Linearity for Assay by HPLC Method

1.0 OBJECTIVE 

To lay down the procedure for the Linearity study for Assay by HPLC Method

2.0 SCOPE

This SOP is applicable to for the Linearity study for Assay by HPLC Method in company.

3.0 BACKGROUND 

NIL

4.0 RESPONSIBILITY

4.1 QC- Chemist

4.2 QC-Executive 

4.3 Head Analytical research or his designee to ensure overall compliance.

5.0 PROCEDURE

5.1 ICH defines linearity of an analytical procedure as its ability (within a given range) to obtain test results that are directly proportional to the concentration (amount) of analyte in the sample.

5.2 Linearity may be demonstrated directly on the test substance (by dilution of a standard stock solution) or by separately weighing synthetic mixtures of the test product components.

5.3 Linearity is determined by a series of five to six injections of five or more standards whose concentrations span 80–120 percent of the expected concentration range. The response should be directly proportional to the concentrations of the analytes or proportional by means of a well-defined mathematical calculation. A linear regression equation applied to the results should have an intercept not significantly different from zero. If a significant nonzero intercept is obtained, it should be demonstrated that this has no effect on the accuracy of the method.

5.4 A graph is plotted with the relative responses on the y-axis and the corresponding concentrations on the x-axis, on a log scale. The obtained line should be horizontal over the full linear range. At higher concentrations, there will typically be a negative deviation from linearity.

5.5 Plotting the sensitivity (response/amount) gives a clear indication of the linear range. Plotting the amount on a logarithmic scale has a significant advantage for wide linear ranges. ICH recommends the linearity curve’s correlation coefficient, y-intercept, slope of the regression line and residual sum of squares for accuracy reporting. A plot of the data should be included in the report. In addition, an analysis of the deviation of the actual data points from the regression line may also be helpful for evaluating linearity.

5.4 Experimental Determination

5.4.1 Prepare five standard solutions of the analyte at 80%, 90%, 100%, 110%, and 120% of the method concentration using serial dilutions from a stock solution.

5.4.2 Prepare five test solutions of the analyte at 80%, 90%, 100%, 110%, and 120% of the method concentration using serial dilutions from a stock solution.

Note: Some People do the 50,75,100,125 and 150% concentrations for linearity check. Some people combined accuracy and linearity. There is nothing wrong in doing so.

5.5.3 Make triplicate injections (in practice 5 injections) at each concentration of standard solution.

5.5.4 Make three (in practice 5 injections) injections at each concentration of test solution, adequately bracketed by the standard.

5.5.5 Make sure to inject samples from the lowest concentration to the highest concentration to reduce the effects, if any, of carryover from the higher concentration samples.

5.5.6 Calculate the % RSD at each concentration.

5.5.7 Plot the analyte concentration for each set of dilutions separately versus the signal response (average area of each set of injections).

5.5.8 Perform linear regression analysis, but do not include the origin as a point made and do not force the line through the origin.

5.5.9 Plot the sign and magnitude of the residuals versus analyte concentration.

5.5.10 Check residual plot for outlying values and curvature.

5.5.11 Evaluate y intercept to determine if there is significant departure from zero.

5.5.12 Recommendations

5.5.12.1 The %RSD for the area of five replicate injections due to the major peak obtained from standard solution preparation should not be more than 2.0.

5.5.12.2 Theoretical plates(N) for the main peak from the first injection of standard solution Preparation should not be less than 3000.

5.5.12.3 Tailing Factor(T) for the main peak from the first injection of standard solution Preparation should not be more than 2.0.

5.5.12.4 The %RSD for the area of standard solutions at 80,90,100,110,120 % triplicate( or 5) injection should not be more than 2.0.

5.5.12.5 The Correlation Coefficient(r2) for the Average area at different concentrations should not be less than, 0.9999 ( in practice 0.99 or some 0.999). 

5.5.12.6 There should be no curvature in the residuals plot. 

5.5.12.7 The y intercept should not significantly depart from zero (e.g., area response of y intercept should be less than 5% of the response of the mid range concentration value).

5.5.12.8 Eg: Let me Explain by taking an example

Prepare 50,75,100,125 and150 % sample solutions and inject in into the chromatographic system. 

[ As per ICH, we should present the correlation coefficient(r), y-intercept, slope of the regression line and residual sum of squares(R² ) and a plot ( graph)]

5.5.12.9  I have the following values after injecting into the chromatographic system. 

5.5.12.10 From  the above values plot the graph with concentrations on X-axis and  Average area on Y-axis and adding the trend line with linear regression. 

Sample Solution Concentration[%]                         Average Area

50                                                                                       374200

75                                                                                       560490

100                                                                                     746792

125                                                                                     937516

150                                                                                    1126522

Legend: On X-axis concentration is taken and Y-axis average area is taken.

From the above graph we have to observe the following things

5.5.12.10  Linearity

Observe the graph for linear response in the area obtained against the concentration injected. Our graph passed this test.  

5.5.12.11 Regression values 

Linear regression analyzes the relationship between two variables, X and Y. For each concentration , you know both X and Y and you want to find the best straight line through the data.

The value r2 is a fraction between 0.0 and 1.0, and has no units. An r2 value of  0.0 means that knowing X does not help you predict Y. There is no linear relationship between X and Y, and the best-fit line is a horizontal line going through the mean of all Y values.  When r2 equals 1.0, all points lie exactly on a straight line with no scatter. Knowing X lets you predict Y perfectly.

5.5.12.12 Slope and intercept

First understand the difference between positive, negative, zero, and undefined slopes. In summary, if the slope is positive, y increases as x increases, and the function runs "uphill" (going left to right). If the slope is negative, y decreases as x increases and the function runs downhill. If the slope is zero, y does not change, thus is constant—a horizontal line. 

The Y intercept is the Y value of the line when X equals zero. It defines the elevation of the line.]

Regression Equation(y) = ax +b

b = The slope of the regression line 

a = The intercept point of the regression line and the y axis

x = Variable

After applying the above equation , 

R² =1

[The coefficient of determination, r ², is 1 which means that 100% of the total variation in y can be explained by the relationship between x and y.  There are no unexplained remains. Yes, it is a "good fit"] 

Slope= 18460

[As the slope is positive, X increases as Y increases. ].

Y-intercept=18816