Examples of analyte-dependent interference will make it easier to understand how to design the studies and interpret the results. Crocker et al. evaluated an enzymatic method for determining creatinine using the 4-aminophenazone/peroxidase detec- tion system with hydrogen peroxide as an intermediate [3]. In short, creatininase converts creatinine to creatine, creatinase converts creatine to sarcosine, sarcosine oxidase converts sarcosine to glycine and hydrogen peroxide, and peroxidase con- verts hydrogen peroxide , phenol derivative and 4-aminophenazone to a red benzo- quinone imine dye .
In the study, Crocker et al. examined potential interference by glucose, acetoac- etate, bilirubin and cefoxitin and compared those interferences with the kinetic Jaffe method (alkaline picrate) [3]. They designed the study with four concentrations of bilirubin (the zero value was whatever was already in the sample pool) and three different concentrations of creatinine, one low, one moderate and one high. The con- centrations of bilirubin used and the three concentrations of creatinine in the pools are shown in Tab. 12.1. The bilirubin concentration as well as each concentration of creatinine is given its own table. In this way, the three concentrations of creatinine
Bilirubin (μmol/L) Creatinine1 (μmol/L) Creatinine2 (μmol/L) Creatinine3 (μmol/L)
0 87 332 572
100 76 291 509
200 60 253 456
300 47 218 396
Tab. 12.1: Enzymatic creatinine bilirubin interference data.
Bilirubin (μmol/L) Creatinine (μmol/L) BiliCreat (μmol/L) Result (μmol/L)
0 87 0 87
100 87 87 76
200 87 174 60
300 87 261 47
0 332 0 332
100 332 332 291
200 332 664 253
300 332 996 218
0 572 0 572
100 572 572 509
200 572 1,144 456
300 572 1,716 396
Tab. 12.2: Independent and dependent variables for the bilirubin-creatinine interactive term.
are referred to as Creatinine1, Creatinine2 and Creatinine3. If one wanted to perform multiple regression analysis using a spreadsheet program, one would enter the data in this form on the spreadsheet. Tab. 12.2 shows the same data as Table 12.1, except additional columns have been entered in addition to that of bilirubin, one for the cre- atinine concentration, and another for the bilirubin-creatinine interaction (BiliCreat).
Fig. 12.1 shows plots of the recovered values for creatinine from the analytical method plotted against the bilirubin concentration.
creatinine (mmol/L)
600 500 400 300 200 100
00 50 100 150 300
bilirubin (mmol/L) creatinine1
creatinine2 creatinine3 enzymatic creatinine and bilirubin
250 200
creatinine (mmol/L)
600 500 400 300 200 100
00 50 100 150 300
bilirubin (mmol/L) creatinine1
creatinine2 creatinine3 jaffe creatinine and bilirubin
250 200
Fig. 12.1: Interference with creatinine by bilirubin showing variation in slopes.
The upper graph shows three curves, one for each creatinine concentration in the base pool for the enzymatic method. The lower graph shows three curves, again for the three creatinine concentrations in the base pool, but for the Jaffe creatinine method. Each curve is negative. For the Jaffe creatinine method, the curves are almost all parallel, but for the enzymatic creatinine method, the curves are not parallel, which means that they have different slopes. For the interference to be independent of the concentration of creatinine (analyte-independent) the slopes of the creatinine values vs the bilirubin concentration should all be the same [4].
Tab. 12.3 shows linear regression analyses of the creatinine vs bilirubin curves at each individual concentration of the creatinine pool. The configuration of these
12.1 Complex Interferences 123
results are the result of the output from the spreadsheet program EXCEL, using the LINEST function. The r-squared values (square of the correlation coefficient) are at least 0.99, meaning that the regressions were adequately run and the data fit well with the model. The intercept for Creatinine 1 is 87.9 which is close to that of 87 in the base pool, for Creatinine 2 it is 330.5, which is close to 332, as found in the base pool, and for Creatinine 3, it is 570.4, which is close to 572, as found in the base pool. Given these results, it is acceptable to go on with this analysis. The slope for each base pool of creatinine is negative. Furthermore, the standard errors of the slopes (SE slope) for each of the creatinine pools is small, especially compared with the magnitude of the
Creatinine 1 vs Bilirubin
Slope −0.136 87.9 Intercept
SE slope 0.006 1.2 SE intercept
r-squared 0.995 1.4 SE regression
F 440 2 degrees of freedom
SSregression 925 4.2 SSresiduals
Creatinine 2 vs Bilirubin
Slope −0.38 330.5 Intercept
SE slope 0.009 1.8 SE intercept
r-squared 0.999 2.1 SE regression
F 1,604 2 degrees of freedom
SSregression 7,220 9 SSresiduals
Creatinine 3 vs Bilirubin
Slope −0.581 570.4 Intercept
SE slope 0.013 2.4 SE intercept
r-squared 0.999 2.9 SE regression
F 2021.323 2 degrees of freedom
SSregression 16,878 16.7 SSresiduals
Slope vs Creatinine
Slope −0.00092 −0.062 Intercept
SE slope 4.6E-05 0.018 SE intercept
r-squared 0.998 0.016 SE regression
F 403 1 degrees of freedom
SSregression 0.099 0.00025 SSresiduals
Creatinine vs Slope
Slope −1,087 −67.1 Intercept
SE slope 54 22.1 SE intercept
r-squared 0.998 17.1 SE regression
F 403 1 degrees of freedom
SSregression 117,325 291 SSresiduals
Tab. 12.3: Linear regression analysis of enzymatic creatinine method with bilirubin.
