Emil W. Ciurczak, Contributing Writer03.11.24
Over the years, I have commented that all the chemistry we learned in college simply disappears when we get our first job. All too many “degreed” chemists seem to forget how to calculate significant digits or molarity or any such simple thing. As more pharma and biopharma companies are moving into the 21st century, all too many analysts are enamored by instrumentation, they forget how to make a simple solution properly.
Why are significant figures important? Let me give you a real-life example: a number of years back at a former job, a set of stability data came across my desk. The “unknowns” level was 0.05% and my supervisor wanted to send a recall notice, because the unknowns were above limit. The limit? Less than 0.1%. So, I said that it passes, not fails. How did I ascertain that? The data was officially reported to one sig. fig., so he rounded 0.05 to 0.1 and claimed it was above the limit. I tried to convince him using no less than five analytical texts that when even numbers precede the “5” is truncated, while when odd numbers precede the “5” is rounded up. The reason is simply that in any measurement, the last stated digit, unless noted otherwise, is understood to be +/- 1 unit. In other words, 0.05 could be 0.06 or 0.04. If all numbers ending in 5 were rounded up, there would be a bias and the answer would always be higher, indicating your method was undermeasuring. Now, 1, 3, 5, 7, and 9 are odd numbers, so 0.15 becomes 0.2. Since 0, 2, 4, 6, and 8 are even numbers, the 0.05 becomes 0 and the product does not fail stability testing. He ignored me and recalled the product, costing the company many thousands of dollars.
Another quick example was a 10-tablet CU run. The stated values were, in % of label claim, 97.52, 99.86. 100.4, 102.5, 98.74, 104.3, 102.8, 99.66, 101.7, and 97.89. The average was listed as 100.5%.
This is wrong, largely because, for example, 97.52% implies that the error is +/- 0.01%; the 100.4% assay implies that the error was 10-times greater, namely 0.1%! Simply stated, half the values were 10-times more accurate than the other half. Either the values below 100% be reported to a single digit after the decimal point or the values above 100% be reported to two digits after the decimal. Either your error is 0.1% or 0.01%; the same assay procedure cannot have both.
So, even as you adopt PAT/QbD methodology, you will never move away from traditional technologies and lab rules. For example, HPLC is likely always going to be the “go-to” reference technique for calibrating the PAT instruments, which is ironic because HPLC wasn’t accepted by the FDA until almost 1980. However critical it is when used for a reference method, I have witnessed some strange lab techniques over the years. A simple mobile phase for LC is a 50:50 methanol/water solution. I have seen it made by measuring 500mL of methanol into a liter flask and bring to volume with water.
Another company measured 500mL of water into a liter flask and bring to volume with methanol. Yet another (most, actually) pours 500mL of water and 500mL of methanol into a liter flask and mix, ignoring the final volume. Clearly, all will generate different chromatograms. Spoiler alert: the third method is correct.
Another enemy of PAT/QbD is a common mind-set from the 1960s. Namely, when placebos were generated for clinical trials, it was important that they look just like the tablets containing the active (i.e., size, color, and weight). So, the formulators usually used one of the excipients to make up for the lost mass of the API. This is fine for traditional lab analyses, such as HPLC or titrations, but it is not good for spectroscopic analyses of the intact tablets. Since methods such as near-infrared “see” all the ingredients in a dosage form, the ratio of the excipients needs to remain constant. The best way to make a PAT placebo is to simply make a tablet from the tablet mix, minus the active, keeping all the other proportions constant. This “cocktail” segways into another difference in process monitoring versus lab analyses: the correlation coefficient.
The standard lab procedure has been, and mostly still is, to first remove the API or material to be analyzed from its matrix. Simply stated, nearly every lab analysis depends on determining the analyte, despite its matrix. A tablet, capsule, or paste is normally dissolved in some solvent, filtered, and an analysis performed: titration, thin-layer, gas, or liquid chromatography, atomic absorption or emission, or even an electrochemical method (i.e., polarography, ion selective electrodes, etc.). An analogy might be reading a letter: we open the envelope, unfold the contents, and read the words. In something like NIRS, we read the contents folded, inside the envelope. Consequently, unlike an HPLC chromatogram, there is seldom an area where a NIR spectrum has a baseline with zero absorbance. Why does that matter? Basically, the way the equation is built—on actual spectra, with values from a reference method—when values are plotted (NIR v. HPLC), the resultant calibration line may not go through zero, like a UV/Vis or HPLC calibration (Beer’s law plot) would.
