Terminology in Analytical Methods Validation

Analytical Methods Validation Terminology

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Evaluation of Data in Analytical Methods Validation

During the method validation there is huge quantity of the data is generated. The data generated should be evaluated with statistical methods. Here i am listing the statistical methods used in the evaluation of the data generated during the method validation
1. Standard Deviation 
2. Relative standard deviation
3. Linear Regression 


1. Standard deviation:(σ)
It is used to measure the variability in the data from the average value. A low standard deviation indicates that the data points tend to be very close to the average, whereas high standard deviation indicates that the data are spread out over a large range of values.


It is square root of the variance. variance is the average of squared differences from the mean(or average). Average is sum of the individual results divided by sum of the number of individual values 


Eg: calculation of average, variance and Standard deviation.


You and your friends have just measured the heights of your dogs (in millimeters) and the heights are: 600mm, 470mm, 170mm, 430mm and 300mm.


Average = 600 + 470+170+430+300/5= 394


calculate the variance values from the mean for above 5 values 


mean is 394 so the difference from mean for the first value is 600-394=206 calculate for the others also
                       206^2 x  76^2 x (-224^2) x 36^2 x (-94^2)
Variance =----------------------------------------------- = 21,704
                                                      5


So the variance is 21,704 and standard deviation is square root of Variance 


SD(σ) = Square root of 21,704 =147


Do not worry about these calculation Excel gives the functions to calculate the average (AVERAGE) and standard deviation(STDEV) directly.


Relative standard Deviation(RSD):
It is obtained by multiplying the standard deviation with 100 and divided by average


RSD = 100 σ / Average


These two parameters are most commonly used in the analysis of the data.


Eg: Following table shows the data obtained during the sample precision with n=6 with respective areas in the chromatogram.

Sample Area 
 1              212135 
 2              212356 
 3              212455 
 4              212344 
 5              212433 
 6              212566 
 Avg         212381.5 
 SD           144.8541 
 RSD        0.068205


Linear Regression Analysis:
Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.


A valuable numerical measure of association between two variables is the correlation coefficient, which is a value between -1 and 1 indicating the strength of the association of the observed data for the two variables.


A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0). Do not worry about theory. The linear regression is useful for the relation between the concentration and against the response in the Linearity parameter of the Analytical method validation. This can be done by drawing the graph between the Concentrations against the response in the chromatographic system.


Eg: Linearity results of Drug substance X shown in the following table 

Conc   Area 
 25      41369 
 50      51787 
 75      60972 
 100    71419 
 125    80140 
 150    89444


Draw the graph with Area on y-axis and concentration in x-axis . Add trend line to that give the following graph in Excel.

Calculations in Analytical Methods(HPLC and GC)

I want to write this topic for giving an idea about how to calculate the Assay, related substances and Residual solvents.

Calculations for Assay Method (Tirtimetry)

Titire value(Sample - Blank) x M x Factor x 100 x 100

--------------------------------------------------------

                            Ws x (100-LOD)

M= Molarity of the volumetric solution 

Ws= Weight of the sample 

Factor = Factor for Drug substance 

LOD is Loss on drying or MC is water content 

Calculations for Assay Substances Method (HPLC)

             

                    At x Ws x P x (100-WC of std)

Assay % = ----------------------------------

                    As x Wt x (100-WC of sample)

At = Area due to sample Preparation 

As= Area due to working standard solution 

Wt= Weight of the sample in mg

Ws= Weight of the working standard

P=Potency  or Assay of the standard 

WC=% water content of the sample or standard 

Note: WC may be replaced by LOD based on the drug substance 

Calculations for Related Substances Method (HPLC)

                                          ri

% of Known Impurity = ---x 100 X RF

                                         rs

                                              ri

% of unknown Impurity = ---x 100

                                              rs

Total Impurities = Sum of all known and unknown impurities 

ri =Area of each impurity Peak in the chromatogram of the sample solution preparation

rs=Sum of areas of Main drug and all impurity Peaks in the chromatogram of the sample solution preparation

RF= Response factor 

Calculations for Residual solvents Method (GC)

     

    At        Volume of solvent taken x density     0.1 ml       dilution of sample(ml)

= ------x -------------------------------------------x ---------x-------------------------------x 10 ^ 6

    As                     10 ml                                                                   10 ml        Weight of the sample

At= Area of the solvent in the sample - Blank

As= Area of the solvents in the standard -blank 

Note: Volume of the solvents taken should be mentioned in microliters 

As we are multiplying with 10 power 6 we can get the results in PPM 

Note: Refer Merck index for solvent densities

Where to start Method Validation

The Analytical methods methods must be validated before they are going to use. Method validation is a laborious process include number of parameters such as specificity, Linearity, precision etc... As this process involves number of parameters a question may arise where to start the validation?


Before answering this question i would like to mention specificity should be done separately along with Forced degradation studies.


Now i am suggesting a sequence for method validation parameters to be followed during analytical method validation.


