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