The linearity of a traditional method may be inferred from the calibration plot (curve) by the correlation coefficient, R. That is because the spectra are carefully generated with known solutions of pure reference material in a known volume. The absorbance maximum (UV or Visible) or peak height/area (GC or LC) is easily distinguished and increases in a linear fashion. In the case of simple Beer’s law, yes, the R is a strong indicator for linearity.
In a multivariate technique (spectroscopic examination of the dosage form), even when the analyte is missing (true placebo), there will be an absorbance value seen. In addition, there is an excellent chance that there are very likely absorbances from materials in the matrix imposing themselves on the analyte spectrum—if NIR was easy, it would have been used decades ago. Consequently, the R or R2 merely indicate that there is some correlation between the observed wavelength(s) and the analyte concentration. It does not prove linearity; it just assumes causation.
Unfortunately, the EMA, FDA, and USP Guidances and chapter <856>, which was recently rewritten by a UV/Vis expert, not a NIR person, all claim R is the linearity. Not to beat the subject to death, but statistics are usually used to show inequalities: the t-test will tell you two methods are not significantly different, a Q-test will tell you that a single value does not belong in a set—it is significantly different.
And the list goes on. So, from my experience, the correlation coefficient, in reality, will tell you that a single point of points does not statistically correlate with another set. It has little to do with linearity. For an example, when the transmittance of a set of samples is calculated and graphed v. the concentrations, the graph is parabolic. So, to make it look better, we use a logarithm to generate a straight line.
Either curve works for an analysis, just that one looks nicer! So, in essence, even ideal Beer’s law (the Beer-Bouget-Lambert law, actually) isn’t a straight line and needs a “fix.”
To summarize, if a company wishes to save money and make a better product through a PAT/QbD program, they need to work with their chemometricians and statisticians when designing and validating the process control technologies. I would strongly advise any company willing to begin a PAT program to tighten up the training of the lab personnel validating all the software and hardware used in the production of drugs. You don’t have the option of re-analyzing a sample set after you have finished making the full batch of millions of tablets or capsules.
Emil W. Ciurczak, also known as the NIR Professor, has roughly 50 years of cGMP pharmaceutical experience and more than 35 years of Near-Infrared Spectroscopy (NIRS) experience with industries, universities, and instrument manufacturers. Emil teaches courses in NIRS, NIR/Raman, Design of Experiment, and PAT/QbD; has designed and patented hardware and software (including hardware and software related to anti-counterfeiting; written numerous technical texts and chapters; published extensively in journals; and presented hundreds of technical papers at many conferences, worldwide. He has worked in the pharmaceutical industry since 1970 for companies that include Ciba-Geigy, Sandoz, Berlex, Merck, and Purdue Pharma, where he specialized in performing method development on most types of analytical equipment. For more info: [email protected].
Why are significant figures important? Let me give you a real-life example: a number of years back at a former job, a set of stability data came across my desk. The “unknowns” level was 0.05% and my supervisor wanted to send a recall notice, because the unknowns were above limit. The limit? Less than 0.1%. So, I said that it passes, not fails. How did I ascertain that? The data was officially reported to one sig. fig., so he rounded 0.05 to 0.1 and claimed it was above the limit. I tried to convince him using no less than five analytical texts that when even numbers precede the “5” is truncated, while when odd numbers precede the “5” is rounded up. The reason is simply that in any measurement, the last stated digit, unless noted otherwise, is understood to be +/- 1 unit. In other words, 0.05 could be 0.06 or 0.04. If all numbers ending in 5 were rounded up, there would be a bias and the answer would always be higher, indicating your method was undermeasuring. Now, 1, 3, 5, 7, and 9 are odd numbers, so 0.15 becomes 0.2. Since 0, 2, 4, 6, and 8 are even numbers, the 0.05 becomes 0 and the product does not fail stability testing. He ignored me and recalled the product, costing the company many thousands of dollars.
Another quick example was a 10-tablet CU run. The stated values were, in % of label claim, 97.52, 99.86. 100.4, 102.5, 98.74, 104.3, 102.8, 99.66, 101.7, and 97.89. The average was listed as 100.5%.
This is wrong, largely because, for example, 97.52% implies that the error is +/- 0.01%; the 100.4% assay implies that the error was 10-times greater, namely 0.1%! Simply stated, half the values were 10-times more accurate than the other half. Either the values below 100% be reported to a single digit after the decimal point or the values above 100% be reported to two digits after the decimal. Either your error is 0.1% or 0.01%; the same assay procedure cannot have both.
