# Linearity: Non-linear response - Quick Response Requested

Hello to all,

We are validating an HPLC method for related substances of an Active Pharmaceutical Ingredient (API) and we have found that there isn´t a linear relationship between response and the concentration of the analyte at impurity levels. It has been evaluated by visual inspection and using the most common statistycal parameters to do it. Main results of this statistycal analysis are: when we plot signals as a function of the analyte concentration we find that the curve has the potencial tendency and, because that, we don’t have good precision for response factors and the residual graph obtained is a parabolic curve.

I have never found that before, which means that low concentrations have more response than higher concentrations (Note that the lowest concentrations are higher than the Quantitation Limit using the signal-to-noise method to determine it).

In that case, and according to ICH Q2B, test data may need to be subjected to a mathematical transformation prior to the regression analysis. But, what mathematical transformation is needed? Is it normal for a HPLC method for related substances of an API? Does it mean that for the routine analysis the calibration curve must always be carried out prior to the analysis of samples?

I am looking forward to your kind responses. Thank you.

Dear
First of all you should decide the range for Linearity, whether u r following the proper range or not? As per the ICH Q2R1 (Current) “for the determination of an impurity: Range should be from the reporting level of an impurity to 120% of the specification”. So this is quite changed from the Normal Linearity range for ASSAY tests. And how come ? low conc. having more response than for higher conc. There must be OOS that u need to investigate!! To establish linearity 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. these are the mutual criteria of ICH Q2R1 and USP. in USP limit for r=correlation coefficient has been given and that must be complied.

Regards,

Wow, this is highly unusual. Usually, non-linearity usually occurs as a result of response saturation at higher concentrations. I have never encountered a result where lower concs respond more intensely than higher concs. Ordinarily I wouldn’t query the data, but I would most certainly re-evaluate the plot. Additionally, have you ensured chromatographic purity via PDA or MS? Eliminated solvent effects? Considered baseline subtraction?

LOQ established using signal to noise. Following on from your post, your LOQ should technically be lower than your LOD if lower concs are giving higher responses, yes? But I am guessing this is not the case, since, if using S/N method, you would have used very low conc to establish S/N, then performed calculation and relevant multiplications to establish LOD and LOQ. You would then have tested LOD and LOQ concs for repeatability to confirm, yes? LOD should theoretically give poorer repeatability than LOQ due to expected lower response, but I get the feeling this was not the case and LOQ response was, as expected, better than LOD response. This you would have done before trying to establish your Linearity, because, as stated, your linearity samples were higher than LOQ when you encountered your problem. What was your system suitability like for each linearity concentration when you did the test, or did you make single measurements for each test conc? I would guess that you either have a system fault, or the analytical system is compromised in some way…degradation, solvent interferences, etc.

Dear Sirs,

Thank you very much for your comments. As Marwaan suggested, we have studied this Linearity several times and we have confirmed that the curve has a potencial tendency and graph residual shows a clear porabolic curve.

In relation to what Marwaan asked:

• We haven´t checked chromatographic purity because we work with Pharmacopeias reference standards. In addition, we have confirmed this behaviour using the Ph Eur reference standard and USP reference standard. On the other hand, I think we do not have solvent effects and baseline correction is not needed.

• LOQ/LOD: We have checked our LOQ/LOD precision and we have found that, as expected, LOQ has better response, and so that, better precision than LOD.

• System suitability: System suitability for each linearity concentration is OK because we have %RSD of 1% for each level at the most.

• I don’t think we have a system fault because we have obtained good results for linearity at impurity levels when working with other API’s and with the same HPLC.

How we are dealing with:

Because we have a potencial tendency, we are using the logaritmic mathematical transformation to deal with raw data, and we are obtaining a very good linear adjustment which confirm the potencial behaviour between concentration and Area. After that, residual graph shows an aleatory distribution along the x-axis. As a result, we think that for routine analysis the calibration curve must always be carried out prior to the analysis of samples and calculate samples with the same mathematical transformation. The problem is that it means a great invest of time to analyse samples. What do you think?

Regards,

Fantastic! log conversion to invert data, obtain linear response. I didn’t consider this. Typically see this kind of behaviour in ionic analysis as a consequence of the Nernst equation, such as in fluorine analysis. Have never seen it with LC data though. Perfectly acceptable as per ICH and Pharmas. Good post. I will keep this in mind when we do our method validations for Cleaning Validation. Never know what you might encounter at those low concs!!!

As far as dealing with your sample analysis, most CDS software has the capability to automatically perform the necessary transform and calculate the relevant cal curve. I would suggest you use a system suit standard up front, and use a multipoint calibration with the relevant quantification maths applied (single injection per cal standard is acceptable, as your system suit is already demonstrated). It is usually good chromatography practice to do system suit up front before running samples or calibration standards in any case. Means you invest the time constructively in ensuring your system is ok before analysing samples. How many times have you had to repeat samples because system suit was not demonstrated beforehand, analyst is in a hurry to go home, takes a chance on a system, etc? Just good practice, imo.

Thanks for the info and the lesson learned!!!

[quote=NVL]Hello to all,

We are validating an HPLC method for related substances of an Active Pharmaceutical Ingredient (API) and we have found that there isn´t a linear relationship between response and the concentration of the analyte at impurity levels. It has been evaluated by visual inspection and using the most common statistycal parameters to do it. Main results of this statistycal analysis are: when we plot signals as a function of the analyte concentration we find that the curve has the potencial tendency and, because that, we don’t have good precision for response factors and the residual graph obtained is a parabolic curve.

I have never found that before, which means that low concentrations have more response than higher concentrations (Note that the lowest concentrations are higher than the Quantitation Limit using the signal-to-noise method to determine it).

In that case, and according to ICH Q2B, test data may need to be subjected to a mathematical transformation prior to the regression analysis. But, what mathematical transformation is needed? Is it normal for a HPLC method for related substances of an API? Does it mean that for the routine analysis the calibration curve must always be carried out prior to the analysis of samples?

I am looking forward to your kind responses. Thank you.[/QUOT