQ(3) and EQ(4), is that the standard error, sigma(N), of the average is reduced from the standard deviation of a single, sigma, by a factor of sqrt(N). Smaller standard deviation means higher accuracy.

6 – Accuracy improvement by taking the average of N consecutive measurements

From EQ(2), the accuracy for the meter is

Accuracy (1 measurement) = ±3sigma,  ….EQ(5).

Similarly, the average of N measurements is

Accuracy (average of N measurements) = ±3sigma(N) ….. EQ(6).    

Thus, from CLT, the improvement is

Accuracy-Improvement = Accuracy (1 measurement) / Accuracy (average of N measurements) = ±3sigma/±3sigma(N) = sigma/sigma(N) = sqrt(N)…EQ(7).

EQ(7) is the main conclusion of this post and is true because of the Central Limit Theorem.

7 – Accuracy improvement of the Contour Next by taking the average of N consecutive measurements

The Contour Next accuracy (or errors) is given in two forms: (1) 100% of the time, the accuracy is within ±10 mg/dL (given by the manufacturer); and (2) MRAD of 3% (MARDs given in a publication).

7.1 – When the accuracy is given as: 100% of the time, the accuracy is within ±10 mg/dL.

From discussion in section 2, 100% of the time translates to an accuracy of ±3sigma; thus, from EQ(2)

Accuracy (1 measurement) = ±3sigma = ±10 mg/dL, or

sigma = 3.33 mg/dL (1 measurement)

From EQ(3), for the average of 4 meter measurements, we have

sigma (average of 4 measurements) = 3.33 / sqrt(4) = 1.67 (mg/dL) …. EQ(8)

Accuracy (average of 4 measurements) = ±3sigma ( average of 4 measurements) = ±5.1 (mg/dL).

Likewise, for the average of 5 meter measurements:

sigma (average of 5 measurements) = 3.33/sqrt(5) = 2 (mg/dL)…. EQ(9)

Accuracy (average of 4 measurements) = ±3sigma (average of 5 measurements) = ±4.47 (mg/dL)

Compared to the accuracy of just one measurement, the accuracy of the average of 4 or 5 measurements has improved by a factor of ~2.

7.2 – How does MARD connect to the standard deviation?

The Central Limit Theorem states the improvement of accuracy by taking the average of N consecutive measurements in terms of standard deviation. Thus, in order to use the CLM, we need to connect MARD to the standard deviation. It took me a lot of effort to find the reference: 

The Relationships between Common Measures of Glucose Meter Performance by Daniel R Wilmoth, who, using complex math, works out the following relationship:

MARD = CV * sqrt(2/pi)

= (sigma/mu) * sqrt(2/pi),     …. EQ(10).

From EQ(10), I obtained my objective, which is:

(sigma/mu) = MARD * sqrt(pi/2)   …. EQ(11 )

Thus, according to section 3, EQ(2), I can define

Accuracy_relative (%) = ±3(sigma/mu)= ±3 MARD * sqrt(pi/2)   …. EQ(12 )

In the above, CV(%) = (sigma/mu) is the coefficient of variation (also called relative standard deviation), and m here is not equal to zero as in section 3, but it is the biased mean value measured from 0 mg/dL.

EQ(11) translates MARD to the relative accuracy (%) given in EQ(12). Both equations are the sought-after results. 

7.3 –- When the accuracy spec is given in MARD, what is the accuracy for the average of N measurements?

Using EQ(11) and EQ(3) ( the CLT), I obtain the relative standard of error  and accuracy for the average of N measurements:

[sigma(N)/mu]= [(sigma/mu)] / sqrt(N)

= MARD * sqrt(pi/2) / sqrt(N)   …… EQ(13)

Accuracy_relative(average of N measurements) = ±3[sigma(N) / mu] = ±3*MARD * sqrt(pi/2) / sqrt(N)    ….EQ(14)     

Thus, when N measurements  is averaged, just like before, both the relative standard deviation and MARD are reduced by sqrt(N), and, as a result, the accuracy also improves by the same factor.

7.4  – How much does the accuracy of the average improve when the Contour Next has 3% MARD

MARD is the average absolute relative error and is reported in serval references given in the following table. I used the middle value of 3% from reference 3 (the choice is based on Libre 3’s MARD is 8.2.).