So, even as you adopt PAT/QbD methodology, you will never move away from traditional technologies and lab rules. For example, HPLC is likely always going to be the “go-to” reference technique for calibrating the PAT instruments, which is ironic because HPLC wasn’t accepted by the FDA until almost 1980. However critical it is when used for a reference method, I have witnessed some strange lab techniques over the years. A simple mobile phase for LC is a 50:50 methanol/water solution. I have seen it made by measuring 500mL of methanol into a liter flask and bring to volume with water.
Another company measured 500mL of water into a liter flask and bring to volume with methanol. Yet another (most, actually) pours 500mL of water and 500mL of methanol into a liter flask and mix, ignoring the final volume. Clearly, all will generate different chromatograms. Spoiler alert: the third method is correct.
Another enemy of PAT/QbD is a common mind-set from the 1960s. Namely, when placebos were generated for clinical trials, it was important that they look just like the tablets containing the active (i.e., size, color, and weight). So, the formulators usually used one of the excipients to make up for the lost mass of the API. This is fine for traditional lab analyses, such as HPLC or titrations, but it is not good for spectroscopic analyses of the intact tablets. Since methods such as near-infrared “see” all the ingredients in a dosage form, the ratio of the excipients needs to remain constant. The best way to make a PAT placebo is to simply make a tablet from the tablet mix, minus the active, keeping all the other proportions constant. This “cocktail” segways into another difference in process monitoring versus lab analyses: the correlation coefficient.
The standard lab procedure has been, and mostly still is, to first remove the API or material to be analyzed from its matrix. Simply stated, nearly every lab analysis depends on determining the analyte, despite its matrix. A tablet, capsule, or paste is normally dissolved in some solvent, filtered, and an analysis performed: titration, thin-layer, gas, or liquid chromatography, atomic absorption or emission, or even an electrochemical method (i.e., polarography, ion selective electrodes, etc.). An analogy might be reading a letter: we open the envelope, unfold the contents, and read the words. In something like NIRS, we read the contents folded, inside the envelope. Consequently, unlike an HPLC chromatogram, there is seldom an area where a NIR spectrum has a baseline with zero absorbance. Why does that matter? Basically, the way the equation is built—on actual spectra, with values from a reference method—when values are plotted (NIR v. HPLC), the resultant calibration line may not go through zero, like a UV/Vis or HPLC calibration (Beer’s law plot) would.
The linearity of a traditional method may be inferred from the calibration plot (curve) by the correlation coefficient, R. That is because the spectra are carefully generated with known solutions of pure reference material in a known volume. The absorbance maximum (UV or Visible) or peak height/area (GC or LC) is easily distinguished and increases in a linear fashion. In the case of simple Beer’s law, yes, the R is a strong indicator for linearity.
In a multivariate technique (spectroscopic examination of the dosage form), even when the analyte is missing (true placebo), there will be an absorbance value seen. In addition, there is an excellent chance that there are very likely absorbances from materials in the matrix imposing themselves on the analyte spectrum—if NIR was easy, it would have been used decades ago. Consequently, the R or R2 merely indicate that there is some correlation between the observed wavelength(s) and the analyte concentration. It does not prove linearity; it just assumes causation.
Unfortunately, the EMA, FDA, and USP Guidances and chapter <856>, which was recently rewritten by a UV/Vis expert, not a NIR person, all claim R is the linearity. Not to beat the subject to death, but statistics are usually used to show inequalities: the t-test will tell you two methods are not significantly different, a Q-test will tell you that a single value does not belong in a set—it is significantly different.
And the list goes on. So, from my experience, the correlation coefficient, in reality, will tell you that a single point of points does not statistically correlate with another set. It has little to do with linearity. For an example, when the transmittance of a set of samples is calculated and graphed v. the concentrations, the graph is parabolic. So, to make it look better, we use a logarithm to generate a straight line.
Either curve works for an analysis, just that one looks nicer! So, in essence, even ideal Beer’s law (the Beer-Bouget-Lambert law, actually) isn’t a straight line and needs a “fix.”
To summarize, if a company wishes to save money and make a better product through a PAT/QbD program, they need to work with their chemometricians and statisticians when designing and validating the process control technologies. I would strongly advise any company willing to begin a PAT program to tighten up the training of the lab personnel validating all the software and hardware used in the production of drugs. You don’t have the option of re-analyzing a sample set after you have finished making the full batch of millions of tablets or capsules.
