# Statistics in Check/Replicate Analysis - HPLC Assay (Sample Duplicates)

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#### superkidz

Let say I have a result of 90 and 100% from HPLC assay (sample duplicates). By simply looking the two data, the values are far from each other. How will I know statistically, if indeed the two are different? I understand I have to compute the relative percent difference and determine the upper control limit through below formula. My limit for assay let say is 90 to 120%.
RPD =(( R1-R2)/R) x 100
Where R1-R2 = absolute difference between determinations and R is the arithmetic mean of the two values.
Upper control limit =3.27 x RPD
Where RPD = mean relative percent difference

Question then is given the data above, to get the upper control limit, I have just to multiply the 10.52 RPD ((90-110)/95)*100) to 3.27 which is 34.42%. How will then I interpret my data? Is it ok to AVERAGE the 90 and 100% to get the my reportable value? Average of 90 and 100 is 95% plus 34.42 = 129.42 which exceeded my assay limit of 90-120 so my two data is not precise. Is my interpretation correct or not? Let me know pls. I understand 3.27 is shewhart’s factor but what this 3.27 really means? Standard deviation? Since the two results of my sample duplicate are not precise, I would then need to repeat my analysis.

Assuming that I got an 88% assay result in my 1st test and the sample duplicate results are precise or within the 3.27 upper control limit but the average of the sample duplicate is OOS, we plan to have a replicate test (sample duplicate also). I understand OOS requires a certain number of retests (usually 9) to determine that the OOs result is an outlier but since we are only testing laboratory and not manufacturing company, our primary goal is then is to confirm if indeed our 1st test result is valid, by having a replicate test (sample duplicate just like the first) only.. But what statistical tool shall I apply to know that the 1st (which generated the 88% result) and the 2nd test are not significant different? What if my replicate test (2nd test) is not OOS having me a mixed of FAIL and PASS? To confirm which of the 1st test and replicate test (2nd test) is correct, I have to make 5 sample preparations and the average of 5 sample preparations is my reportable result for my 3rd test. I will set an RSD of 2 % among the results of 5 sample preparations. How will then I report my 3 results (the 1st, the replicate, and the 3rd test)? Assuming I have an OOS reportable result also for the 5 preparations confirming the OOS results of my 1st test. What will reflect as my result in CA is the result of both OOS (the result of 1st test and the 3rd test). But what acceptance criteria should I set between the 1st test and my 3rd test? And what is my basis for not reporting the result of my 2nd test (the replicate test). What statistical tool shall I apply?

I have been reading a lot of OOS and statistics articles but I find it confusing.

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#### NumberCruncher

Hi superkidz

It's been a very long time since I last worked in an analytical lab. However the classic approach is simply report the average value along with an uncertainty. Yes, in the case of HPLC the uncertainty is large, but this is a fundamental limitation of the technology. I hardly need to tell you that getting chromatographic data is time consuming and doing 9 replicates is uneconomic on a regular basis. (With inorganic analysis, results can take just seconds to generate, and repeatability of 1% is unremarkable, the only important limitation is sample size).

Unfortunately, this leaves you with the problem of calculating the uncertainty. The modern approach is to calculate the uncertainty using the guidelines in the "Guide to the expression of uncertainty in measurement"(commonly referred to as GUM), available from the BIPM website. You can try reading it, but I wouldn't recommend it. It's highly mathematical and very difficult to understand.

Is it acceptable to your customer to simply report all of your results, along with an explanation that the different results are due to the limitations of the technology?

I know that this is a dangerous option as many people believe that a lab will give 'THE result' so if you provide several estimates, it looks like incompetence. But it is the reality.

Not the simple, definitive answer you were looking for, but there isn't a single accepted method for combining analytical results or for calculating uncertainties. Even GUM does not give a single approach for calculating uncertainty.

Here is a quote from GUM (GGCM 109:2009)

"7.1.1
The propagation stage of uncertainty evaluation is known as the propagation of distributions [JCGM 101:2008 5.2], various approaches for which are available, including
a) the GUM uncertainty framework, constituting the application of the law of propagation of uncertainty, and the characterization of the output quantity Y by a Gaussian or a t-distribution (see 7.2),
b) analytic methods, in which mathematical analysis is used to derive an algebraic form for the probability distribution for Y (see 7.3), and
c) a Monte Carlo method (MCM), in which an approximation to the distribution function for Y is established numerically by making random draws from the probability distributions for the input quantities, and evaluating the model at the resulting values (see 7.4).

7.1.2

For any particular uncertainty evaluation problem, approach a), b) or c) (or some other approach) is used, a) being generally approximate, b) exact, and c) providing a solution with a numerical accuracy that can be controlled.

7.1.3

The application of approaches a) and c) to measurement functions with any number of output quantities, and general measurement models, is considered in 7.5."

Same document, three different approaches!

Personally, I would use Result +/- Uncertainty. However, I would then have to find a way of estimating the uncertainty which I currently don't know how to do.

NC