Reference	MARD (%)	SD, SE or CV (%)
1	4.8	3.5 SD
2	5.5	2.4 SE
3	3.0	4.0 CV
4	3.6 and 4.29
5	5.5	2.4 SE
6	2.4	1.6SD

For one measurement, from EQ(11), we have

(sigma/mu) = MARD * sqrt(pi/2)      

= 1.25 MARD

= 3.75% (when MARD = 3%)

For the average of N measurements, from EQ(13) and EQ(14), we obtained the following values:

[sigma (average of 4 measurements)/mu]= [(sigma/mu] / sqrt(4) = 1.87%, and         

[sigma (average of 5 measurements)/m]= [(sigma/mu] / sqrt(5) = 1.68%

Accuracy_relative (average of 4 measurements) = ±3 [sigma(average of 4 measurements) / mu = ±5.61%

Accuracy_relative (average of 5 measurements) = ±3 [sigma(average of 5 measurements) / mu] = ±5.04%

For a BG of 100 mg/dL, they translate into 5 and 5.6 mg/dL, respectively, similar to the accuracy for the average calculated from the spec of ±10mg/dL.

I re-read some of u/Equalizer6338 's posts and was intrigued by what he said: "But one that truly can flip the scale is something like the Eversense 365 days sensor. That is true market disruption."

If you know the reason why and could share your knowledge, I would appreciate learning from you.

Hello friends,

Wishing you all a Happy Father's day, a day of relaxation and happiness you deserve!

Special thanks to u/Equalizer6338, u/Ok-Dress-341 and u/the_owlyn , who answered my trivial questions!

Top right Fig 4, middle right Fig 3, bottom left Fig 5.

Several months ago, I had never used a glucose meter. But suddenly I had a near-death hypoglycemia episode due to a cascade of unexpected events. Since then, I bought a Contour Next and have been using it to calibrate the Libre 3+.

Libre’s accuracy is given in two different forms: (A) 100% of the time, it is within ±40 mg/dL (or ±40), or 95% of the time, it is within ±20 mg/dL (or ±20) ; or (B) MARD, which is 8.2% overall.

I always use the (A) form because it is very straightforward to use. I have never used the (B) form because it is an average of many measurements (This result cannot be used for one measurement).  MARD is a statistical value, the average of thousands of measurement pairs. Each pair is the percentage error of the CGM value and the true blood glucose value measured by a precision lab requirement, YSI:

MARD = {sum of [|CGM(i)-BG(i)| ]/BG(i)]}/n , i=1,2,…n,    EQ(1), where

CGM(i) and BG(i) are the CGM and blood glucose values at the ith moment, and where

CGM-BG (= bias) is the bias, EQ(2. EQ(2) is the error or accuracy of the CGM in mg/dL, and

|CGM-BG| /BG (= ARD (%)) is the absolute relative difference, EQ(3). EQ(3) is the absolute error of the CGM in %.

Scientists and researchers use bias, ARQ, and MARD to describe the error of the CGM. For CGMs, MARD is the most important accuracy parameter because Abbott is selling the Libre by the millions. Thus, the regulatory agency and Abbott are only interested in the overall performance of thousands of measurements of many Libres on many patients. The performance of one Libre, which the users care about, is not good enough for them. Because of this, there is a lot of data on MARD, and surprisingly, MARD for Libre gives a clue on what day to calibrate the Libre.

For illustration, the bias of CGMs is given in Fig. 2 (from Gemini; data were pulled from different sources). On each day, there are thousands of measurements (indicated by the dots), which include various glucose levels and circumstances (fast rise, fast drop, lag time, etc.); they are then averaged and give the solid curve. The colored band is for data within ± one standard deviation. There are distinctive features of the averaged curve. On the first day, as often pointed out by u/Equalizer6338, the error is due to immune reactions. On days 2-9, it enters into a high-accuracy region where the curve is  almost flat. From days 10-14, the error gradually increases due to exhaustion of the filament enzyme as well as body cell encapsulation on the filament (see a recent post by u/Equalizer6338), and eventually they end the CGM’s life. An example of the distribution (or spread) of MARD is given in Figure 3.

