Blood Glucose Meter: Could the meter's accuracy be improved by doing more measurements and by using the average of the measured values?

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?)

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 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.