For Assay method
System suitability ----> System precision ----> Sample precision ----> Solution stability and mobile phase stability----> accuracy ----> Linearity ----> Ruggedness ----> robustness


For Related substances and Residual solvents method
System suitability ----> System precision  ----> Sample precision ----> Solution stability and mobile phase stability ----> RRF and RRT Establishment ---->LOD ---->LOQ----> Precision at LOQ ---->Accuracy at LOQ ----> Accuracy ----> Linearity ----> Ruggedness ----> Robustness

Validation of Compendial methods

Validation of Analytical procedures which are described in the phamacopoea are to be treated separately unlike inhouse analytical procedures. 

For in-house analytical Procedures the manufacturer must perform full validation studies such as Specificity, precision, linearity, accuracy, ruggedness and robustness for assay methods and LOD and LOD as additional tests + assay parameters for Related substances and Residual sovents methds. 

For regualtory analytical procedures method suitability should be performed instead of method validation. This should include specificity, intermediate precision and stability of the sample solution.

Care should be taken because the regulatory/ compendial analytical procedures may not be stability indicating.

Parameters for Method Validation

For an efficient validation process, it is important to specify the right validation parameters and acceptance criteria. The method’s performance parameters and limits should be based on the intended use of the method. It is not always necessary to validate all analytical parameters available for a specific technique.

For example, if the method is to be used for qualitative trace level analysis, there is no need to test and validate the method’s limit of quantitation, or the linearity over the full dynamic range of the equipment. The more parameters, the more time it will take to validate.

The selection of validation parameters and acceptance criteria should be based on business, regulatory and client requirements and should be justified and documented.

 ICH validation characteristics

Type of analytical procedure	Identification	Testing  for impurities	Assay - content/potency
characteristics		quantitat.   limit
Accuracy	-	+            -	+
Precision     Repeatability     Interm.Precision	- -	+            -        + (1)       -	+                       + (1)
Specificity (2)	+	+            +	+
Detection Limit	-	- (3)        +	-
Quantitation Limit	-	+            -	-
Linearity	-	+            -	+
Range	-	+            -	+

-      signifies that this characteristic is not normally evaluated

+     signifies that this characteristic is normally evaluated

(1)   in cases where reproducibility (see glossary) has been performed, intermediate precision is not needed

(2)   lack of specificity of one analytical procedure could be compensated by other supporting analytical procedure(s)

(3)   may be needed in some cases

Specificity is the ability to assess unequivocally the analyte in the presence of components which may be expected to be present. Typically these might include impurities, degradants, matrix, etc.

The accuracy of an analytical procedure expresses the closeness of agreement between the value which is accepted either as a conventional true value or an accepted reference value and the value found.

The precision of an analytical procedure expresses the closeness of agreement (degree of scatter) between a series of measurements obtained from multiple sampling of the same homogeneous sample under the prescribed conditions. Precision may be considered at three levels:  repeatability, intermediate precision and reproducibility (also called ruggedness) 

The  detection limit of an individual analytical procedure is the lowest amount of analyte in a sample which can be detected but not necessarily quantitated as an exact value.

The quantitation limit of an individual analytical procedure is the lowest amount of analyte in a sample which can be quantitatively determined with suitable precision and accuracy. The quantitation limit is a parameter of quantitative assays for low levels of compounds in sample matrices, and is used particularly for the determination of impurities and/or degradation products.

The linearity of an analytical procedure is its ability (within a given range)  to obtain test results which are directly  proportional to the concentration (amount) of analyte in the sample.

The range of an analytical procedure is the interval between the upper and lower concentration (amounts) of analyte in the sample (including these concentrations) for which it has been demonstrated that the analytical procedure has a suitable level of precision, accuracy and linearity.

The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters and provides an indication of its reliability during normal usage.

USP validation characteristics

Parameter	Assay (cat-I)	Assay (cat-II)		Assay (cat-III)
		Quantitative	Limit tests
Accuracy	Yes	Yes	*	*
Precision	Yes	Yes	Yes	Yes
Specificity	Yes	Yes	Yes	*
Limit of detection	No	No	Yes	*
Limit of quantitation	No	Yes	Yes	*
Linearity	Yes	Yes	Yes	*
Range	Yes	Yes	*	*
Ruggedness	Yes	Yes	Yes	*

Cat-I: Quantification of major compounds

Cat-II: Impurities

Cat-III: Performance characteristics

* May be required

According to the ICH, accuracy, any type of precision and limits of detection and quantitation are not required if the analytical task is for identification purposes. For assays in USP Category 1, the major component or active ingredient to be measured is normally present at high concentrations; therefore, validation of limits of detection and quantitation is not necessary.

Acceptance criteria for the specifications also depend on the intended use of the method.

In practice:

After reviewing the method validation parameters of ICH and USP, we finally concluded the following parameters for method validation.

Accuracy, specificity(with forced degradation), Linearity, Precision(system and sample), Robustness(method parameter variations and Solution and mobile phase stability) Ruggedness and system suitability for Assay method validation.

Accuracy, specificity(with forced degradation), Linearity, Precision(system and sample), Limit of detection, Limit of quantification(precision and accuracy at LOQ level), Robustness(method parameter variations and Solutions and mobile phase stability) Ruggedness and system suitability for Related substances method validation.