When I do finger prick measurements, I wait till my Libre is near 100mg/dL and also stable over tens of minutes. This excludes lag time, various levels of blood glucose, fast rise and fall of BG levels, etc. in the MRAD measurements. When all these adverse factors are excluded, the standard deviation becomes very small.  Thus, I believe, for calibration purposes, it is the solid curve that matters. Libre’s electrical signal will drift, but it is gradual and small: “The total drift in the sensor signal estimated over the 15-day wear duration was 4.2%,” reported by Abbott. (On the average, ~0.3% per day, too small to affect calibration.)

What is most important to calibrating the Libre is the MARD for the Libre 3 itself. These are provided by Dr. Alva from Abbott. The 15-day Libre MARDs are given in Figure 1. Figure 1, in general, follows the general trend of Figure 2 except for days 10-15, on which the Libre’s MARD is almost flat. Perhaps, Abbott’s algorithm has offset the droop near the end days in Figure 2. There are three gaps in these data. For my purpose, I used the 14-day Libre MARD data to fill in two of these gaps and plotted the MARD for Libre 3 in Figure 4.

I assume the glucose meter is perfectly accurate. For calibration, it is the relative change in MARD from one day to the next that determines if a recalibration is needed. From Figure 4, I deduce that calibrations should be done on days 1, 2, 5, and 10. Day 1 is a must to find out how far off the Libre is. Day 2 is because there is a moderate decrease of ~3% from day 1 to 2. Likewise on day 5 because of another moderate decrease of ~3%. From day 5 to 15, there is little change in accuracy, so calibrating on day 10 is to make sure that the calibration is still good.

As a comparison, MARDs and bias measured by other researchers are given in Figures 5 and 6.

For a single Libre, the error would not be the same as MARD unless the Libre were an average Libre. But knowing the MARD over days of wear will give me an idea of how large the error varies from day to day and help me to make decisions on when a recalibration is needed.

I use Contour Next and typically do 5 measurements on the same drop of blood. 5 test strips cost more than 1 test strip. It begs the question: Is there any benefit, or is it just a waste of money and effort? This post attempts to answer this question. Below is some background information and the conclusion reached based on results from calculations from statistics.

1. Accuracy from the manufacturer and a research study

The accuracy of Contour Next is given by the manufacturer, Ascensia Diabetes, which shows that when the BG is less than 100mg/dL, 100% of results are within ±10mg/dL. These are hard limits guaranteed by the manufacturer. 

MARD is given in Table 4 of “User Performance Evaluation and System Accuracy Assessment of Four Blood Glucose Monitoring Systems With Color Coding of Measurement Results” for 3 lots of test strips.

The MARD (in %) for each lot is 2.3 ± 1.7, 2.4 ± 1.6, and 2.3 ± 1.8. I will use the middle value.

2. “The Components of Glucose Meter Error”

“When analyzing the normal distribution of a meter's error, clinical pathologists break the total error down into two primary statistical components (Virdi & Mahoney, 2012; Voss et al., 1996):

a. Random Error (Imprecision)

This is the standard deviation (σ) or Coefficient of Variation (%CV) of the bell curve (Virdi & Mahoney, 2012; Voss et al., 1996). If you test the exact same blood sample 100 times, random error dictates the width or "scatter" of the bell curve (Virdi & Mahoney, 2012; Voss et al., 1996). A lower %CV means a tighter, taller bell curve (higher precision) (Virdi & Mahoney, 2012).

b. Systematic Error (Bias)

This represents a permanent shift of the entire bell curve to the left or right of the "true" laboratory reference value (Virdi & Mahoney, 2012; Voss et al., 1996).”

4. “Meter’s Errors are Normally Distributed”

“When a blood sample is tested repeatedly under stable conditions, the individual random errors (imprecision) fluctuate unpredictably in both positive and negative directions (Voss et al., 1996). Because these minor fluctuations are caused by an accumulation of many independent, small physical and chemical variables—such as slight variations in test strip manufacturing, ambient temperature, enzyme coverage, and tiny electrical current fluctuations—they follow the Central Limit Theorem (Ginsberg, 2009; Voss et al., 1996). 

In contrast, if the errors were uniformly distributed, a massive 18% error would be just as likely to occur as a minor 1% error, which is not how these biochemical sensors behave in reality.”