slope. Presented in the section of Statistical Testing for Significance will be a discus- sion on how to use a t-test to test for the significance of the slope. As one looks at these slopes, it becomes apparent that the absolute magnitude of the slopes increases as the concentration of creatinine increases.
One can plot the slopes, as obtained with the first set of regressions, against the creatinine concentrations in the base pools. The results of such plots are shown in Fig. 12.2 for both the enzymatic and the Jaffe methods.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
200 300 400
0 700
creatinine (mmol/L) enzymatic slope vs creatinine
600 500
slope
100
0 0.05 0.10 0.15
0.200 200 300 400
creatinine (mmol/L)
jaffe creatinine slope vs creatinine
600 500
slope
100
y 0.0009x 0.0625 R2 0.9975
y 0.0002x 0.0316 R2 0.9678
Fig. 12.2: Regression of slope vs creatinine for bilirubin interference.
In both cases, the slopes are negative, but the scale for the kinetic method is much greater in magnitude than for the Jaffe method. Regressing the slopes vs the creati- nine concentrations is a form of multiple regression . The statistical results of this regression are shown in Tab. 12.3 for the kinetic method, under the heading of slope vs creatinine. The slope for this regression is −0.00092 and is much greater than the standard error of the slope. A t-test yields a value of 20 which is statistically signifi- cant because the value for P is less than 0.05. One could also plot the creatinine con- centrations of each pool vs the slopes and obtain a slope for this regression. The result is a slope of −1,087. These two regressions are inverses of each other, as shown by taking the reciprocal of −1,087, which is identical to −0.00092. The implication of the statistical significance of the slope vs creatinine regression means that the magnitude
12.1 Complex Interferences 125
of the interference changes not only with the variation in the bilirubin concentration, but also with the variation in the creatinine concentration. In other words, the inter- ference is analyte-dependent.
One problem with regressing the slopes vs the creatinine concentration proce- dure to perform the multiple regression analysis is that one loses degrees of freedom.
In this case, there is only one degree of freedom. The more degrees of freedom one has, the greater the statistical power of the test.
To circumvent the problem of loss of degrees of freedom, one can perform the multiple regression analysis using all the data at once. One needs to use a special sta- tistical program for that, or one can set it up as a function in a spreadsheet program.
Tab. 12.4 shows the results of a fully-executed multiple regression program output. Tab. 12.2 shows how the data must be arranged to use a fully executed mul- tiple regression program. The first three columns, labeled Bilirubin, Creatinine, and BiliCreat, represent the independent variables. The fourth column, labeled Result, represents the creatinine result reported by the analyzer at that particular bilirubin and creatinine concentration. The column labeled BiliCreat is a combination of the values in the Bilirubin and the Creatinine column. The BiliCreat column is now a new independent variable for the model of the regression. The creation of the BiliCreat column represents the keystone in developing a model for assessing analyte-depend- ent interference .
BiliCreat Creatinine Bilirubin Intercept
Slope −0.092 0.995 −0.062 0.975
SE slope 0.004 0.008 0.016 3.067
r-squared 0.9998 SE regression 3.3
F 11595 DF 8
SS regression 370,673 SS residuals 85
Tab. 12.4: Multiple regression analysis of interference slope vs creatinine for enzymatic method.
The BiliCreat column was created by multiplying the concentration of bilirubin by the concentration of Creatinine. If the creation of this new independent variable had been made by adding the two columns together, or by subtracting one column from another, then the newly created variable would not be independent from the other two. Because the new variable was created by a process (multiplication), it is linearly independent of the other two. Further, because the two variables used to create the third variable are still included in the regression process, the results gleaned from the newly created variable, BiliCreat, will not reflect a dependence on Creatinine alone or Bilirubin alone.
The results from the multiple regression analysis based on the newly created BiliCreat variable are shown in Tab. 12.4. The first thing to note is that the degrees of freedom are 8, which provides much more statistical power. The top row shows the
independent variable being analyzed. The first column shows results for the Biliru- bin-Creatinine interaction, the second column for Creatinine, the third column for Bilirubin and the fourth column for the intercept. The value for the intercept is 0.975, but its standard error is 3.067. The value for t is 0.3, and p>0.05, so it is not statisti- cally significant, which means that the regression should make sense. The value for r-squared is 0.998, which is very high and also a good indication that the regression analysis was carried out in an adequate manner. The slope for Creatinine is 0.995, which is nearly 1.0, which makes sense and the slope of Bilirubin is −0.062, with a t value of 3.8, with p <0.05, which is significant; this information implies that there is an interference caused by bilirubin which is independent of the creatinine. The slope for the BiliCreat variable is −0.092, which is identical to that obtained by the regres- sion of the slope vs creatinine. The value for t for this slope is 23, which is statistically significant. The significance of the slope for this variable is that it means that there is an interference caused by bilirubin that also depends on creatinine. One can write the formula that gives the result based on the regression study as
(12.3)
One can use this formula to predict a result based on the concentrations of creatinine and bilirubin. One can use the formula to find out how much interference there would be at any given concentration of bilirubin for any given concentration of creatinine.
