Regression analysis determines the offsets between different methods and instruments that analyze cell media.
Correlation studies have been incorporated into the protocol for blood gas, electrolyte, and chemistry analyzers used in hospitals. Similar studies are now being applied to the chemistry analyzers used in the biopharmaceutical industry in cell culture applications with the purpose of monitoring key nutrients, metabolites, and gases.
Different chemistry analyzers give different results. These differences typically arise from the use of varying methodologies to measure the same analyte.
To develop this correlation, run a large number of samples on both the new and the reference analyzer over a period of days. Analyze the data by the statistical process known as linear regression analysis.
Linear regression analysis is the standard method used to compare the performance of two analytical systems. The linear regression provides a mathematical mechanism to predict or convert one set of data to another. By inputting comparison-test results between two systems into a linear regression program, slope and intercept adjustments can be calculated to correlate a new system to a pre-existing reference instrument. The slope adjustment is a multiplier, and the intercept adjustment is an addition or subtraction. A slope adjustment represents a percentage change, while the intercept adjustment is a constant.
A plot of the data should cluster along a line. If the data agree perfectly, the line will be at 45 deg, equivalent to a slope of 1.0. The point where the line crosses the Y-axis is the intercept. Ideally, this should be at 0.0. Any deviation from slope = 1.0 and intercept = 0.0 reflects a bias between the two methods. A slope greater than 1.0 shows a positive bias, whereas a slope below 1.0 shows a negative bias. The spreadsheet program will output a correlation in the form of Y = MX + B where M = slope, B = intercept, X = readings from reference instrument, and Y = readings from comparison instrument.
To adjust for bias, calculate the reciprocal of the slope and the negative of the intercept multiplied by the reciprocal of the slope. That is the offset. Thus, if the slope were 0.95, the adjustment would be to multiply by 1.05. An intercept of -2.0 would add on an adjustment of approximately +2.1. With these adjustments or offsets in place, a comparison between the two methods should result in approximately the same results so that both analyzers can be used interchangeably.
Variability over a range is accounted for by a determination coefficient known as R2(R square). This defines how predictive or relative one set of data is to another. Typically, a determination coefficient of R2≥0.95 between two analyzers means the results from these analyzers are highly related to or predictive of each other.
We will demonstrate the practical application of the above by presenting actual correlation studies. All measurements were made using the Nova BioProfile 400 analyzer (BP 400) in the role of new analyzer, compared against competitive instrumentation.
Correlation studies for glucose, lactate, glutamine, and glutamate were performed with BP 400 chemistry analyzers and YSI 2700 Select (Yellow Springs Instruments) analyzers. Both analyzers rely on the enzymatic reaction between the analyte of interest and its respective enzyme to produce H
, which in turn is oxidized to the platinum electrode. Figure 1 shows a 27-point glucose test.
Figure 1. Correlation between BioProfile 400 and YSI 2700 Select Analyzers Testing for Glucose Concentration
Correlation studies for ammonium ion were carried out with a BP 400 instrument and a UV-method ammonia test kit by r-Biopharm (Boehringer Mannheim Cat. No. 1112732). The BP 400 measures ammonium using an ion-selective electrode. The ammonium test kit runs the reaction of ammonium with 2-oxoglutarate to make
L-glutamate in the presence of glutamate dehydrogenase (GIDH) and nicotinamide adenine dinucleotide (NADH). NADH is rapidly oxidized. The amount of NADH oxidized is proportional to the amount of ammonium. Figure 2 shows a 13-point test.
Figure 2. Correlation between BioProfile 400 and Ammonium Test Kit
Our lab tested four blood gas analyzers as the reference machines for pH and partial pressures of CO
. We are reporting three tests as examples. The four analyzers are:
A hydrogen ion selective glass membrane is used to measure pH. One side of the glass is in contact with a solution of constant pH, while the other side is in contact with a solution of unknown pH. This creates a potential gradient that is proportional to the pH difference between these solutions. Figure 3 shows a test with the Corning 248.
Figure 3. Correlation Between BioProfile 400 and Conventional Blood Gas Analyzer Testing for pH
Partial pressure of CO
) is measured using a modified pH electrode. CO
from the sample diffuses through the gas-permeable membrane mounted on a combination pH-reference electrode. CO
dissolves in the thin layer of electrolyte solution trapped between the pH electrode and the gas-permeable membrane to form carbonic acid, which results in a change in hydrogen ion activity. The change in the electrolyte solution produces a potential that is measured against the constant potential of the reference electrode, and is logarithmically proportional to pCO
. Figure 4 shows a test with the Roche AVL 945.
Figure 4. pCO2 Correlation between BioProfile 400 and Conventional Blood Gas Analyzer and in-situ pCO2 Probe
Using the same electrode, O2 is measured amperometrically by reduction of oxygen at the platinum cathode. The O2 diffuses through the gas-permeable membrane and is reduced to the platinum electrode. The resulting current is directly proportional to pO2.
Na+ is measured using a sodium ion-selective polymeric membrane. One side of the membrane is in contact with a solution of constant Na+ concentration. The other side is in contact with a solution of unknown Na+ concentration. A change in potential develops that is proportional to the concentration difference between these solutions. Similarly, the K+ sensor uses a potassium ion-selective polymeric membrane. Figure 5 shows tests for K+ with the ABL 500, representative of tests with all four analyzers.
Figure 5. Correlation between BioProfile 400 and Conventional Electrolyte Analyzer for Potassium Ion
You should be able to place a statement similar to the following in your QA files. "Correlation studies assure that the results from a new analyzer will be comparable to the reference analyzer in service. The results demonstrated excellent correlation of the BioProfile 400 with competitive instrumentation for each of the parameters measured by the analyzer."
The author acknowledges Ravi Meruva and Nicole Pouliot of Nova's Research & Development group for their contributions in developing the data included in this review.