5. I asked, "If the long-term average of the meter is 100mg/dL, given ±10mg/dL accuracy and 2.4% and 4% MARD, what are the boundaries of the average (95% confidence level) if I do the measurements 5 times?"

I am interested in the glucose range of blood glucose near 100mg/dL. During finger pricks, I keep the glucose level steady. I don’t know statistics, so I ask Gemini to do the math (it used the Gaussian function and based on 5 measurements) for two types of errors: (a) uniformly distributed, and (b) normally distributed (from above, in practice, this is what the meter has); also for MARD of 2.4% and 4%. Answers are given in the following table.

Metric	0% MARD Constraints (Uniform Distribution) (in mg/dL)	2.4% MARD (Normal, σ≈3.0) (in mg/dL)	4.0% MARD (Normal,  σ≈5.0) (in mg/dL)
Typical Single Reading Error	Anywhere from -10 to +10	Mostly within ±3	Mostly within ±5
95% Boundary (1 Measurement)	109.0 (and 91)	$105.9 (and 94.1)	109.8 (and $90.2)
95% Boundary (5 Measurements)	$104.2 (and 95.8)	$102.6 (and 97.4	104.4 (and 95.6)

When the errors are uniformly distributed, the average of the 5 measurements is within 95.8 to 104.2 (mg/dL).

 “With the 2.4% MARD condition included, 19 times out of 20, the average of .. 5 measurements will be incredibly tight between 97.4 and 102.6 (mg/dL). The 2.4% MARD ensures that the device is already quite accurate on its own, meaning 5 measurements are now more than enough to crush the remaining variance and give … a highly dependable average.” However, for 4% MARD, the result is similar to the result of the uniform distributed error.

I note that for both 2.4% and 4% MARD, the results of 5 measurements are similar to just adding MARD to the long-term average of 100 mg/dL.

Conclusion: doing finger pricks 5 times increases the accuracy of the blood glucose meter. The average value has a smaller error with the true blood glucose value than a single measurement does.

The answer seems to be NO and YES, depending on how we interpret the results.  I am not sure if my interpretations, given below, are correct, or just garbage (garbage in, garbage out?)

New results obtained in this post are due to the realization that when I do finger pricks, my blood glucose is typically steady, that is the BG is a straight line over the measurement time. This realization allows simplification of the formulas and obtaining the expected results.

Recently, I have been thinking about the accuracy of my blood glucose meter, Contour Next, and have been wondering if the accuracy could be improved if I did multiple measurements and used the averaged measured values (I have an earlier post that shows that when I use the Contour Next to calibrate the Libre 3, the accuracy of the latter could be improved by a factor of 4.)

The accuracy of Contour Next is given in two ways: (A) percentage of measurements that will have an error of less than 10mg/dL (the performance guaranty) and (B) MARD (how close the measured value is to the true blood glucose value due to built-in limitations of the meter’s hardware, software, and electrochemical reaction).

The accuracy of Contour Next is given by the manufacturer, Ascensia Diabetes, which shows that when the BG is less than 100mg/dL, 100% of results are within ±10mg/dL.

MARD is given in Table 4 of “User Performance Evaluation and System Accuracy Assessment of Four Blood Glucose Monitoring Systems With Color Coding of Measurement Results” for 3 lots of test strips. The MARD (in %) for each lot is 2.3 ± 1.7, 2.4 ± 1.6, and 2.3 ± 1.8. I will use the middle value.

(A) From the “percentage of measurements that will have an error of less than 10mg/dL” perspective, the answer is NO. The following analysis shows that the accuracy is not improved, but in practice, the averaging helps to average out the random errors due to the strips, such as enzyme variation, dust, etc.

For the spec of “when the BG is <100mg/dL, 100% of results are within ±10mg/dL”, what is interesting is that 100% means that it happens with absolute certainty that is the case. Then, we can write the following equation:

| M1 - BG1 | < 10 mg/dL,  EQ(1),

where M1 and BG1 are the meter value and blood glucose value for the first measurement. Similarly, for the second and third measurements, we have

| M2 – BG2 | < 10 mg/dL,  EQ(2),

| M3 – BG3 | < 10 mg/dL,  EQ(3).