Tab. 12.5 shows the table of the creatinine results and the effect of bilirubin as in Tab. 12.1, but this time for the Jaffe method for determining creatinine. Tab. 12.6 shows the regression results for this method. Again there is negative interference, but it is less than for the enzymatic method. Fig. 12.1 shows the graph of these results. The slope vs creatinine is only 0.00022 and the t-test result is only 5.5, which is not sig- nificant. Tab. 12.7 shows the three independent variable results for the Jaffe reaction method. One difference here in the calculations is that the column created by multi- plying the concentrations of bilirubin by those of creatinine, was then multiplied by 100 because the numbers were so small. The slope and the SE of the slope should be multiplied by 0.01 to make them equivalent to the values in Tab. 12.6. The multiplica- tion by 100 does not alter the results of the t-test. The value for t is 3.14, but with 8 degrees of freedom the critical value for t is 2.3, which is less than 3.1, so p <0.05, and the coefficient for analyte-dependent interference is statistically significant. Using a direct multiple regression calculation is more powerful than applying a simple linear regression multiple times.
Result =0.995[creatinine]−0.062[bilirubin]−0.092[bilirubin][creatinine]+0.975.
12.1 Complex Interferences 127
Bilirubin (μmol/L) Creatinine 1 (μmol/L) Creatinine 2 (μmol/L) Creatinine 3 (μmol/L)
0 81 317 551
100 64 297 535
200 68 290 526
300 65 282 505
Tab. 12.5: Jaffe reaction method creatinine bilirubin interference data.
Creatinine 1 vs Bilirubin
Slope −0.044 76.1 Intercept
SE slope 0.030 5.6 SE intercept
r-squared 0.523 6.6 SE regression
F 2 2 degrees of freedom
SSregression 97 88.2 SSresiduals
Creatinine 2 vs Bilirubin
Slope −0.112 313.3 Intercept
SE slope 0.021 4.0 SE intercept
r-squared 0.932 4.8 SE regression
F 27 2 degrees of freedom
SSregression 627.2 45.8 SSresiduals
Creatinine 3 vs Bilirubin
Slope −0.147 551.3 Intercept
SE slope 0.016 2.9 SE intercept
r-squared 0.978 3.5 SE regression
F 88.926 2 degrees of freedom
SSregression 1,080 24.3 SSresiduals
Slope vs Creatinine
Slope −0.00022 −0.032 Intercept
SE slope 0.00004 0.015 SE intercept
r-squared 0.968 0.013 SE regression
F 30 1 degrees of freedom
SSregression 0.005 0.00018 SSresiduals
Creatinine vs Slope
Slope −4414 −129.5 Intercept
SE slope 805 88.3 SE intercept
r-squared 0.968 59.6 SE regression
F 30 1 degrees of freedom
SSregression 106,893 3,558 SSresiduals
Tab. 12.6: Linear regression analysis of Jaffe creatinine with bilirubin.
BiliCreat Creatinine Bilirubin Intercept
Slope −0.022 1.011 −0.032 −6.264
SE slope 0.007 0.013 0.025 4.735
r-squared 0.9995 SE regression 5.1
F 5,476 DF 8
SS regression 424,518 SS residuals 207
Tab. 12.7: Multiple regression analysis of bilirubin interference vs creatinine.
Fig. 12.3 shows another enzymatic assay for creatinine, this time using the Vitros, and its interference by bilirubin. It is plotted in a fashion similar to that of Fig. 12.1.
creatinine (mmol/L)
300 250 200 150 100 50 0
200
0 800
bilirubin (mmol/L)
Jaffe creatinine interference by bilirubin
600 400
creatinine1
creatinine2 creatinine3
creatinine (mmol/L)
400 350 300 250 200 150 100 50
00 200 800
bilirubin (mmol/L)
Vitros interference by bilirubin
600 400
creatinine1
creatinine2 creatinine3
Fig. 12.3: Difference in plot appearance for bilirubin interference for Jaffe creatinine and enzymatic creatinine methods; the interference with the enzymatic (Vitros) method is nonlinear.
Not only are the curves formed by each of the varying concentrations of creatinine not parallel, suggesting analyte-dependent interference , but they are not straight.
In fact, these curves need to be fitted with a second-order polynomial regression to adequately fit the data. As an example, at the high concentration of creatinine, the regression that fits the data is given by