Should we use "only linear relation for a calibration curve"

[Karthik C]

I have been working on a LCMS method development. I am not getting a standard graph with linear relationship between the data points. Is it mandatory that we should get only a linear relationship as I observed that we have a few types on excel [quadratic, polynomial, logarithmic]. Tried to get some references but couldn't get a satisfying answer. Can I get some help regarding this issue. Thank you

[dap]

Nope, ICH Validation of Analytical Procedures https://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Quality/Q2_R1/Step4/Q2_R1__Guideline.pdf :

2. LINEARITY
A linear relationship should be evaluated across the range (see section 3) of the
analytical procedure. It may be demonstrated directly on the drug substance (by
dilution of a standard stock solution) and/or separate weighings of synthetic mixtures
of the drug product components, using the proposed procedure. The latter aspect can
be studied during investigation of the range.
Linearity should be evaluated by visual inspection of a plot of signals as a function of
analyte concentration or content. If there is a linear relationship, test results should
be evaluated by appropriate statistical methods, for example, by calculation of a
regression line by the method of least squares. In some cases, to obtain linearity
between assays and sample concentrations, the test data may need to be subjected to
a mathematical transformation prior to the regression analysis. Data from the
regression line itself may be helpful to provide mathematical estimates of the degree
of linearity.
The correlation coefficient, y-intercept, slope of the regression line and residual sum of
squares should be submitted. A plot of the data should be included. In addition, an
analysis of the deviation of the actual data points from the regression line may also be
helpful for evaluating linearity.
Some analytical procedures, such as immunoassays, do not demonstrate linearity
after any transformation. In this case, the analytical response should be described by
an appropriate function of the concentration (amount) of an analyte in a sample.
For the establishment of linearity, a minimum of 5 concentrations is recommended.
Other approaches should be justified.

[lmh]

MS is often non-linear. You should, however, be suspicious of suspicious behaviour. For example, electrospray tends to tail off as concentration rises; if your calibration curves get steeper rather than flatter at higher concentration, maybe something odd is going on, and it's good to understand what.
If the curve becomes very flat at high concentration, then it becomes increasingly hard to calculate the concentration - small errors in the signal lead to large changes in calculated concentration. For this reason, although it's not evil to fit a curve through points that are obviously on a curved line, it is evil not to consider the consequences, and try to analyse samples over the range where the measurement works with good accuracy and precision.

Fitting a straight line through points that are on a curve, and declaring that everything is fine because the R-squared value doesn't look too bad (it rarely does) is definitely evil.

By the way, it's almost always a good idea to do the curve-fitting in the instrument's data analysis software rather than Excel. For a start it's usually easier (especially if you have to reintegrate for any reason), and also it will provide all sorts of useful options such as weighting of points. Most instrument software will also refuse to extrapolate too wildly (it is much, much more dangerous to extrapolate a quadratic fit to MS data than a linear fit to PDA data), while Excel will do what you ask it to, whether or not that's sensible.

[James_Ball]

MS is often non-linear. You should, however, be suspicious of suspicious behaviour. For example, electrospray tends to tail off as concentration rises; if your calibration curves get steeper rather than flatter at higher concentration, maybe something odd is going on, and it's good to understand what.
If the curve becomes very flat at high concentration, then it becomes increasingly hard to calculate the concentration - small errors in the signal lead to large changes in calculated concentration. For this reason, although it's not evil to fit a curve through points that are obviously on a curved line, it is evil not to consider the consequences, and try to analyse samples over the range where the measurement works with good accuracy and precision.

Fitting a straight line through points that are on a curve, and declaring that everything is fine because the R-squared value doesn't look too bad (it rarely does) is definitely evil.

By the way, it's almost always a good idea to do the curve-fitting in the instrument's data analysis software rather than Excel. For a start it's usually easier (especially if you have to reintegrate for any reason), and also it will provide all sorts of useful options such as weighting of points. Most instrument software will also refuse to extrapolate too wildly (it is much, much more dangerous to extrapolate a quadratic fit to MS data than a linear fit to PDA data), while Excel will do what you ask it to, whether or not that's sensible.

Only lawyers and theoretical chemists insist on curve fits that are perfectly linear )

[tom jupille]

Or, as Ted Neubert, my undergraduate instrumental analysis prof years ago, used to say: "Nothing is truly linear but everything is approximately linear over a narrow enough range."