For simplicity, I assume all the meter values are higher than the blood glucose values, so I can remove the absolute sign from the above equations. Adding EQ(1), EQ(2), and EQ(3) together gives

{(M1 - BG1) + (M2 – BG2) + (M3 – BG3)}  <  (10+10+10 ) mg/dL,     EQ(4)

When I do meter measurements, I wait until my glucose level is steady, that the BG is a straight line, so I can set

B1=B2=B3=B,   EQ(5) 

Also, I divide EQ(4) by 3; EQ(4) becomes

{(M1 + M2 +M3)/3 – (3B)/3}  <  (10+10+10 )/3 mg/dL,     EQ(6)

Note that (M1 + M2 +M3)/3 = M(av), is the average of the meter measurements; thus, EQ(6) can be written as

|M(av) – B|  <  10 mg/,    EQ(7)

EQ(7) is the same as EQ(1), but the single meter measurement in EQ(1) is replaced by the average of all the meter measurements in EQ(7). Thus, from EQ(7), the accuracy is not improved, but in practice, all the random errors due to the strips, such as enzyme variation, dust, etc., will be averaged out, resulting in better accuracy, independent of what the equation says.

(B) From the “MARD” perspective, the answer is YES.

What is also interesting is that if we divide EQ(1) by B, we have

| M1 - B| /B < (10mg/dL/B) = 10% ,  EQ(8),

where, for simplicity, I assume 10mg/dL/B = 10%. Doing the same thing to EQ(2) and EQ(3), we have

| M1 - B| /B   + | M2 - B| /B + | M3 - B| /B  <  (10% + 10% + 10%),  EQ(9) 

Dividing EQ(9) by 3, we have

{| M1 - B| /B   + | M2 - B| /B + | M3 - B| /B}/3  < 10% ,  EQ(10)

By definition, {| M1 - B| /B   + | M2 - B| /B +  | M3 - B| /B}/3 = MARD,

Thus, we have,

MARD < 10%,  EQ(11).

This is a surprising and unexpected result, averaging the results of all measurements gives MARD and MARD for the Contour Next is 2.4 ± 1.6 (%). For 100mg/dL, 2.4% is 2.4mg/dL and is only a quarter of 10 mg/dL given in (A), thus it is a far more accurate result.  However, the caveat is in scientific studies, MARD is obtained by doing thousand pairs of measurements, but in daily use of the meter, I can only do, at most, 5 measurements; and doing just 5 measurements does not give an accurate MARD. Also, another downside is that doing multiple measurements greatly increases the cost per calibration. Thus, better accuracy comes at a higher cost.

(C) A set of measurements

The Contour Next gave the following results: 71, 84, 92, 84 mg/dL. The spread is about +-10mg/dL within and at the limit of the spec given in (A). I used the average of 84. I do not have a YSI to further test the accuracy.

https://preview.redd.it/mqrf56giho5h1.png?width=626&format=png&auto=webp&s=89dffd1c74fb08cec2e29b98246fe78e6f224e5c

For CGMs, accuracy is given in two forms:

(A) Percentage of matched glucose pairs within ±20mg/dL (or 20%) of reference values within glucose ranges, or

(B) MARD. ARD is the absolute percentage difference between the CGM value and the true blood glucose value at the same time point, whereas MARD is the average of many pairs of ARDs. It tells how accurate the CGM is when compared to the true blood glucose. It is mainly used to compare different brands of CGMs. Measurement of MARD is complex and has to specify the condition.

(A) is also given in ±40mg/dL (or 40%) and what is interesting is that the percentage is 100% that is with absolute certainty that is the case.

I am using Contour Next and interested in the range from 70-100 mg/dL because <70 is hypoglycemia and because I do not expect calibration will cover a range greater than 30 mg/dL.

Below is hand-waving in order to get a ball part number.

(A) Accuracy of Contour Next given by the manufacturer, ascensiadiabetes, is given in the above figure, which shows that when the BG is <100mg/dL, 100% of results is within ±10mg/dL

Accuracy of the Libre 3 is given in Table 3a (reproduced in above figure) of  “Accuracy of a 15-day Factory-Calibrated Continuous Glucose Monitoring System With Improved Sensor Design”.

For the range of 70-100 mg/dL, “% Within ±40 mg/dL”, it is ~100% and the MARD is ~9% (I interpolate).

Thus, ratio of accuracy of Libre 3 to Contour One is **±**40mg/dL/ **±**10mg/dL= 4/1.

(B) MARD for the Contour One is given in Table 4 of  “User Performance Evaluation and System Accuracy Assessment of Four Blood Glucose Monitoring Systems With Color Coding of Measurement Results” for 3 lots of test strips.

They are 2.3 ± 1.7, 2.4 ± 1.6, 2.3 ± 1.8.

Thus, MARD ratio of Libre 3 to Contour Next is ~9/2.3 = ~4. Approximately the same as the ratio in mg/dL.

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I am re-reading “Accuracy of a 15-day Factory-Calibrated Continuous Glucose Monitoring System With Improved Sensor Design” by Shridhara Alva and coworkers. This is a study of the Libre 3’s performance.

Table 4 (Percent Within 20%/20 mg/dL and Mean Absolute Relative Difference Performance at Different Wear Periods for Adult and Pediatric Populations.) shows that the % of wearers Within ±20%/±20 mg/dL on day 1 is 83.5% as oppose to ~95% for days 5-15. This seems to justify pre-soaking for 1 day.

I also note that there is certainty % within the 15 days of usage that a sensor will become bad as they are “Outside ±40%/±40 mg/dL.”  For example, 0.2% for days 5-7. Given that there are millions of L3 wearers, 0.2% is a large number. This may explain why there are so many posts complaining sensors go bad and need to be replaced.

However, I don't understand what does 7.2% MARD mean for sensors Outside ±40%/±40 mg/dL. Why when a sensor is bad, it can have so low MARD? Would appreciate help.

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Each Libre 3 behaves differently.

In the past, some of my Libre 3’s glucose readings fluctuated a lot, especially during the initial days.  These fluctuations caused anxiety as I was not sure if they could be trusted and if I should take countermeasures. One obvious solution is to compare the readings with a trusted Libre 3 side by side. This could be done by overlapping one day with the expiring L3, which had been calibrated several times (with Contour Next) and whose performance had been observed over the last 14 days. I pre-soaked the new L3 arbitrarily for 15 hours to minimize immune response to filament insertion. The results of this comparison are given in the above figures and their explanations are given below.

Fig. 1 shows the last day’s performance of the old L3. The accuracy is within 5mg/dL with a Contour Next. At times, it shows fluctuations of ~7mg/dL peak to peak. These fluctuations are normal. and they illustrate the dynamic process of glucose absorption inside the body. Fig. 1 shows that L3 having a low amplitude fluctuation is normal and should be acceptable. On the Libre app, they will be averaged out.

Fig. 2 shows that within the first 6 hours after activation, the new L3 had sustained fluctuations at the times when the old L3 had no fluctuations. So, trust of the new L3 has not been established. How the pre-soak time affects these fluctuations is currently not known.

Fig.3: After t=8 hours, the glucose waveform of the new L3 starts to closely match the old L3. So, I start to trust the new L3’s readings. Also, after t=13 hrs, fluctuation of the new L3 has stopped. Definitely, I start to trust the new L3 readings confidently.

Fig. 4 shows the performance of the new L3 on day 2. It has no more fluctuation. Its glucose reading at t=29 hrs is within 3mg/dL of the Contour Next.

In summary, I found that overlapping the old and new L3s by one day and using the old L3 as a bench mark will give me assurance the new L3 is working properly. For this specific L3, pre-soaked for 15 hours, its readings could be trusted after half a day.

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In the past, when Zukka was connected to two Libre 3s, only dots would be shown for one of them at 5 or 10 minute intervals. But now, Zukka will display them equally. The only shortcoming is the two traces use the same colors.

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I had a device check during which the rate response gain and base rate were changed; the former was reduced from 3 to 2, and the latter was increased from 60 to 65 bpm to compensate for the decrease in RR gain. The effect of these changes was captured on the attached heart rate plots. They are self-explanatory. Each plot lasted ~12 hours.

For my pacemaker, the huge surges at RR gain of 3 are similar to the feedback of a high gain microphone when the microphone picks up its own amplified sound from the speakers, creating high-pitched, a screaming sound.